diff --git a/.gitignore b/.gitignore index 3580f95..1a33ea8 100644 --- a/.gitignore +++ b/.gitignore @@ -1,5 +1,4 @@ -_build/ -Makefile -Parallel -*.byte -*.native +*~ +_build +.merlin +*.install diff --git a/.merlin b/.merlin deleted file mode 100644 index 6b6690c..0000000 --- a/.merlin +++ /dev/null @@ -1,7 +0,0 @@ -B _build/ -B _build/** -S . -S ./** -FLG -w @a-4-29-40-41-42-44-45-48-58-59-60-40 -strict-sequence -strict-formats -short-paths -keep-locs -PKG str unix bigarray lacaml alcotest zarith getopt - diff --git a/.ocamlinit b/.ocamlinit index af6a68b..9bb7beb 100644 --- a/.ocamlinit +++ b/.ocamlinit @@ -1,25 +1,2 @@ -let () = - try Topdirs.dir_directory (Sys.getenv "OCAML_TOPLEVEL_PATH") - with Not_found -> () -;; - #use "topfind";; -#require "lacaml";; -#require "alcotest";; -#require "zarith";; -#require "getopt";; -#directory "_build";; -#directory "_build/Basis";; -#directory "_build/CI";; -#directory "_build/MOBasis";; -#directory "_build/Nuclei";; -#directory "_build/Parallel";; -#directory "_build/Perturbation";; -#directory "_build/SCF";; -#directory "_build/Utils";; - -#load "Constants.cmo";; -#load_rec "Util.cma";; - - - +open Printf;; diff --git a/.ocp-indent b/.ocp-indent new file mode 100644 index 0000000..fb580a5 --- /dev/null +++ b/.ocp-indent @@ -0,0 +1,22 @@ +# See https://github.com/OCamlPro/ocp-indent/blob/master/.ocp-indent for more + +# Indent for clauses inside a pattern-match (after the arrow): +# match foo with +# | _ -> +# ^^^^bar +# the default is 2, which aligns the pattern and the expression +match_clause = 4 + +# When nesting expressions on the same line, their indentation are in +# some cases stacked, so that it remains correct if you close them one +# at a line. This may lead to large indents in complex code though, so +# this parameter can be used to set a maximum value. Note that it only +# affects indentation after function arrows and opening parens at end +# of line. +# +# for example (left: `none`; right: `4`) +# let f = g (h (i (fun x -> # let f = g (h (i (fun x -> +# x) # x) +# ) # ) +# ) # ) +max_indent = 2 diff --git a/Basis/.merlin b/Basis/.merlin deleted file mode 100644 index 2ba6169..0000000 --- a/Basis/.merlin +++ /dev/null @@ -1 +0,0 @@ -REC diff --git a/Basis/AOBasis.ml b/Basis/AOBasis.ml deleted file mode 100644 index 819de2c..0000000 --- a/Basis/AOBasis.ml +++ /dev/null @@ -1,187 +0,0 @@ -open Lacaml.D -open Util - -type t = -{ - basis : Basis.t ; - overlap : Overlap.t lazy_t; - multipole : Multipole.t lazy_t; - ortho : Orthonormalization.t lazy_t; - eN_ints : NucInt.t lazy_t; - kin_ints : KinInt.t lazy_t; - ee_ints : ERI.t lazy_t; - ee_lr_ints : ERI_lr.t lazy_t; - f12_ints : F12.t lazy_t; - f12_over_r12_ints : ScreenedERI.t lazy_t; - cartesian : bool ; -} - -let basis t = t.basis -let overlap t = Lazy.force t.overlap -let multipole t = Lazy.force t.multipole -let ortho t = Lazy.force t.ortho -let eN_ints t = Lazy.force t.eN_ints -let kin_ints t = Lazy.force t.kin_ints -let ee_ints t = Lazy.force t.ee_ints -let ee_lr_ints t = Lazy.force t.ee_lr_ints -let f12_ints t = Lazy.force t.f12_ints -let f12_over_r12_ints t = Lazy.force t.f12_over_r12_ints -let cartesian t = t.cartesian - -module Cs = ContractedShell - -let values t point = - let result = Vec.create (Basis.size t.basis) in - Array.iter (fun shell -> - Cs.values shell point - |> Array.iteri - (fun i_c value -> - let i = Cs.index shell + i_c + 1 in - result.{i} <- value) - ) (Basis.contracted_shells t.basis); - result - - -let make ~cartesian ~basis ?f12 nuclei = - - let overlap = - lazy ( - Overlap.of_basis basis - ) in - - let ortho = - lazy ( - Orthonormalization.make ~cartesian ~basis (Lazy.force overlap) - ) in - - let eN_ints = - lazy ( - NucInt.of_basis_nuclei ~basis nuclei - ) in - - let kin_ints = - lazy ( - KinInt.of_basis basis - ) in - - let ee_ints = - lazy ( - ERI.of_basis basis - ) in - - let ee_lr_ints = - lazy ( - ERI_lr.of_basis basis - ) in - - let f12_ints = - lazy ( - F12.of_basis basis - ) in - - let f12_over_r12_ints = - lazy ( - ScreenedERI.of_basis basis - ) in - - let multipole = - lazy ( - Multipole.of_basis basis - ) in - - { basis ; overlap ; multipole ; ortho ; eN_ints ; kin_ints ; ee_ints ; - ee_lr_ints ; f12_ints ; f12_over_r12_ints ; cartesian ; - } - - - -let test_case name t = - - let check_matrix title a r = - let a = Mat.to_array a in - Mat.to_array r - |> Array.iteri (fun i x -> - let message = - Printf.sprintf "%s line %d" title i - in - Alcotest.(check (array (float 1.e-10))) message a.(i) x - ) - in - - let check_eri a r = - let f { ERI.i_r1 ; j_r2 ; k_r1 ; l_r2 ; value } = - (i_r1, (j_r2, (k_r1, (l_r2, value)))) - in - let a = ERI.to_list a |> List.rev_map f |> List.rev in - let r = ERI.to_list r |> List.rev_map f |> List.rev in - Alcotest.(check (list (pair int (pair int (pair int (pair int (float 1.e-10))))))) "ERI" a r - in - - let check_eri_lr a r = - let f { ERI_lr.i_r1 ; j_r2 ; k_r1 ; l_r2 ; value } = - (i_r1, (j_r2, (k_r1, (l_r2, value)))) - in - let a = ERI_lr.to_list a |> List.rev_map f |> List.rev in - let r = ERI_lr.to_list r |> List.rev_map f |> List.rev in - Alcotest.(check (list (pair int (pair int (pair int (pair int (float 1.e-10))))))) "ERI_lr" a r - in - - let test_overlap () = - let reference = - sym_matrix_of_file ("test_files/"^name^"_overlap.ref") - in - let overlap = - Lazy.force t.overlap |> Overlap.matrix - in - check_matrix "Overlap" overlap reference - in - - let test_eN_ints () = - let reference = - sym_matrix_of_file ("test_files/"^name^"_nuc.ref") - in - let eN_ints = - Lazy.force t.eN_ints |> NucInt.matrix - in - check_matrix "eN_ints" eN_ints reference - in - - let test_kin_ints () = - let reference = - sym_matrix_of_file ("test_files/"^name^"_kin.ref") - in - let kin_ints = - Lazy.force t.kin_ints |> KinInt.matrix - in - check_matrix "kin_ints" kin_ints reference - in - - let test_ee_ints () = - let reference = - ERI.of_file ("test_files/"^name^"_eri.ref") ~sparsity:`Dense ~size:(Basis.size t.basis) - in - let ee_ints = - Lazy.force t.ee_ints - in - check_eri ee_ints reference - ; - in - - let test_ee_lr_ints () = - let reference = - ERI_lr.of_file ("test_files/"^name^"_eri_lr.ref") ~sparsity:`Dense - ~size:(Basis.size t.basis) - in - let ee_lr_ints = - Lazy.force t.ee_lr_ints - in - check_eri_lr ee_lr_ints reference - in - - [ - "Overlap", `Quick, test_overlap; - "eN_ints", `Quick, test_eN_ints; - "kin_ints", `Quick, test_kin_ints; - "ee_ints", `Quick, test_ee_ints; - "ee_lr_ints", `Quick, test_ee_lr_ints; - ] diff --git a/Basis/AOBasis.mli b/Basis/AOBasis.mli deleted file mode 100644 index 853aa6b..0000000 --- a/Basis/AOBasis.mli +++ /dev/null @@ -1,53 +0,0 @@ -(** Data structure for Atomic Orbitals. *) - -open Lacaml.D - -type t - -(** {1 Accessors} *) - -val basis : t -> Basis.t -(** One-electron basis set *) - -val overlap : t -> Overlap.t -(** Overlap matrix *) - -val multipole : t -> Multipole.t -(** Multipole matrices *) - -val ortho : t -> Orthonormalization.t -(** Orthonormalization matrix of the overlap *) - -val eN_ints : t -> NucInt.t -(** Electron-nucleus potential integrals *) - -val ee_ints : t -> ERI.t -(** Electron-electron potential integrals *) - -val ee_lr_ints : t -> ERI_lr.t -(** Electron-electron long-range potential integrals *) - -val f12_ints : t -> F12.t -(** Electron-electron potential integrals *) - -val kin_ints : t -> KinInt.t -(** Kinetic energy integrals *) - -val cartesian : t -> bool -(** If true, use cartesian Gaussians (6d, 10f, ...) *) - -val values : t -> Coordinate.t -> Vec.t -(** Values of the AOs evaluated at a given point *) - - - -(** {1 Creators} *) - -val make : cartesian:bool -> basis:Basis.t -> ?f12:F12factor.t -> Nuclei.t -> t -(** Creates the data structure for atomic orbitals from a {Basis.t} and the - molecular geometry {Nuclei.t} *) - - -(** {2 Tests} *) - -val test_case : string -> t -> unit Alcotest.test_case list diff --git a/Basis/ERI.ml b/Basis/ERI.ml deleted file mode 100644 index 9884ccd..0000000 --- a/Basis/ERI.ml +++ /dev/null @@ -1,55 +0,0 @@ -(** Electron-electron repulsion integrals *) - -open Constants -open Util - -module Csp = ContractedShellPair -module Cspc = ContractedShellPairCouple - -module T = struct - - let name = "Electron repulsion integrals" - - open Zero_m_parameters - - let zero_m z = - let expo_pq_inv = z.expo_p_inv +. z.expo_q_inv in - assert (expo_pq_inv <> 0.); - let expo_pq = 1. /. expo_pq_inv in - let t = - if z.norm_pq_sq > integrals_cutoff then - z.norm_pq_sq *. expo_pq - else 0. - in - let maxm = z.maxm in - let result = boys_function ~maxm t in - let rec aux accu k = function - | 0 -> result.(k) <- result.(k) *. accu - | l -> - begin - result.(k) <- result.(k) *. accu; - let new_accu = -. accu *. expo_pq in - (aux [@tailcall]) new_accu (k+1) (l-1) - end - in - let f = two_over_sq_pi *. (sqrt expo_pq) in - aux f 0 maxm; - result - - let class_of_contracted_shell_pair_couple ~basis shell_pair_couple = - let shell_p = Cspc.shell_pair_p shell_pair_couple - and shell_q = Cspc.shell_pair_q shell_pair_couple - in - if Array.length (Csp.shell_pairs shell_p) + - (Array.length (Csp.shell_pairs shell_q)) < 4 then - TwoElectronRR.contracted_class_shell_pair_couple - ~basis ~zero_m shell_pair_couple - else - TwoElectronRRVectorized.contracted_class_shell_pairs - ~basis ~zero_m shell_p shell_q - -end - -module M = TwoElectronIntegrals.Make(T) -include M - diff --git a/Basis/ERI_lr.ml b/Basis/ERI_lr.ml deleted file mode 100644 index a3e364c..0000000 --- a/Basis/ERI_lr.ml +++ /dev/null @@ -1,64 +0,0 @@ -(** Long-range electron-electron repulsion integrals. - See Eq(52) in 10.1039/b605188j -*) - -open Constants -open Util - -module Csp = ContractedShellPair -module Cspc = ContractedShellPairCouple - -module T = struct - - let name = "Long-range electron repulsion integrals" - - open Zero_m_parameters - - let zero_m z = - let mu_erf = - match Basis.range_separation z.basis with - | Some x -> x - | None -> invalid_arg "range_separation is None" - in - let m = mu_erf *. mu_erf in - let expo_pq_inv = z.expo_p_inv +. z.expo_q_inv in - let fG_inv = expo_pq_inv +. 1. /. m in - let fG = 1. /. fG_inv in - assert (expo_pq_inv <> 0.); - let t = - if z.norm_pq_sq > integrals_cutoff then - z.norm_pq_sq *. fG - else 0. - in - let maxm = z.maxm in - let result = boys_function ~maxm t in - let rec aux accu k = function - | 0 -> result.(k) <- result.(k) *. accu - | l -> - begin - result.(k) <- result.(k) *. accu; - let new_accu = -. accu *. fG in - (aux [@tailcall]) new_accu (k+1) (l-1) - end - in - let f = two_over_sq_pi *. (sqrt fG) in - aux f 0 maxm; - result - - let class_of_contracted_shell_pair_couple ~basis shell_pair_couple = - let shell_p = Cspc.shell_pair_p shell_pair_couple - and shell_q = Cspc.shell_pair_q shell_pair_couple - in - if Array.length (Csp.shell_pairs shell_p) + - (Array.length (Csp.shell_pairs shell_q)) < 4 then - TwoElectronRR.contracted_class_shell_pair_couple - ~basis ~zero_m shell_pair_couple - else - TwoElectronRRVectorized.contracted_class_shell_pairs - ~basis ~zero_m shell_p shell_q - -end - -module M = TwoElectronIntegrals.Make(T) -include M - diff --git a/Basis/F12.ml b/Basis/F12.ml deleted file mode 100644 index 03c1b69..0000000 --- a/Basis/F12.ml +++ /dev/null @@ -1,30 +0,0 @@ -(** Two electron integral functor for operators that are separable among %{ $(x,y,z)$ %}. - It is parameterized by the [zero_m] function. -*) - -open Constants -let cutoff = integrals_cutoff - -module T = struct - - let name = "F12" - - let class_of_contracted_shell_pair_couple ~basis shell_pair_couple = - let f12 = - match Basis.f12 basis with - | Some f12 -> f12 - | None -> invalid_arg "f12 factor should not be None" - in - let g = f12.F12factor.gaussian in - F12RR.contracted_class_shell_pair_couple ~basis - g.GaussianOperator.expo_g_inv - g.GaussianOperator.coef_g - shell_pair_couple - -end - -module M = TwoElectronIntegrals.Make(T) -include M - - - diff --git a/Basis/F12RR.ml b/Basis/F12RR.ml deleted file mode 100644 index 863a24d..0000000 --- a/Basis/F12RR.ml +++ /dev/null @@ -1,289 +0,0 @@ -open Util -open Constants - -module Am = AngularMomentum -module Asp = AtomicShellPair -module Aspc = AtomicShellPairCouple -module Co = Coordinate -module Cs = ContractedShell -module Csp = ContractedShellPair -module Cspc = ContractedShellPairCouple -module Po = Powers -module Psp = PrimitiveShellPair -module Pspc = PrimitiveShellPairCouple -module Ps = PrimitiveShell - -let cutoff = Constants.integrals_cutoff -let cutoff2 = cutoff *. cutoff - -exception NullQuartet - -type four_idx_intermediates = - { - zero : float array array; - gp : float array; - gg : float array; - gq : float array; - coef_g : float array ; - center_ra : Co.t array ; - center_rc : Co.t array ; - center_ab : Co.t ; - center_cd : Co.t ; - } - -(** Horizontal and Vertical Recurrence Relations (HVRR) *) -let rec hvrr angMom_a angMom_b angMom_c angMom_d - abcd map_x map_y map_z = - - let gp = abcd.gp in - let gg = abcd.gg in - let gq = abcd.gq in - - let coef_g = abcd.coef_g in - - let run xyz map = - - let zero = - match xyz with - | Co.X -> abcd.zero.(0) - | Co.Y -> abcd.zero.(1) - | Co.Z -> abcd.zero.(2) - in - let angMom_a = Po.get xyz angMom_a in - let angMom_b = Po.get xyz angMom_b in - let angMom_c = Po.get xyz angMom_c in - let angMom_d = Po.get xyz angMom_d in - let center_ab = Co.get xyz abcd.center_ab in - let center_cd = Co.get xyz abcd.center_cd in - let center_ra = Array.map (fun x -> Co.get xyz x) abcd.center_ra in - let center_rc = Array.map (fun x -> Co.get xyz x) abcd.center_rc in - - let rec vrr angMom_a angMom_c = - match angMom_a, angMom_c with - | 0, -1 - | -1, 0 -> assert false - | 0, 0 -> zero - | 1, 0 -> - let v1 = zero in - Array.mapi (fun i v1i -> center_ra.(i) *. v1i ) v1 - | 0, 1 -> - let v1 = zero in - Array.mapi (fun i v1i -> center_rc.(i) *. v1i ) v1 - | 1, 1 -> - let v1 = vrr 1 0 in - let v2 = zero in - Array.mapi (fun i v1i -> center_rc.(i) *. v1i +. - gg.(i) *. v2.(i) ) v1 - | 2, 0 -> - let v1 = vrr 1 0 in - let v2 = zero in - Array.mapi (fun i v1i -> center_ra.(i) *. v1i +. gp.(i) *. v2.(i)) v1 - | _, 0 -> - let v1 = - vrr (angMom_a-1) 0 - in - let a = float_of_int_fast (angMom_a-1) in - let v2 = - vrr (angMom_a-2) 0 - in - Array.mapi (fun i v1i -> center_ra.(i) *. v1i +. a *. gp.(i) *. v2.(i)) v1 - | _, 1 -> - let v1 = - vrr angMom_a 0 - in - let a = float_of_int_fast angMom_a in - let v2 = - vrr (angMom_a-1) 0 - in - Array.mapi (fun i v1i -> center_rc.(i) *. v1i +. - a *. gg.(i) *. v2.(i) ) v1 - | 0, _ -> - let v1 = - vrr 0 (angMom_c-1) - in - let b = float_of_int_fast (angMom_c-1) in - let v3 = - vrr 0 (angMom_c-2) - in - Array.mapi (fun i v1i -> center_rc.(i) *. v1i +. - b *. gq.(i) *. v3.(i)) v1 - | _ -> - let v1 = - vrr angMom_a (angMom_c-1) - in - let a = float_of_int_fast angMom_a in - let b = float_of_int_fast (angMom_c-1) in - let v2 = - vrr (angMom_a-1) (angMom_c-1) - in - let v3 = - vrr angMom_a (angMom_c-2) - in - Array.mapi (fun i v1i -> center_rc.(i) *. v1i +. - a *. gg.(i) *. v2.(i) +. b *. gq.(i) *. v3.(i)) v1 - in - - let rec hrr angMom_a angMom_b angMom_c angMom_d = - let key = Zkey.of_int_four angMom_a angMom_b angMom_c angMom_d in - - try Zmap.find map key with - | Not_found -> - let result = - match angMom_b, angMom_d with - | -1, 0 - | 0, -1 -> assert false - | 0, 0 -> - vrr angMom_a angMom_c - | _, 0 -> - let h1 = - hrr (angMom_a+1) (angMom_b-1) angMom_c angMom_d - in - if center_ab = 0. then - h1 - else - let h2 = - hrr angMom_a (angMom_b-1) angMom_c angMom_d - in - Array.mapi (fun i h1i -> h1i +. center_ab *. h2.(i)) h1 - | _ -> - let h1 = - hrr angMom_a angMom_b (angMom_c+1) (angMom_d-1) - in - if center_cd = 0. then - h1 - else - let h2 = - hrr angMom_a angMom_b angMom_c (angMom_d-1) - in - Array.mapi (fun i h1i -> h1i +. center_cd *. h2.(i)) h1 - in (Zmap.add map key result; result) - - in - hrr angMom_a angMom_b angMom_c angMom_d - in - let x, y, z = - (run Co.X map_x), (run Co.Y map_y), (run Co.Z map_z) - in - let rec aux accu = function - | 0 -> accu +. coef_g.(0) *. x.(0) *. y.(0) *. z.(0) - | i -> (aux [@tailcall]) (accu +. coef_g.(i) *. x.(i) *. y.(i) *. z.(i)) (i-1) - in - aux 0. (Array.length x - 1) - - -let contracted_class_shell_pair_couple ~basis expo_g_inv coef_g shell_pair_couple : float Zmap.t = - - (* Pre-computation of integral class indices *) - let class_indices = Cspc.zkey_array shell_pair_couple in - - let contracted_class = - Array.make (Array.length class_indices) 0.; - in - - (* Compute all integrals in the shell for each pair of significant shell pairs *) - - let shell_p = Cspc.shell_pair_p shell_pair_couple - and shell_q = Cspc.shell_pair_q shell_pair_couple - in - - let center_ab = Csp.a_minus_b shell_p - and center_cd = Csp.a_minus_b shell_q - in - - let norm_scales = Cspc.norm_scales shell_pair_couple in - - List.iter (fun (coef_prod, spc) -> - - let sp_ab = Pspc.shell_pair_p spc - and sp_cd = Pspc.shell_pair_q spc - in - - let expo_p_inv = Psp.exponent_inv sp_ab in - let expo_q_inv = Psp.exponent_inv sp_cd in - let expo_pgq = Array.map (fun e -> - 1. /. (expo_p_inv +. expo_q_inv +. e) - ) expo_g_inv - in - - let fp = Array.map (fun e -> expo_p_inv *. e) expo_pgq in - let fq = Array.map (fun e -> expo_q_inv *. e) expo_pgq in - - let gp = - let x = 0.5 *. expo_p_inv in - Array.map (fun f -> (1. -. f) *. x) fp - in - let gq = - let x = 0.5 *. expo_q_inv in - Array.map (fun f -> (1. -. f) *. x) fq - in - let gg = - let x = 0.5 *. expo_q_inv in - Array.map (fun f -> f *. x) fp - in - - let center_pq = Co.(Psp.center sp_ab |- Psp.center sp_cd) in - let center_qc = Psp.center_minus_a sp_cd in - let center_pa = Psp.center_minus_a sp_ab in - - let center_ra = Array.map (fun f -> Co.(center_pa |- (f |. center_pq))) fp in - let center_rc = Array.map (fun f -> Co.(center_qc |+ (f |. center_pq))) fq in - - (* zero_m is defined here *) - let zero = Array.map (fun xyz -> - let x = Co.get xyz center_pq in - Array.mapi (fun i ei -> - let fg = expo_g_inv.(i) *. ei in - (sqrt fg) *. exp (-. x *. x *. ei )) expo_pgq - ) Co.[| X ; Y ; Z |] - in - begin - match Cspc.ang_mom shell_pair_couple with - (* - | Am.S -> - let integral = - zero.(0) *. zero.(1) *. zero.(2) - in - contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral - *) - | _ -> - let map_x, map_y, map_z = - Zmap.create (Array.length class_indices), - Zmap.create (Array.length class_indices), - Zmap.create (Array.length class_indices) - in - (* Compute the integral class from the primitive shell quartet *) - class_indices - |> Array.iteri (fun i key -> - let (angMom_a,angMom_b,angMom_c,angMom_d) = - match Zkey.to_powers key with - | Zkey.Twelve x -> x - | _ -> assert false - in - let norm = norm_scales.(i) in - let coef_prod = coef_prod *. norm in - let abcd = { - zero ; gp ; gg ; gq ; - center_ab ; center_cd ; - center_ra ; center_rc ; - coef_g ; - } in - let integral = - hvrr - angMom_a angMom_b angMom_c angMom_d - abcd map_x map_y map_z - in - contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral - ) - end - ) (Cspc.coefs_and_shell_pair_couples shell_pair_couple); - - let result = - Zmap.create (Array.length contracted_class) - in - - - Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices; - result - - - diff --git a/Basis/F12factor.ml b/Basis/F12factor.ml deleted file mode 100644 index 0156399..0000000 --- a/Basis/F12factor.ml +++ /dev/null @@ -1,78 +0,0 @@ -(** Type for f12 correlation factors *) - -open Constants - -type t = - { - expo_s : float ; - gaussian : GaussianOperator.t - } - - -let make_gaussian_corr_factor expo_s coef_g expo_sg = - let expo_sg = - Array.map (fun x -> x *. expo_s *. expo_s) expo_sg - in - let gaussian = GaussianOperator.make coef_g expo_sg in - { expo_s ; gaussian } - - -(* -1/expo_s *. exp (-expo_s r) *) -let gaussian_geminal expo_s = - let coef_g = - [| 0.3144 ; 0.3037 ; 0.1681 ; 0.09811 ; 0.06024 ; 0.03726 |] - |> Array.map (fun x -> -. x /. expo_s) - and expo_sg = - [| 0.2209 ; 1.004 ; 3.622 ; 12.16 ; 45.87 ; 254.4 |] - in - make_gaussian_corr_factor expo_s coef_g expo_sg - - - -(* exp (-expo_s r) *) -let simple_gaussian_geminal expo_s = - let coef_g = - [| 0.3144 ; 0.3037 ; 0.1681 ; 0.09811 ; 0.06024 ; 0.03726 |] - and expo_sg = - [| 0.2209 ; 1.004 ; 3.622 ; 12.16 ; 45.87 ; 254.4 |] - in - make_gaussian_corr_factor expo_s coef_g expo_sg - - - -(** r12 * exp ( -expo_s * r) *) -let gaussian_geminal_times_r12 expo_s = - let coef_g = - [| 0.2454 ; 0.2938 ; 0.1815 ; 0.11281 ; 0.07502 ; 0.05280 |] - and expo_sg = - [| 0.1824 ; 0.7118; 2.252 ; 6.474 ; 19.66 ; 77.92 |] - in make_gaussian_corr_factor expo_s coef_g expo_sg - - -(* exp (-expo_s r) *) -let simple_gaussian_geminal' expo_s = - let coef_g = - [| - -3.4793465193721626604883567779324948787689208984375 ; - -0.00571703486454788484955047422886309504974633455276489257812 ; - 4.14878218728681513738365538301877677440643310546875 ; - 0.202874298181392742623785352407139725983142852783203125 ; - 0.0819187742387294803858566183407674543559551239013671875 ; - 0.04225945671351955673644695821167260874062776565551757812 ; - |] - and expo_sg = - [| - 0.63172472556807146570889699432882480323314666748046875; - 26.3759196683467962429858744144439697265625; - 0.63172102793029016876147352377302013337612152099609375; - 7.08429025944207335641067402320913970470428466796875; - 42.4442841447001910637482069432735443115234375; - 391.44036073596890901171718724071979522705078125 ; - |] - in make_gaussian_corr_factor expo_s coef_g expo_sg - - - - - - diff --git a/Basis/GamessReader.ml b/Basis/GamessReader.ml deleted file mode 100644 index 4b17765..0000000 --- a/Basis/GamessReader.ml +++ /dev/null @@ -1,17 +0,0 @@ -(** Reads a basis set in GAMESS format *) -let read_basis filename = - let lexbuf = - let ic = open_in filename in - Lexing.from_channel ic - in - let rec aux accu = - try - let key, basis = - GamessParser.input BasisLexer.read_all lexbuf - in - aux ((key, basis)::accu) - with - | Parsing.Parse_error -> List.rev accu - in - aux [] - diff --git a/Basis/GaussianOperator.ml b/Basis/GaussianOperator.ml deleted file mode 100644 index 717525f..0000000 --- a/Basis/GaussianOperator.ml +++ /dev/null @@ -1,39 +0,0 @@ -(** Representation for two-electron operators expressed in a Gaussian basis set. *) - -open Constants - -type t = -{ - coef_g : float array; - expo_g : float array; - expo_g_inv : float array; -} - -let make coef_g expo_g = - let expo_g_inv = - Array.map (fun x -> 1. /. x ) expo_g - in - { coef_g ; expo_g ; expo_g_inv } - - -let one_over_r = - - let coef_g = [| - 841.88478132 ; 70.590185207 ; 18.3616020768 ; 7.2608642093 ; - 3.57483416444 ; 2.01376031082 ; 1.24216542801 ; 0.81754348620 ; - 0.564546514023 ; 0.404228610699 ; 0.297458536575 ; 0.223321219537 ; - 0.169933732064 ; 0.130190978230 ; 0.099652303426 ; 0.075428246546 ; - 0.0555635614051 ; 0.0386791283055 ; 0.0237550435652 ; 0.010006278387 ; - |] - and expo_g = - [| 84135.654509 ; 2971.58727634 ; 474.716025959 ; 130.676724560 ; - 47.3938388887 ; 20.2078651631 ; 9.5411021938 ; 4.8109546955 ; - 2.52795733067 ; 1.35894103210 ; 0.73586710268 ; 0.39557629706 ; - 0.20785895177 ; 0.104809693858 ; 0.049485682527 ; 0.021099788990 ; - 0.007652472186 ; 0.0021065225215 ; 0.0003365204879 ; 0.0000118855674 |] - in make coef_g expo_g - - - - - diff --git a/Basis/Orthonormalization.ml b/Basis/Orthonormalization.ml deleted file mode 100644 index 37b4f3f..0000000 --- a/Basis/Orthonormalization.ml +++ /dev/null @@ -1,68 +0,0 @@ -open Util -open Lacaml.D - -type t = Mat.t - -module Am = AngularMomentum -module Bs = Basis -module Cs = ContractedShell -module Ov = Overlap - - - -let make_canonical ~thresh ~basis ~cartesian ~overlap = - - let overlap_matrix = Ov.matrix overlap in - - let make_canonical_spherical basis = - let ao_num = Bs.size basis in - let cart_sphe = Mat.make ao_num ao_num 0. - and i = ref 0 - and n = ref 0 in - Array.iter (fun shell -> - let submatrix = - SphericalToCartesian.matrix (Cs.ang_mom shell) - in - ignore @@ lacpy ~b:cart_sphe ~br:(!i+1) ~bc:(!n+1) submatrix; - i := !i + Mat.dim1 submatrix; - n := !n + Mat.dim2 submatrix; - ) (Bs.contracted_shells basis); - let s = gemm ~transa:`T ~m:!n cart_sphe overlap_matrix in - let overlap_matrix = gemm s ~n:!n cart_sphe in - let s = canonical_ortho ~thresh ~overlap:overlap_matrix (Mat.identity !n) in - gemm cart_sphe ~k:!n s - in - - if cartesian then - canonical_ortho ~thresh ~overlap:overlap_matrix (Mat.identity @@ Mat.dim1 overlap_matrix) - else - match basis with - | None -> invalid_arg - "Basis.t is required when cartesian=false in make_canonical" - | Some basis -> make_canonical_spherical basis - - - -let make_lowdin ~thresh ~overlap = - - let overlap_matrix = Ov.matrix overlap in - let u_vec, u_val = diagonalize_symm overlap_matrix in - - Vec.iter (fun x -> if x < thresh then - invalid_arg (__FILE__^": make_lowdin") ) u_val; - - let u_val = Vec.reci (Vec.sqrt u_val) in - - let u_vec' = - Mat.init_cols (Mat.dim1 u_vec) (Mat.dim2 u_vec) (fun i j -> u_vec.{i,j} *. u_val.{j}) - in - gemm u_vec' ~transb:`T u_vec - - - -let make ?(thresh=1.e-12) ?basis ~cartesian overlap = - (* - make_lowdin ~thresh ~overlap - *) - make_canonical ~thresh ~basis ~cartesian ~overlap - diff --git a/Basis/ScreenedERI.ml b/Basis/ScreenedERI.ml deleted file mode 100644 index 60e0b86..0000000 --- a/Basis/ScreenedERI.ml +++ /dev/null @@ -1,95 +0,0 @@ -(** Screened Electron-electron repulsion integrals (Yukawa potential). Required for F12/r12. *) - -open Constants -open Util - -module Csp = ContractedShellPair -module Cspc = ContractedShellPairCouple - -module T = struct - - let name = "Screened electron repulsion integrals" - - let f12_factor = F12factor.gaussian_geminal 1.0 - - open Zero_m_parameters - - let zero_m z = - let expo_pq_inv = z.expo_p_inv +. z.expo_q_inv in - assert (expo_pq_inv <> 0.); - (* - let f12_factor = - match z.f12_factor with - | Some f -> f - | None -> assert false - in - *) - - let expo_G_inv, coef_G = - f12_factor.F12factor.gaussian.GaussianOperator.expo_g_inv, - f12_factor.F12factor.gaussian.GaussianOperator.coef_g - in - - let expo_pq = 1. /. expo_pq_inv in - let maxm = z.maxm in - - let result = Array.init (maxm+1) (fun _ -> 0.) in - array_range 0 (Array.length coef_G) - |> Array.iter (fun i -> - let fG_inv = expo_pq_inv +. expo_G_inv.(i) in - let fG = 1. /. fG_inv in - let t = - if z.norm_pq_sq > integrals_cutoff then - z.norm_pq_sq *. (expo_pq -. fG) - else 0. - in - let fm = boys_function ~maxm t in - - let tmp_array = - let result = Array.init (maxm+1) (fun k -> 1.) in - array_range 1 maxm - |> Array.iter (fun k -> result.(k) <- result.(k-1) *. expo_pq *. expo_G_inv.(i)); - result - in - - let tmp_result = Array.init (maxm+1) (fun _ -> 0.) in - let rec aux accu m = function - | 0 -> tmp_result.(m) <- fm.(m) *. accu - | j -> - begin - let f = - array_range 0 m - |> Array.fold_left (fun v k -> - v +. (binom_float m k) *. tmp_array.(k) *. fm.(k)) 0. - in - tmp_result.(m) <- accu *. f; - let new_accu = -. accu *. expo_pq in - (aux [@tailcall]) new_accu (m+1) (j-1) - end - in - let f = - two_over_sq_pi *. (sqrt expo_pq) *. fG *. expo_G_inv.(i) *. exp (-.fG *. z.norm_pq_sq) - in - aux f 0 maxm; - Array.iteri (fun k v -> - result.(k) <- result.(k) +. coef_G.(i) *. v - ) tmp_result) ; - result - - let class_of_contracted_shell_pair_couple ~basis shell_pair_couple = - let shell_p = Cspc.shell_pair_p shell_pair_couple - and shell_q = Cspc.shell_pair_q shell_pair_couple - in - if Array.length (Csp.shell_pairs shell_p) + - (Array.length (Csp.shell_pairs shell_q)) < 4 then - TwoElectronRR.contracted_class_shell_pair_couple - ~basis ~zero_m shell_pair_couple - else - TwoElectronRRVectorized.contracted_class_shell_pairs - ~basis ~zero_m shell_p shell_q - -end - -module M = TwoElectronIntegrals.Make(T) -include M - diff --git a/Basis/TwoElectronIntegrals.ml b/Basis/TwoElectronIntegrals.ml deleted file mode 100644 index 42c2565..0000000 --- a/Basis/TwoElectronIntegrals.ml +++ /dev/null @@ -1,296 +0,0 @@ -(** Two electron integrals -*) - -open Constants -let cutoff = integrals_cutoff - -module Bs = Basis -module Cs = ContractedShell -module Csp = ContractedShellPair -module Cspc = ContractedShellPairCouple -module Fis = FourIdxStorage - -module type TwoEI_structure = - sig - val name : string - val class_of_contracted_shell_pair_couple : - basis:Basis.t -> ContractedShellPairCouple.t -> float Zmap.t - end - - -module Make(T : TwoEI_structure) = struct - - include FourIdxStorage - - let class_of_contracted_shell_pair_couple = T.class_of_contracted_shell_pair_couple - - (* - let filter_contracted_shell_pairs ?(cutoff=integrals_cutoff) ~basis shell_pairs = - List.rev_map (fun pair -> - match Cspc.make ~cutoff pair pair with - | Some cspc -> - let cls = class_of_contracted_shell_pair_couple ~basis cspc in - (pair, Zmap.fold (fun _key value accu -> max (abs_float value) accu) cls 0. ) - (* TODO \sum_k |coef_k * integral_k| *) - | None -> (pair, -1.) - ) shell_pairs - |> List.filter (fun (_, schwartz_p_max) -> schwartz_p_max >= cutoff) - |> List.rev_map fst - *) - - -(* TODO - let filter_contracted_shell_pair_couples - ?(cutoff=integrals_cutoff) shell_pair_couples = - List.rev_map (fun pair -> - let cls = - class_of_contracted_shell_pairs pair pair - in - (pair, Zmap.fold (fun key value accu -> max (abs_float value) accu) cls 0. ) - ) shell_pairs - |> List.filter (fun (_, schwartz_p_max) -> schwartz_p_max >= cutoff) - |> List.rev_map fst - -*) - - - let store_class ?(cutoff=integrals_cutoff) data contracted_shell_pair_couple cls = - let to_powers x = - let open Zkey in - match to_powers x with - | Three x -> x - | _ -> assert false - in - - let shell_p = Cspc.shell_pair_p contracted_shell_pair_couple - and shell_q = Cspc.shell_pair_q contracted_shell_pair_couple - in - - Array.iteri (fun i_c powers_i -> - let i_c = Cs.index (Csp.shell_a shell_p) + i_c + 1 in - let xi = to_powers powers_i in - Array.iteri (fun j_c powers_j -> - let j_c = Cs.index (Csp.shell_b shell_p) + j_c + 1 in - let xj = to_powers powers_j in - Array.iteri (fun k_c powers_k -> - let k_c = Cs.index (Csp.shell_a shell_q) + k_c + 1 in - let xk = to_powers powers_k in - Array.iteri (fun l_c powers_l -> - let l_c = Cs.index (Csp.shell_b shell_q) + l_c + 1 in - let xl = to_powers powers_l in - let key = Zkey.of_powers_twelve xi xj xk xl in - let value = Zmap.find cls key in - set_chem data i_c j_c k_c l_c value - ) (Cs.zkey_array (Csp.shell_b shell_q)) - ) (Cs.zkey_array (Csp.shell_a shell_q)) - ) (Cs.zkey_array (Csp.shell_b shell_p)) - ) (Cs.zkey_array (Csp.shell_a shell_p)) - - - - - - - let of_basis_serial basis = - - let n = Bs.size basis - and shell = Bs.contracted_shells basis - in - - let eri_array = - Fis.create ~size:n `Dense - (* - Fis.create ~size:n `Sparse - *) - in - - let t0 = Unix.gettimeofday () in - - let shell_pairs = - Csp.of_contracted_shell_array shell - in - - Printf.printf "%d significant shell pairs computed in %f seconds\n" - (List.length shell_pairs) (Unix.gettimeofday () -. t0); - - - let t0 = Unix.gettimeofday () in - let ishell = ref 0 in - - List.iter (fun shell_p -> - let () = - if (Cs.index (Csp.shell_a shell_p) > !ishell) then - (ishell := Cs.index (Csp.shell_a shell_p) ; print_int !ishell ; print_newline ()) - in - - let sp = - Csp.shell_pairs shell_p - in - - try - List.iter (fun shell_q -> - let () = - if Cs.index (Csp.shell_a shell_q) > - Cs.index (Csp.shell_a shell_p) then - raise Exit - in - let sq = Csp.shell_pairs shell_q in - let cspc = - if Array.length sp < Array.length sq then - Cspc.make ~cutoff shell_p shell_q - else - Cspc.make ~cutoff shell_q shell_p - in - - match cspc with - | Some cspc -> - let cls = - class_of_contracted_shell_pair_couple ~basis cspc - in - store_class ~cutoff eri_array cspc cls - | None -> () - ) shell_pairs - with Exit -> () - ) shell_pairs ; - Printf.printf "Computed ERIs in %f seconds\n%!" (Unix.gettimeofday () -. t0); - eri_array - - - - - - - - (* Parallel functions *) - - - - let of_basis_parallel basis = - - let n = Bs.size basis - and shell = Bs.contracted_shells basis - in - - let store_class_parallel - ?(cutoff=integrals_cutoff) contracted_shell_pair_couple cls = - let to_powers x = - let open Zkey in - match to_powers x with - | Three x -> x - | _ -> assert false - in - - let shell_p = Cspc.shell_pair_p contracted_shell_pair_couple - and shell_q = Cspc.shell_pair_q contracted_shell_pair_couple - in - - let result = ref [] in - Array.iteri (fun i_c powers_i -> - let i_c = Cs.index (Csp.shell_a shell_p) + i_c + 1 in - let xi = to_powers powers_i in - Array.iteri (fun j_c powers_j -> - let j_c = Cs.index (Csp.shell_b shell_p) + j_c + 1 in - let xj = to_powers powers_j in - Array.iteri (fun k_c powers_k -> - let k_c = Cs.index (Csp.shell_a shell_q) + k_c + 1 in - let xk = to_powers powers_k in - Array.iteri (fun l_c powers_l -> - let l_c = Cs.index (Csp.shell_b shell_q) + l_c + 1 in - let xl = to_powers powers_l in - let key = Zkey.of_powers_twelve xi xj xk xl in - let value = Zmap.find cls key in - result := (i_c, j_c, k_c, l_c, value) :: !result - ) (Cs.zkey_array (Csp.shell_b shell_q)) - ) (Cs.zkey_array (Csp.shell_a shell_q)) - ) (Cs.zkey_array (Csp.shell_b shell_p)) - ) (Cs.zkey_array (Csp.shell_a shell_p)); - !result - in - - - - let t0 = Unix.gettimeofday () in - - let shell_pairs = - Csp.of_contracted_shell_array shell - in - - if Parallel.master then - Printf.printf "%d significant shell pairs computed in %f seconds\n" - (List.length shell_pairs) (Unix.gettimeofday () -. t0); - - - let t0 = Unix.gettimeofday () in - let ishell = ref max_int in - - let input_stream = Stream.of_list shell_pairs in - - let f shell_p = - let () = - if Parallel.rank < 2 && Cs.index (Csp.shell_a shell_p) < !ishell then - (ishell := Cs.index (Csp.shell_a shell_p) ; print_int !ishell ; print_newline ()) - in - - let sp = - Csp.shell_pairs shell_p - in - - let result = ref [] in - let () = - try - List.iter (fun shell_q -> - let () = - if Cs.index (Csp.shell_a shell_q) > - Cs.index (Csp.shell_a shell_p) then - raise Exit - in - let sq = Csp.shell_pairs shell_q in - let cspc = - if Array.length sp < Array.length sq then - Cspc.make ~cutoff shell_p shell_q - else - Cspc.make ~cutoff shell_q shell_p - in - - match cspc with - | Some cspc -> - let cls = - class_of_contracted_shell_pair_couple ~basis cspc - in - result := (store_class_parallel ~cutoff cspc cls) :: !result; - | None -> () - ) shell_pairs; - with Exit -> () - in - List.concat !result |> Array.of_list - in - - let eri_array = - if Parallel.master then - Fis.create ~size:n `Dense - else - Fis.create ~size:n `Dense - in - - Farm.run ~ordered:true ~f input_stream - |> Stream.iter (fun l -> - Array.iter (fun (i_c,j_c,k_c,l_c,value) -> - set_chem eri_array i_c j_c k_c l_c value) l); - - if Parallel.master then - Printf.printf - "Computed %s Integrals in parallel in %f seconds\n%!" T.name (Unix.gettimeofday () -. t0); - Fis.broadcast eri_array - - - - let of_basis = - match Parallel.size with - | 1 -> of_basis_serial - | _ -> of_basis_parallel - - -end - - - diff --git a/Basis/TwoElectronIntegrals.mli b/Basis/TwoElectronIntegrals.mli deleted file mode 100644 index 49b2499..0000000 --- a/Basis/TwoElectronIntegrals.mli +++ /dev/null @@ -1,38 +0,0 @@ -(** Two-electron integrals with an arbitrary operator, with a functorial interface - parameterized by the fundamental two-electron integrals. - - {% $(00|00)^m = \int \int \phi_p(r1) \hat{O} \phi_q(r2) dr_1 dr_2 $ %} : Fundamental two-electron integral - -*) - - -module type TwoEI_structure = - sig -val name : string -(** Name of the kind of integrals, for printing purposes. *) - -val class_of_contracted_shell_pair_couple : - basis:Basis.t -> ContractedShellPairCouple.t -> float Zmap.t -(** Returns an integral class from a couple of contracted shells. - The results is stored in a Zmap. -*) - end - - - -module Make : functor (T : TwoEI_structure) -> - sig - include module type of FourIdxStorage - -(* - val filter_contracted_shell_pairs : - ?cutoff:float -> basis:Basis.t -> - ContractedShellPair.t list -> ContractedShellPair.t list - (** Uses Schwartz screening on contracted shell pairs. *) -*) - - val of_basis : Basis.t -> t - (** Compute all ERI's for a given {!Basis.t}. *) - - end - diff --git a/Basis/TwoElectronRR.ml b/Basis/TwoElectronRR.ml deleted file mode 100644 index 93a5354..0000000 --- a/Basis/TwoElectronRR.ml +++ /dev/null @@ -1,522 +0,0 @@ -open Util - -module Am = AngularMomentum -module Asp = AtomicShellPair -module Aspc = AtomicShellPairCouple -module Co = Coordinate -module Cs = ContractedShell -module Csp = ContractedShellPair -module Cspc = ContractedShellPairCouple -module Po = Powers -module Psp = PrimitiveShellPair -module Pspc = PrimitiveShellPairCouple -module Ps = PrimitiveShell -module Zp = Zero_m_parameters - -let cutoff = Constants.integrals_cutoff -let cutoff2 = cutoff *. cutoff - - -exception NullQuartet - -type four_idx_intermediates = -{ - expo_b : float ; - expo_d : float ; - expo_p_inv : float ; - expo_q_inv : float ; - center_ab : Co.t ; - center_cd : Co.t ; - center_pq : Co.t ; - center_pa : Co.t ; - center_qc : Co.t ; - zero_m_array : float array ; -} - -(** Horizontal and Vertical Recurrence Relations (HVRR) *) -let rec hvrr_two_e - angMom_a angMom_b angMom_c angMom_d - abcd map_1d map_2d = - - (* Swap electrons 1 and 2 so that the max angular momentum is on 1 *) - if angMom_a.Po.tot + angMom_b.Po.tot < angMom_c.Po.tot + angMom_d.Po.tot then - let abcd = { - expo_b = abcd.expo_d ; - expo_d = abcd.expo_b ; - expo_p_inv = abcd.expo_q_inv ; - expo_q_inv = abcd.expo_p_inv ; - center_ab = abcd.center_cd ; - center_cd = abcd.center_ab ; - center_pq = Co.neg abcd.center_pq ; - center_pa = abcd.center_qc ; - center_qc = abcd.center_pa ; - zero_m_array = abcd.zero_m_array ; - } in - hvrr_two_e - angMom_c angMom_d angMom_a angMom_b - abcd map_1d map_2d - - else - - let maxm = angMom_a.Po.tot + angMom_b.Po.tot + angMom_c.Po.tot + angMom_d.Po.tot in - let maxsze = maxm+1 in - - - let get_xyz angMom = - match angMom with - | { Po.y=0 ; z=0 ; _ } -> Co.X - | { z=0 ; _ } -> Co.Y - | _ -> Co.Z - in - - let expo_p_inv = abcd.expo_p_inv - and expo_q_inv = abcd.expo_q_inv - and center_ab = abcd.center_ab - and center_cd = abcd.center_cd - and center_pq = abcd.center_pq - in - - (** Vertical recurrence relations *) - let rec vrr0 angMom_a = - - match angMom_a.Po.tot with - | 0 -> abcd.zero_m_array - | _ -> - let key = Zkey.of_powers_three angMom_a in - - try Zmap.find map_1d key with - | Not_found -> - let result = - let xyz = get_xyz angMom_a in - let am = Po.decr xyz angMom_a in - let amxyz = Po.get xyz am in - - let f1 = expo_p_inv *. Co.get xyz center_pq - and f2 = abcd.expo_b *. expo_p_inv *. Co.get xyz center_ab - in - let result = Array.create_float (maxsze - angMom_a.Po.tot) in - if amxyz = 0 then - begin - let v1 = vrr0 am in - Array.iteri (fun m _ -> - result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m)) result - end - else - begin - let amm = Po.decr xyz am in - let v3 = vrr0 amm in - let v1 = vrr0 am in - let f3 = (float_of_int_fast amxyz) *. expo_p_inv *. 0.5 in - Array.iteri (fun m _ -> - result.(m) <- f1 *. v1.(m+1) -. f2 *. v1.(m) - +. f3 *. (v3.(m) +. expo_p_inv *. v3.(m+1)) ) result - end; - result - in Zmap.add map_1d key result; - result - - - and vrr angMom_a angMom_c = - - match angMom_a.Po.tot, angMom_c.Po.tot with - | (i,0) -> if (i>0) then vrr0 angMom_a - else abcd.zero_m_array - | (_,_) -> - let key = Zkey.of_powers_six angMom_a angMom_c in - - try Zmap.find map_2d key with - | Not_found -> - let result = - (* angMom_c.Po.tot > 0 so cm.Po.tot >= 0 *) - let xyz = get_xyz angMom_c in - let cm = Po.decr xyz angMom_c in - let cmxyz = Po.get xyz cm in - let axyz = Po.get xyz angMom_a in - - let f1 = - -. abcd.expo_d *. expo_q_inv *. Co.get xyz center_cd - and f2 = - expo_q_inv *. Co.get xyz center_pq - in - let result = Array.make (maxsze - angMom_a.Po.tot - angMom_c.Po.tot) 0. in - if axyz > 0 then - begin - let am = Po.decr xyz angMom_a in - let f5 = - (float_of_int_fast axyz) *. expo_p_inv *. expo_q_inv *. 0.5 - in - if (abs_float f5 > cutoff) then - let v5 = - vrr am cm - in - Array.iteri (fun m _ -> - result.(m) <- result.(m) -. f5 *. v5.(m+1)) result - end; - if cmxyz > 0 then - begin - let f3 = - (float_of_int_fast cmxyz) *. expo_q_inv *. 0.5 - in - if (abs_float f3 > cutoff) || - (abs_float (f3 *. expo_q_inv) > cutoff) then - begin - let v3 = - let cmm = Po.decr xyz cm in - vrr angMom_a cmm - in - Array.iteri (fun m _ -> - result.(m) <- result.(m) +. - f3 *. (v3.(m) +. expo_q_inv *. v3.(m+1)) ) result - end - end; - if ( (abs_float f1 > cutoff) || (abs_float f2 > cutoff) ) then - begin - let v1 = - vrr angMom_a cm - in - Array.iteri (fun m _ -> - result.(m) <- result.(m) +. f1 *. v1.(m) -. f2 *. v1.(m+1) ) result - end; - result - in Zmap.add map_2d key result; - result - - (* - and trr angMom_a angMom_c = - - match (angMom_a.Po.tot, angMom_c.Po.tot) with - | (i,0) -> if (i>0) then (vrr0 angMom_a).(0) - else abcd.zero_m_array.(0) - | (_,_) -> - let key = Zkey.of_powers_six angMom_a angMom_c in - - try (Zmap.find map_2d key).(0) with - | Not_found -> - let result = - let xyz = get_xyz angMom_c in - let axyz = Po.get xyz angMom_a in - let cm = Po.decr xyz angMom_c in - let cmxyz = Po.get xyz cm in - - let expo_inv_q_over_p = expo_q_inv /. expo_p_inv in - let f = - Co.get xyz center_qc +. expo_inv_q_over_p *. - Co.get xyz center_pa - in - let result = 0. in - - let result = - if cmxyz < 1 then result else - let f = 0.5 *. (float_of_int_fast cmxyz) *. expo_q_inv in - if abs_float f < cutoff then 0. else - let cmm = Po.decr xyz cm in - let v3 = trr angMom_a cmm in - result +. f *. v3 - in - let result = - if abs_float f < cutoff then result else - let v1 = trr angMom_a cm in - result +. f *. v1 - in - let result = - if cmxyz < 0 then result else - let f = -. expo_inv_q_over_p in - let ap = Po.incr xyz angMom_a in - let v4 = trr ap cm in - result +. v4 *. f - in - let result = - if axyz < 1 then result else - let f = 0.5 *. (float_of_int_fast axyz) *. expo_q_inv in - if abs_float f < cutoff then result else - let am = Po.decr xyz angMom_a in - let v2 = trr am cm in - result +. f *. v2 - in - result - in - Zmap.add map_2d key [|result|]; - result - -*) - in - - - let vrr a c = - (vrr a c).(0) - (* - if maxm < 10 then (vrr a c).(0) else trr a c - *) - in - - - (** Horizontal recurrence relations *) - let rec hrr0 angMom_a angMom_b angMom_c = - - match angMom_b.Po.tot with - | 1 -> - let xyz = get_xyz angMom_b in - let ap = Po.incr xyz angMom_a in - let v1 = vrr ap angMom_c in - let f2 = Co.get xyz center_ab in - if (abs_float f2 < cutoff) then v1 else - let v2 = vrr angMom_a angMom_c in - v1 +. f2 *. v2 - | 0 -> vrr angMom_a angMom_c - | _ -> - let xyz = get_xyz angMom_b in - let bxyz = Po.get xyz angMom_b in - if bxyz > 0 then - let ap = Po.incr xyz angMom_a in - let bm = Po.decr xyz angMom_b in - let h1 = hrr0 ap bm angMom_c in - let f2 = Co.get xyz center_ab in - if abs_float f2 < cutoff then h1 else - let h2 = hrr0 angMom_a bm angMom_c in - h1 +. f2 *. h2 - else 0. - - - and hrr angMom_a angMom_b angMom_c angMom_d = - - match (angMom_b.Po.tot, angMom_d.Po.tot) with - | (_,0) -> - if (angMom_b.Po.tot = 0) then - vrr angMom_a angMom_c - else - hrr0 angMom_a angMom_b angMom_c - | (_,_) -> - let xyz = get_xyz angMom_d in - let cp = Po.incr xyz angMom_c in - let dm = Po.decr xyz angMom_d in - let h1 = hrr angMom_a angMom_b cp dm in - let f2 = Co.get xyz center_cd in - if abs_float f2 < cutoff then h1 else - let h2 = hrr angMom_a angMom_b angMom_c dm in - h1 +. f2 *. h2 - - in - hrr angMom_a angMom_b angMom_c angMom_d - - - - -let contracted_class_shell_pair_couple ~basis ~zero_m shell_pair_couple : float Zmap.t = - - let maxm = Am.to_int (Cspc.ang_mom shell_pair_couple) in - - (* Pre-computation of integral class indices *) - let class_indices = Cspc.zkey_array shell_pair_couple in - - let contracted_class = - Array.make (Array.length class_indices) 0.; - in - - let monocentric = - Cspc.monocentric shell_pair_couple - in - - (* Compute all integrals in the shell for each pair of significant shell pairs *) - - let shell_p = Cspc.shell_pair_p shell_pair_couple - and shell_q = Cspc.shell_pair_q shell_pair_couple - in - - let center_ab = Csp.a_minus_b shell_p - and center_cd = Csp.a_minus_b shell_q - in - - let norm_scales = Cspc.norm_scales shell_pair_couple in - - List.iter (fun (coef_prod, spc) -> - - let sp_ab = Pspc.shell_pair_p spc - and sp_cd = Pspc.shell_pair_q spc - in - - let center_pq = Co.(Psp.center sp_ab |- Psp.center sp_cd) in - let center_pa = Psp.center_minus_a sp_ab in - let center_qc = Psp.center_minus_a sp_cd in - let norm_pq_sq = Co.dot center_pq center_pq in - let expo_p_inv = Psp.exponent_inv sp_ab in - let expo_q_inv = Psp.exponent_inv sp_cd in - let zero = Zp.zero basis zero_m in - let zero_m_array = zero_m - { zero with - maxm ; expo_p_inv ; expo_q_inv ; norm_pq_sq ; - center_pq ; center_pa ; center_qc ; - } - in - - begin - match Cspc.ang_mom shell_pair_couple with - | Am.S -> - let integral = zero_m_array.(0) in - contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral - | _ -> - let expo_b = Ps.exponent (Psp.shell_b sp_ab) - and expo_d = Ps.exponent (Psp.shell_b sp_cd) - in - let map_1d = Zmap.create (4*maxm) - and map_2d = Zmap.create (Array.length class_indices) - in - - (* Compute the integral class from the primitive shell quartet *) - class_indices - |> Array.iteri (fun i key -> - let (angMom_a,angMom_b,angMom_c,angMom_d) = - match Zkey.to_powers key with - | Zkey.Twelve x -> x - | _ -> assert false - in - try - if monocentric then - begin - if ( ((1 land angMom_a.Po.x + angMom_b.Po.x + angMom_c.Po.x + angMom_d.Po.x)=1) || - ((1 land angMom_a.Po.y + angMom_b.Po.y + angMom_c.Po.y + angMom_d.Po.y)=1) || - ((1 land angMom_a.Po.z + angMom_b.Po.z + angMom_c.Po.z + angMom_d.Po.z)=1) - ) then - raise NullQuartet - end; - - let norm = norm_scales.(i) in - let coef_prod = coef_prod *. norm in - - let abcd = { - expo_b ; expo_d ; expo_p_inv ; expo_q_inv ; - center_ab ; center_cd ; center_pq ; - center_pa ; center_qc ; zero_m_array ; - } in - let integral = - hvrr_two_e - angMom_a angMom_b angMom_c angMom_d - abcd map_1d map_2d - in - contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral - with NullQuartet -> () - ) - end - ) (Cspc.coefs_and_shell_pair_couples shell_pair_couple); - - let result = - Zmap.create (Array.length contracted_class) - in - Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices; - result - - - - - - - - -let contracted_class_atomic_shell_pair_couple ~basis ~zero_m atomic_shell_pair_couple : float Zmap.t = - - let maxm = Am.to_int (Aspc.ang_mom atomic_shell_pair_couple) in - - (* Pre-computation of integral class indices *) - let class_indices = Aspc.zkey_array atomic_shell_pair_couple in - - let contracted_class = - Array.make (Array.length class_indices) 0.; - in - - let monocentric = - Aspc.monocentric atomic_shell_pair_couple - in - - let shell_p = Aspc.atomic_shell_pair_p atomic_shell_pair_couple - and shell_q = Aspc.atomic_shell_pair_q atomic_shell_pair_couple - in - - (* Compute all integrals in the shell for each pair of significant shell pairs *) - - let center_ab = Asp.a_minus_b shell_p - and center_cd = Asp.a_minus_b shell_q - in - - let norm_scales = Aspc.norm_scales atomic_shell_pair_couple in - - - List.iter (fun cspc -> - List.iter (fun (coef_prod, spc) -> - let sp_ab = Pspc.shell_pair_p spc - and sp_cd = Pspc.shell_pair_q spc - in - - let expo_p_inv = Psp.exponent_inv sp_ab - in - - let center_pq = Co.(Psp.center sp_ab |- Psp.center sp_cd) in - let center_qc = Psp.center_minus_a sp_cd in - let center_pa = Psp.center_minus_a sp_ab in - let norm_pq_sq = Co.dot center_pq center_pq in - let expo_q_inv = Psp.exponent_inv sp_cd in - - let zero = Zp.zero basis zero_m in - let zero_m_array = zero_m - { zero with - maxm ; expo_p_inv ; expo_q_inv ; norm_pq_sq ; - center_pq ; center_pa ; center_qc ; - } - in - - begin - match Aspc.ang_mom atomic_shell_pair_couple with - | Am.S -> - let integral = zero_m_array.(0) in - contracted_class.(0) <- contracted_class.(0) +. coef_prod *. integral - | _ -> - let expo_b = Ps.exponent (Psp.shell_b sp_ab) - and expo_d = Ps.exponent (Psp.shell_b sp_cd) - in - let map_1d = Zmap.create (4*maxm) - and map_2d = Zmap.create (Array.length class_indices) - in - - (* Compute the integral class from the primitive shell quartet *) - class_indices - |> Array.iteri (fun i key -> - let (angMom_a,angMom_b,angMom_c,angMom_d) = - match Zkey.to_powers key with - | Zkey.Twelve x -> x - | _ -> assert false - in - try - if monocentric then - begin - if ( ((1 land angMom_a.Po.x + angMom_b.Po.x + angMom_c.Po.x + angMom_d.Po.x)=1) || - ((1 land angMom_a.Po.y + angMom_b.Po.y + angMom_c.Po.y + angMom_d.Po.y)=1) || - ((1 land angMom_a.Po.z + angMom_b.Po.z + angMom_c.Po.z + angMom_d.Po.z)=1) - ) then - raise NullQuartet - end; - - let norm = norm_scales.(i) in - let coef_prod = coef_prod *. norm in - - let abcd = { - expo_b ; expo_d ; expo_p_inv ; expo_q_inv ; - center_ab ; center_cd ; center_pq ; - center_pa ; center_qc ; zero_m_array ; - } in - let integral = - hvrr_two_e - angMom_a angMom_b angMom_c angMom_d - abcd - map_1d map_2d - in - contracted_class.(i) <- contracted_class.(i) +. coef_prod *. integral - with NullQuartet -> () - ) - end - ) (Cspc.coefs_and_shell_pair_couples cspc) - ) (Aspc.contracted_shell_pair_couples atomic_shell_pair_couple); - - let result = - Zmap.create (Array.length contracted_class) - in - Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices; - result - diff --git a/Basis/TwoElectronRRVectorized.ml b/Basis/TwoElectronRRVectorized.ml deleted file mode 100644 index 5a5c789..0000000 --- a/Basis/TwoElectronRRVectorized.ml +++ /dev/null @@ -1,875 +0,0 @@ -open Util -open Lacaml.D -open Bigarray - -module Am = AngularMomentum -module Co = Coordinate -module Cs = ContractedShell -module Csp = ContractedShellPair -module Cspc = ContractedShellPairCouple -module Po = Powers -module Psp = PrimitiveShellPair -module Ps = PrimitiveShell -module Zp = Zero_m_parameters - -exception NullQuartet -exception Found - -let cutoff = Constants.integrals_cutoff -let cutoff2 = cutoff *. cutoff -let empty = Zmap.create 0 - -let at_least_one_valid arr = - try - Array.iter (fun x -> if (abs_float x > cutoff) then raise Found) arr ; false - with Found -> true - -type four_idx_intermediate = -{ - expo_b : float array; - expo_d : float array; - expo_p_inv : float array; - expo_q_inv : float array; - center_ab : Co.t ; - center_cd : Co.t ; - center_pq : Co.axis -> float array array; - center_pa : Co.axis -> float array; - center_qc : Co.axis -> float array; - zero_m_array : float array array array; -} - - - -(** Horizontal and Vertical Recurrence Relations (HVRR) *) -let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d) - abcd map_1d map_2d np nq - = - - let expo_p_inv = abcd.expo_p_inv - and expo_q_inv = abcd.expo_q_inv - and center_ab = abcd.center_ab - and center_cd = abcd.center_cd - and center_pq = abcd.center_pq - in - - let zero_m_array = abcd.zero_m_array in - - let maxm = Array.length zero_m_array - 1 in - - let get_xyz angMom = - match angMom with - | { Po.y=0 ; z=0 ; _ } -> Co.X - | { z=0 ; _ } -> Co.Y - | _ -> Co.Z - in - - (** Vertical recurrence relations *) - let rec vrr0_v angMom_a = - match angMom_a.Po.tot with - | 0 -> zero_m_array - | _ -> - let key = Zkey.of_powers_three angMom_a - in - - try Zmap.find map_1d key with - | Not_found -> - let result = - let xyz = get_xyz angMom_a in - let am = Po.decr xyz angMom_a in - let cab = Co.get xyz center_ab in - let result = Array.init (maxm+1-angMom_a.Po.tot) (fun _ -> Array.make_matrix np nq 0.) in - let v_am= vrr0_v am in - - begin - if abs_float cab >= cutoff then - let expo_b = abcd.expo_b in - Array.iteri (fun m result_m -> - let v0 = v_am.(m) in - Array.iteri (fun l result_ml -> - let f0 = -. expo_b.(l) *. expo_p_inv.(l) *. cab - and v0_l = v0.(l) - in - Array.iteri (fun k v0_lk -> - result_ml.(k) <- v0_lk *. f0) v0_l - ) result_m - ) result - end; - let amxyz = Po.get xyz am in - if amxyz < 1 then - Array.iteri (fun l expo_inv_p_l -> - let center_pq_xyz_l = (center_pq xyz).(l) in - Array.iteri (fun m result_m -> - let result_ml = result_m.(l) in - let p0 = v_am.(m+1) in - let p0_l = p0.(l) - in - Array.iteri (fun k p0_lk -> - result_ml.(k) <- result_ml.(k) - +. expo_inv_p_l *. center_pq_xyz_l.(k) *. p0_lk - ) p0_l - ) result - ) expo_p_inv - else - begin - let amm = Po.decr xyz am in - let amxyz = float_of_int_fast amxyz in - let v_amm = vrr0_v amm in - Array.iteri (fun l expo_inv_p_l -> - let f = amxyz *. expo_p_inv.(l) *. 0.5 - and center_pq_xyz_l = (center_pq xyz).(l) - in - Array.iteri (fun m result_m -> - let v1 = v_amm.(m) in - let v1_l = v1.(l) in - let result_ml = result_m.(l) in - let v2 = v_amm.(m+1) in - let p0 = v_am.(m+1) in - let v2_l = v2.(l) - in - Array.iteri (fun k p0_lk -> - result_ml.(k) <- result_ml.(k) +. - expo_inv_p_l *. center_pq_xyz_l.(k) *. p0_lk +. - f *. (v1_l.(k) +. v2_l.(k) *. expo_inv_p_l) - ) p0.(l) - ) result - ) expo_p_inv - end; - result - in - Zmap.add map_1d key result; - result - - and vrr_v m angMom_a angMom_c = - - match (angMom_a.Po.tot, angMom_c.Po.tot) with - | (_,0) -> Some (vrr0_v angMom_a).(m) - | (_,_) -> - - let key = Zkey.of_powers_six angMom_a angMom_c in - - try Zmap.find map_2d.(m) key with - | Not_found -> - let result = - begin - let xyz = get_xyz angMom_c in - let cm = Po.decr xyz angMom_c in - let axyz = Po.get xyz angMom_a in - - let do_compute = ref false in - let v1 = - let f = -. (Co.get xyz center_cd) in - - let f1 = - let expo_d = abcd.expo_d in - Array.init nq (fun k -> - let x = expo_d.(k) *. expo_q_inv.(k) *. f in - if ( (not !do_compute) && (abs_float x > cutoff) ) then - do_compute := true; - x) - in - if (!do_compute) then - match vrr_v m angMom_a cm with - | None -> None - | Some v1 -> - begin - Some (Array.init np (fun l -> - let v1_l = v1.(l) in - Array.mapi (fun k f1k -> v1_l.(k) *. f1k) f1 - ) ) - end - else None - in - - let v2 = - let f2 = - Array.init np (fun l -> - let cpq_l = (center_pq xyz).(l) in - Array.init nq (fun k -> - let x = expo_q_inv.(k) *. cpq_l.(k) in - if (!do_compute) then x - else (if abs_float x > cutoff then do_compute := true ; x) - ) ) - in - if (!do_compute) then - match vrr_v (m+1) angMom_a cm with - | None -> None - | Some v2 -> - begin - for l=0 to np-1 do - let f2_l = f2.(l) - and v2_l = v2.(l) - in - for k=0 to nq-1 do - f2_l.(k) <- -. v2_l.(k) *. f2_l.(k) - done - done; - Some f2 - end - else None - in - - let p1 = - match v1, v2 with - | None, None -> None - | None, Some v2 -> Some v2 - | Some v1, None -> Some v1 - | Some v1, Some v2 -> - begin - for l=0 to np-1 do - let v1_l = v1.(l) - and v2_l = v2.(l) - in - for k=0 to nq-1 do - v2_l.(k) <- v2_l.(k) +. v1_l.(k) - done - done; - Some v2 - end - in - - let cxyz = Po.get xyz angMom_c in - let p2 = - if cxyz < 2 then p1 else - let cmm = Po.decr xyz cm in - let fcm = (float_of_int_fast (cxyz-1)) *. 0.5 in - let f1 = - Array.init nq (fun k -> - let x = fcm *. expo_q_inv.(k) in - if (!do_compute) then x - else (if abs_float x > cutoff then do_compute := true ; x) - ) - in - let v1 = - if (!do_compute) then - match vrr_v m angMom_a cmm with - | None -> None - | Some v1 -> - begin - let result = Array.make_matrix np nq 0. in - for l=0 to np-1 do - let v1_l = v1.(l) - and result_l = result.(l) - in - for k=0 to nq-1 do - result_l.(k) <- v1_l.(k) *. f1.(k) - done; - done; - Some result - end - else None - in - - let v3 = - let f2 = - Array.init nq (fun k -> - let x = expo_q_inv.(k) *. f1.(k) in - if (!do_compute) then x - else (if abs_float x > cutoff then do_compute := true ; x) - ) - in - if (!do_compute) then - match vrr_v (m+1) angMom_a cmm with - | None -> None - | Some v3 -> - begin - let result = Array.make_matrix np nq 0. in - for l=0 to np-1 do - let v3_l = v3.(l) - and result_l = result.(l) - in - for k=0 to nq-1 do - result_l.(k) <- v3_l.(k) *. f2.(k) - done - done; - Some result - end - else None - in - match p1, v1, v3 with - | None, None, None -> None - | Some p1, None, None -> Some p1 - | None, Some v1, None -> Some v1 - | None, None, Some v3 -> Some v3 - | Some p1, Some v1, Some v3 -> - begin - for l=0 to np-1 do - let v3_l = v3.(l) - and v1_l = v1.(l) - and p1_l = p1.(l) - in - for k=0 to nq-1 do - v3_l.(k) <- p1_l.(k) +. v1_l.(k) +. v3_l.(k) - done - done; - Some v3 - end - | Some p1, Some v1, None -> - begin - for l=0 to np-1 do - let v1_l = v1.(l) - and p1_l = p1.(l) - in - for k=0 to nq-1 do - p1_l.(k) <- v1_l.(k) +. p1_l.(k) - done - done; - Some p1 - end - | Some p1, None, Some v3 -> - begin - for l=0 to np-1 do - let v3_l = v3.(l) - and p1_l = p1.(l) - in - for k=0 to nq-1 do - p1_l.(k) <- p1_l.(k) +. v3_l.(k) - done - done; - Some p1 - end - | None , Some v1, Some v3 -> - begin - for l=0 to np-1 do - let v3_l = v3.(l) - and v1_l = v1.(l) - in - for k=0 to nq-1 do - v3_l.(k) <- v1_l.(k) +. v3_l.(k) - done - done; - Some v3 - end - in - if (axyz < 1) || (cxyz < 1) then p2 else - let am = Po.decr xyz angMom_a in - let v = - vrr_v (m+1) am cm - in - match (p2, v) with - | None, None -> None - | Some p2, None -> Some p2 - | _, Some v -> - begin - let p2 = - match p2 with - | None -> Array.make_matrix np nq 0. - | Some p2 -> p2 - in - for l=0 to np-1 do - let fa = (float_of_int_fast axyz) *. expo_p_inv.(l) *. 0.5 in - let p2_l = p2.(l) - and v_l = v.(l) - in - for k=0 to nq-1 do - p2_l.(k) <- p2_l.(k) -. fa *. expo_q_inv.(k) *. v_l.(k) - done - done; - Some p2 - end - end - in Zmap.add map_2d.(m) key result; - result - -(* - and trr_v angMom_a angMom_c = - - match (angMom_a.Po.tot, angMom_c.Po.tot) with - | (i,0) -> Some (vrr0_v angMom_a).(0) - | (_,_) -> - - let key = Zkey.of_powers_six angMom_a angMom_c in - - try Zmap.find map_2d.(0) key with - | Not_found -> - let xyz = get_xyz angMom_c in - let axyz = Po.get xyz angMom_a in - let cm = Po.decr xyz angMom_c in - let cmxyz = Po.get xyz cm in - let expo_inv_q_over_p = - Array.mapi (fun l expo_inv_p_l -> - let expo_p_l = 1./.expo_inv_p_l in - Array.mapi (fun k expo_inv_q_k -> - expo_inv_q_k *. expo_p_l) expo_q_inv ) expo_p_inv - in - let result = None in - - let result = - if cmxyz < 1 then result else - begin - let f = 0.5 *. (float_of_int_fast cmxyz) in - let cmm = Po.decr xyz cm in - match result, trr_v angMom_a cmm with - | None, None -> None - | None, Some v3 -> - Some (Array.init np (fun l -> - let v3_l = v3.(l) in - Array.mapi (fun k v3_lk -> - expo_q_inv.(k) *. f *. v3_lk) v3_l - ) ) - | Some result, None -> Some result - | Some result, Some v3 -> - (Array.iteri (fun l v3_l -> - let result_l = result.(l) in - Array.iteri (fun k v3_lk -> - result_l.(k) <- result_l.(k) +. - expo_q_inv.(k) *. f *. v3_lk) v3_l - ) v3 ; Some result) - end - in - let result = - begin - match result, trr_v angMom_a cm with - | Some result, None -> Some result - | Some result, Some v1 -> - (Array.iteri (fun l v1_l -> - let cpa = (center_pa xyz).(l) - and result_l = result.(l) - and expo_inv_q_over_p_l = expo_inv_q_over_p.(l) - in - Array.iteri (fun k v1_lk -> - let cqc = (center_qc xyz).(k) in - result_l.(k) <- result_l.(k) +. - (cqc +. expo_inv_q_over_p_l.(k) *. cpa) *. v1_lk - ) v1_l - ) v1 ; Some result) - | None, None -> None - | None, Some v1 -> - Some (Array.init np (fun l -> - let v1_l = v1.(l) - and cpa = (center_pa xyz).(l) - and expo_inv_q_over_p_l = expo_inv_q_over_p.(l) - in - Array.mapi (fun k v1_lk -> - let cqc = (center_qc xyz).(k) in - (cqc +. expo_inv_q_over_p_l.(k) *. cpa) *. v1_lk - ) v1_l - ) ) - end - in - let result = - if cmxyz < 0 then result else - begin - let ap = Po.incr xyz angMom_a in - match result, trr_v ap cm with - | Some result, None -> Some result - | Some result, Some v4 -> - (Array.iteri (fun l v4_l -> - let result_l = result.(l) in - Array.iteri (fun k v4_lk -> - let expo_inv_q_over_p_l = expo_inv_q_over_p.(l) in - result_l.(k) <- result_l.(k) - -. expo_inv_q_over_p_l.(k) *. v4_lk) v4_l - ) v4 ; Some result) - | None, None -> None - | None, Some v4 -> - Some (Array.init np (fun l -> - let v4_l = v4.(l) in - let expo_inv_q_over_p_l = expo_inv_q_over_p.(l) in - Array.mapi (fun k v4_lk -> - -. expo_inv_q_over_p_l.(k) *. v4_lk) v4_l - ) ) - end - in - let result = - if axyz < 1 then result else - begin - let f = 0.5 *. (float_of_int_fast axyz) in - let am = Po.decr xyz angMom_a in - match result, trr_v am cm with - | Some result, None -> Some result - | Some result, Some v2 -> - (Array.iteri (fun l v2_l -> - let result_l = result.(l) in - Array.iteri (fun k v2_lk -> - result_l.(k) <- result_l.(k) +. - expo_q_inv.(k) *. f *. v2_lk) v2_l - ) v2; Some result) - | None, None -> None - | None, Some v2 -> - Some (Array.init np (fun l -> - let v2_l = v2.(l) in - Array.mapi (fun k v2_lk -> - expo_q_inv.(k) *. f *. v2_lk) v2_l - ) ) - end - in - Zmap.add map_2d.(0) key result; - result - *) - in - - let sum matrix = - Array.fold_left (fun accu c -> accu +. Array.fold_left (+.) 0. c) 0. matrix - in - - let vrr_v a c = - let v = - (* - if c.Po.tot <> 0 then - vrr_v 0 a c - else trr_v a c - *) - vrr_v 0 a c - in - match v with - | Some matrix -> sum matrix - | None -> 0. - in - - - (** Horizontal recurrence relations *) - let rec hrr0_v angMom_a angMom_b angMom_c = - - match angMom_b.Po.tot with - | 0 -> - begin - match (angMom_a.Po.tot, angMom_c.Po.tot) with - | (0,0) -> sum zero_m_array.(0) - | (_,_) -> vrr_v angMom_a angMom_c - end - | 1 -> - let xyz = get_xyz angMom_b in - let ap = Po.incr xyz angMom_a in - let f = Co.get xyz center_ab in - let v1 = vrr_v ap angMom_c in - if (abs_float f < cutoff) then v1 else - let v2 = vrr_v angMom_a angMom_c in - v1 +. v2 *. f - | _ -> - let xyz = get_xyz angMom_b in - let bxyz = Po.get xyz angMom_b in - if (bxyz < 0) then 0. else - let ap = Po.incr xyz angMom_a in - let bm = Po.decr xyz angMom_b in - let h1 = hrr0_v ap bm angMom_c in - let f = Co.get xyz center_ab in - if abs_float f < cutoff then h1 else - let h2 = hrr0_v angMom_a bm angMom_c in - h1 +. h2 *. f - - and hrr_v angMom_a angMom_b angMom_c angMom_d = - - match (angMom_b.Po.tot, angMom_d.Po.tot) with - | (_,0) -> if angMom_b.Po.tot = 0 then - vrr_v angMom_a angMom_c - else - hrr0_v angMom_a angMom_b angMom_c - | (_,_) -> - let xyz = get_xyz angMom_d in - let cp = Po.incr xyz angMom_c in - let dm = Po.decr xyz angMom_d in - let h1 = - hrr_v angMom_a angMom_b cp dm - in - let f = Co.get xyz center_cd in - if abs_float f < cutoff then - h1 - else - let h2 = - hrr_v angMom_a angMom_b angMom_c dm - in h1 +. f *. h2 - in - hrr_v angMom_a angMom_b angMom_c angMom_d - - - - - - - -let contracted_class_shell_pairs ~basis ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t = - - let sp = Csp.shell_pairs shell_p - and sq = Csp.shell_pairs shell_q - and cp = Csp.coefficients shell_p - and cq = Csp.coefficients shell_q - in - - let np, nq = - Array.length sp, - Array.length sq - in - - try - match Cspc.make ~cutoff shell_p shell_q with - | None -> raise NullQuartet - | Some shell_pair_couple -> - - let shell_a = Cspc.shell_a shell_pair_couple - and shell_c = Cspc.shell_c shell_pair_couple - in - - let maxm = Am.to_int (Cspc.ang_mom shell_pair_couple) in - - - (* Pre-computation of integral class indices *) - let class_indices = Cspc.zkey_array shell_pair_couple in - - let contracted_class = - Array.make (Array.length class_indices) 0.; - in - - let monocentric = - Cspc.monocentric shell_pair_couple - in - - (* Compute all integrals in the shell for each pair of significant shell pairs *) - - begin - match Cspc.ang_mom shell_pair_couple with - | Am.S -> - contracted_class.(0) <- - begin - try - let expo_p_inv = - Vec.init np (fun ab -> Psp.exponent_inv sp.(ab-1)) - and expo_q_inv = - Vec.init nq (fun cd -> Psp.exponent_inv sq.(cd-1)) - in - - let coef = - let result = Mat.make0 nq np in - Lacaml.D.ger (Vec.of_array @@ cq) (Vec.of_array @@ cp) result; - result - in - let zm_array = Mat.init_cols np nq (fun i j -> - try - if (abs_float coef.{j,i} ) < 1.e-3*.cutoff then - raise NullQuartet; - - let expo_p_inv, expo_q_inv = - expo_p_inv.{i}, expo_q_inv.{j} - in - - let center_pq = - Co.(Psp.center sp.(i-1) |- Psp.center sq.(j-1)) - and center_pa = - Co.(Psp.center sp.(i-1) |- Cs.center shell_a) - and center_qc = - Co.(Psp.center sq.(i-1) |- Cs.center shell_c) - in - let norm_pq_sq = - Co.dot center_pq center_pq - in - - let zero = Zp.zero basis zero_m in - let zero_m_array = - zero_m - {zero with - expo_p_inv ; expo_q_inv ; norm_pq_sq ; - center_pq ; center_pa ; center_qc ; - } - in - zero_m_array.(0) - with NullQuartet -> 0. - ) - in - Mat.gemm_trace zm_array coef - with (Invalid_argument _) -> 0. - end - | _ -> - - let coef = - Array.init np (fun l -> Array.init nq (fun k -> cq.(k) *. cp.(l)) ) - in - - let norm = Cspc.norm_scales shell_pair_couple in - - let expo_p_inv = - Array.map (fun shell_ab -> Psp.exponent_inv shell_ab) sp - and expo_q_inv = - Array.map (fun shell_cd -> Psp.exponent_inv shell_cd) sq - in - - let expo_b = - Array.map (fun shell_ab -> Ps.exponent (Psp.shell_b shell_ab) ) sp - and expo_d = - Array.map (fun shell_cd -> Ps.exponent (Psp.shell_b shell_cd) ) sq - in - - let center_pq = - let result = - Array.init 3 (fun xyz -> - Array.init np (fun ab -> - let shell_ab = sp.(ab) in - Array.init nq (fun cd -> - let shell_cd = sq.(cd) - in - let cpq = - Co.(Psp.center shell_ab |- Psp.center shell_cd) - in - match xyz with - | 0 -> Co.get X cpq; - | 1 -> Co.get Y cpq; - | _ -> Co.get Z cpq; - ) - ) - ) - in function - | Co.X -> result.(0) - | Co.Y -> result.(1) - | Co.Z -> result.(2) - in - let center_pa = - let result = - Array.init 3 (fun xyz -> - Array.init np (fun ab -> - let shell_ab = sp.(ab) in - let cpa = - Co.(Psp.center shell_ab |- Cs.center shell_a) - in - match xyz with - | 0 -> Co.(get X cpa); - | 1 -> Co.(get Y cpa); - | _ -> Co.(get Z cpa); - ) - ) - in function - | Co.X -> result.(0) - | Co.Y -> result.(1) - | Co.Z -> result.(2) - in - let center_qc = - let result = - Array.init 3 (fun xyz -> - Array.init nq (fun cd -> - let shell_cd = sq.(cd) in - let cqc = - Co.(Psp.center shell_cd |- Cs.center shell_c) - in - match xyz with - | 0 -> Co.(get X cqc); - | 1 -> Co.(get Y cqc); - | _ -> Co.(get Z cqc); - ) - ) - in function - | Co.X -> result.(0) - | Co.Y -> result.(1) - | Co.Z -> result.(2) - in - let zero_m_array = - let result = - Array.init (maxm+1) (fun _ -> - Array.init np (fun _ -> Array.make nq 0. ) ) - in - let empty = Array.make (maxm+1) 0. in - let center_qc_tmp = Array.init nq (fun cd -> - Coordinate.make { Coordinate. - x = (center_qc Co.X).(cd) ; - y = (center_qc Co.Y).(cd) ; - z = (center_qc Co.Z).(cd) ; - }) - in - Array.iteri (fun ab _shell_ab -> - let center_pa = Coordinate.make { Coordinate. - x = (center_pa Co.X).(ab) ; - y = (center_pa Co.Y).(ab) ; - z = (center_pa Co.Z).(ab) ; - } - in - let zero_m_array_tmp = - Array.mapi (fun cd _shell_cd -> - if (abs_float coef.(ab).(cd) < cutoff) then - empty - else - let expo_p_inv, expo_q_inv = - expo_p_inv.(ab), expo_q_inv.(cd) - in - let x = (center_pq X).(ab).(cd) - and y = (center_pq Y).(ab).(cd) - and z = (center_pq Z).(ab).(cd) - in - let norm_pq_sq = - x *. x +. y *. y +. z *. z - in - let zero = Zp.zero basis zero_m in - zero_m {zero with - maxm ; expo_p_inv ; expo_q_inv ; norm_pq_sq ; - center_pq = Coordinate.make Coordinate.{x ; y ; z} ; - center_pa ; center_qc = center_qc_tmp.(cd) ; - } - ) sq - in - (* Transpose result *) - let coef_ab = coef.(ab) in - for m=0 to maxm do - let result_m_ab = result.(m).(ab) - in - for cd=0 to nq-1 do - result_m_ab.(cd) <- zero_m_array_tmp.(cd).(m) *. coef_ab.(cd) - done - done - ) sp; - result - in - - let map_1d = Zmap.create (4*maxm) - and map_2d = Array.init (maxm+1) (fun _ -> Zmap.create (Array.length class_indices)) - in - (* Compute the integral class from the primitive shell quartet *) - Array.iteri (fun i key -> - let (angMom_a,angMom_b,angMom_c,angMom_d) = - match Zkey.to_powers key with - | Zkey.Twelve x -> x - | _ -> assert false - in - try - if monocentric then - begin - if ( ((1 land angMom_a.x + angMom_b.x + angMom_c.x + angMom_d.x) =1) || - ((1 land angMom_a.y + angMom_b.y + angMom_c.y + angMom_d.y) =1) || - ((1 land angMom_a.z + angMom_b.z + angMom_c.z + angMom_d.z) =1) - ) then - raise NullQuartet - end; - - (* Schwartz screening *) - if (np+nq> 24) then - ( - let schwartz_p = - let key = Zkey.of_powers_twelve - angMom_a angMom_b angMom_a angMom_b - in - match schwartz_p with - | None -> 1. - | Some schwartz_p -> Zmap.find schwartz_p key - in - if schwartz_p < cutoff then raise NullQuartet; - let schwartz_q = - let key = Zkey.of_powers_twelve - angMom_c angMom_d angMom_c angMom_d - in - match schwartz_q with - | None -> 1. - | Some schwartz_q -> Zmap.find schwartz_q key - in - if schwartz_p *. schwartz_q < cutoff2 then raise NullQuartet; - ); - - let abcd = - { expo_b ; expo_d ; expo_p_inv ; expo_q_inv ; - center_ab = Csp.a_minus_b shell_p; - center_cd = Csp.a_minus_b shell_q ; - center_pq ; center_pa ; - center_qc ; zero_m_array } - in - - let integral = - hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d) - abcd map_1d map_2d np nq - in - contracted_class.(i) <- contracted_class.(i) +. integral *. norm.(i) - with NullQuartet -> () - ) class_indices - - end; - - let result = - Zmap.create (Array.length contracted_class) - in - Array.iteri (fun i key -> Zmap.add result key contracted_class.(i)) class_indices; - result - with NullQuartet -> empty - - diff --git a/Basis/Zero_m_parameters.ml b/Basis/Zero_m_parameters.ml deleted file mode 100644 index 9ac4983..0000000 --- a/Basis/Zero_m_parameters.ml +++ /dev/null @@ -1,27 +0,0 @@ -type t = -{ - expo_p_inv : float ; - expo_q_inv : float ; - norm_pq_sq : float ; - maxm : int ; - center_pq : Coordinate.t ; - center_pa : Coordinate.t ; - center_qc : Coordinate.t ; - zero_m_func : t -> float array ; - basis : Basis.t ; -} - -let zero basis zero_m_func = -{ - zero_m_func ; - basis ; - maxm=0 ; - expo_p_inv = 0.; - expo_q_inv = 0.; - norm_pq_sq = 0.; - center_pq = Coordinate.zero ; - center_pa = Coordinate.zero ; - center_qc = Coordinate.zero ; -} - - diff --git a/CI/.merlin b/CI/.merlin deleted file mode 100644 index 2ba6169..0000000 --- a/CI/.merlin +++ /dev/null @@ -1 +0,0 @@ -REC diff --git a/CI/CI.ml b/CI/CI.ml deleted file mode 100644 index 42f7086..0000000 --- a/CI/CI.ml +++ /dev/null @@ -1,1217 +0,0 @@ -open Lacaml.D -open Util - -module Ds = DeterminantSpace -module Sd = Spindeterminant - -type t = - { - e_shift : float ; (* Diagonal energy shift for increasing numerical precision *) - det_space : Ds.t ; - m_H : Matrix.t lazy_t ; - m_S2 : Matrix.t lazy_t ; - eigensystem : (Mat.t * Vec.t) lazy_t; - n_states : int; - } - -let det_space t = t.det_space - -let n_states t = t.n_states - -let m_H t = Lazy.force t.m_H - -let m_S2 t = Lazy.force t.m_S2 - -let eigensystem t = Lazy.force t.eigensystem - -let mo_class t = DeterminantSpace.mo_class t.det_space - -let eigenvectors t = - let (x,_) = eigensystem t in x - -let eigenvalues t = - let (_,x) = eigensystem t in x - -let h_integrals mo_basis = - let one_e_ints = MOBasis.one_e_ints mo_basis - and two_e_ints = MOBasis.two_e_ints mo_basis - in - ( (fun i j _ -> one_e_ints.{i,j}), - (fun i j k l s s' -> - if s' <> s then - ERI.get_phys two_e_ints i j k l - else - (ERI.get_phys two_e_ints i j k l) -. - (ERI.get_phys two_e_ints i j l k) - ), None ) - - - -let h_ij mo_basis ki kj = - let integrals = - List.map (fun f -> f mo_basis) - [ h_integrals ] - in - CIMatrixElement.make integrals ki kj - |> List.hd - - -let h_ij_non_zero mo_basis deg_a deg_b ki kj = - let integrals = - List.map (fun f -> f mo_basis) - [ h_integrals ] - in - CIMatrixElement.non_zero integrals deg_a deg_b ki kj - |> List.hd - - -let create_matrix_arbitrary f det_space = - lazy ( - let ndet = Ds.size det_space in - let data = - match Ds.determinants det_space with - | Ds.Arbitrary a -> a - | _ -> assert false - in - let det_alfa = data.Ds.det_alfa - and det_beta = data.Ds.det_beta - and det = data.Ds.det - and index_start = data.Ds.index_start - in - - - (** Array of (list of singles, list of doubles) in the beta spin *) - let degree_bb = - Array.map (fun det_i -> - let deg = Spindeterminant.degree det_i in - let doubles = - Array.mapi (fun i det_j -> - let d = deg det_j in - if d < 3 then - Some (i,d,det_j) - else - None - ) det_beta - |> Array.to_list - |> Util.list_some - in - let singles = - List.filter (fun (i,d,det_j) -> d < 2) doubles - |> List.rev_map (fun (i,_,det_j) -> (i,det_j)) - |> List.rev - in - let doubles = - List.rev_map (fun (i,_,det_j) -> (i,det_j)) doubles - |> List.rev - in - (singles, doubles) - ) det_beta - in - - let task (i,i_dets) = - let shift = index_start.(i) in - - let result = - Array.init (index_start.(i+1) - shift) - (fun _ -> []) - in - - (** Update function when ki and kj are connected *) - let update i j deg_a deg_b ki kj = - let x = f deg_a deg_b ki kj in - if abs_float x > Constants.epsilon then - result.(i - shift) <- (j, x) :: result.(i - shift) ; - in - - let i_alfa = det_alfa.(i) in - let deg_a = Spindeterminant.degree i_alfa in - - Array.iteri (fun j j_dets -> - let j_alfa = det_alfa.(j) in - let degree_a = deg_a j_alfa in - - begin - match degree_a with - | 2 -> - Array.iteri (fun i' i_b -> - try - Array.iteri (fun j' j_b -> - if j_b >= i_b then - ( if j_b = i_b then - ( let i_beta = det_beta.(i_b) in - let ki = Determinant.of_spindeterminants i_alfa i_beta in - let kj = Determinant.of_spindeterminants j_alfa i_beta in - update (index_start.(i) + i') - (index_start.(j) + j' + 1) 2 0 ki kj); - raise Exit) - ) j_dets - with Exit -> () - ) i_dets - | 1 -> - Array.iteri (fun i' i_b -> - let i_beta = det_beta.(i_b) in - let ki = Determinant.of_spindeterminants i_alfa i_beta in - let singles, _ = degree_bb.(i_b) in - let rec aux singles j' = - match singles with - | [] -> () - | (js, j_beta)::r_singles -> - begin - match compare js j_dets.(j') with - | -1 -> (aux [@tailcall]) r_singles j' - | 0 -> - let kj = - Determinant.of_spindeterminants j_alfa j_beta - in (update - (index_start.(i) + i') (index_start.(j) + j' + 1) - 1 (Determinant.degree_beta ki kj) ki kj; - (aux [@tailcall]) r_singles (j'+1);) - | 1 -> if (j' < Array.length j_dets) then (aux [@tailcall]) singles (j'+1) - | _ -> assert false - end - in aux singles 0 - ) i_dets - | 0 -> - Array.iteri (fun i' i_b -> - let i_beta = det_beta.(i_b) in - let ki = Determinant.of_spindeterminants i_alfa i_beta in - let _, doubles = degree_bb.(i_b) in - let rec aux doubles j' = - match doubles with - | [] -> () - | (js, j_beta)::r_doubles -> - begin - match compare js j_dets.(j') with - | -1 -> (aux [@tailcall]) r_doubles j' - | 0 -> - let kj = - Determinant.of_spindeterminants j_alfa j_beta - in (update - (index_start.(i) + i') (index_start.(j) + j' + 1) - 0 (Determinant.degree_beta ki kj) ki kj; - (aux [@tailcall]) r_doubles (j'+1);) - | 1 -> if (j' < Array.length j_dets) then (aux [@tailcall]) doubles (j'+1) - | _ -> assert false - end - in aux doubles 0 - ) i_dets - | _ -> (); - end - ) det; - let r = - Array.map (fun l -> - List.rev l - |> Vector.sparse_of_assoc_list ndet - ) result - in (i,r) - in - - - let result = - if Parallel.master then - Array.init ndet (fun _ -> Vector.sparse_of_assoc_list ndet []) - else - Array.init ndet (fun _ -> Vector.sparse_of_assoc_list ndet []) - in - - let n_det_alfa = - Array.length det_alfa - in - Array.mapi (fun i i_dets -> i, i_dets) det - |> Array.to_list - |> Stream.of_list - |> Farm.run ~ordered:false ~f:task - |> Stream.iter (fun (k, r) -> - let shift = index_start.(k) in - let det_k = det.(k) in - Array.iteri (fun j r_j -> result.(shift+det_k.(j)) <- r_j) r; - Printf.eprintf "%8d / %8d\r%!" (k+1) n_det_alfa; - ) ; - Matrix.sparse_of_vector_array result - ) - - -(* Create a matrix using the fact that the determinant space is made of - the outer product of spindeterminants. *) -let create_matrix_spin ?(nmax=2) f det_space = - lazy ( - let ndet = Ds.size det_space in - let a, b = - match Ds.determinants det_space with - | Ds.Spin (a,b) -> (a,b) - | _ -> assert false - in - let n_beta = Array.length b in - - - (** Array of (list of singles, list of doubles, list of triples) in the beta spin *) - let degree_bb = - match nmax with - | 2 -> begin - Array.map (fun det_i -> - let deg = Spindeterminant.degree det_i in - let triples = [] in - let doubles = - Array.mapi (fun i det_j -> - let d = deg det_j in - if d < 3 then - Some (i,d,det_j) - else - None - ) b - |> Array.to_list - |> Util.list_some - in - let singles = - List.filter (fun (i,d,det_j) -> d < 2) doubles - |> List.rev_map (fun (i,_,det_j) -> (i,det_j)) - |> List.rev - in - let doubles = - List.rev_map (fun (i,_,det_j) -> (i,det_j)) doubles - |> List.rev - in - (singles, doubles, triples) - ) b - end - | 3 -> begin - Array.map (fun det_i -> - let deg = Spindeterminant.degree det_i in - let triples = - Array.mapi (fun i det_j -> - let d = deg det_j in - if d < 4 then - Some (i,d,det_j) - else - None - ) b - |> Array.to_list - |> Util.list_some - in - let doubles = - List.filter (fun (i,d,det_j) -> d < 3) triples - in - let singles = - List.filter (fun (i,d,det_j) -> d < 2) doubles - in - - let triples = - List.rev_map (fun (i,_,det_j) -> (i,det_j)) triples - |> List.rev - in - let doubles = - List.rev_map (fun (i,_,det_j) -> (i,det_j)) doubles - |> List.rev - in - let singles = - List.rev_map (fun (i,_,det_j) -> (i,det_j)) singles - |> List.rev - in - (singles, doubles, triples) - ) b - end - | _ -> assert false - in - let a = Array.to_list a - and b = Array.to_list b - in - - let task = - let result = - Array.init n_beta (fun _ -> []) - in - - (** Update function when ki and kj are connected *) - let update i j deg_a deg_b ki kj = - let x = f deg_a deg_b ki kj in - if abs_float x > Constants.epsilon then - result.(i) <- (j, x) :: result.(i) ; - in - - fun (i,i_alfa) -> - begin match nmax with - | 2 -> begin - let j = ref 1 in - - let deg_a = Spindeterminant.degree i_alfa in - List.iter (fun j_alfa -> - let degree_a = deg_a j_alfa in - begin - match degree_a with - | 2 -> - let i' = ref 0 in - List.iteri (fun ib i_beta -> - let ki = Determinant.of_spindeterminants i_alfa i_beta in - let kj = Determinant.of_spindeterminants j_alfa i_beta in - update !i' (ib + !j) 2 0 ki kj; - incr i'; - ) b; - | 1 -> - let i' = ref 0 in - List.iteri (fun ib i_beta -> - let ki = Determinant.of_spindeterminants i_alfa i_beta in - let singles, _doubles, _triples = degree_bb.(ib) in - List.iter (fun (j', j_beta) -> - let kj = Determinant.of_spindeterminants j_alfa j_beta in - update !i' (j' + !j) 1 (Determinant.degree_beta ki kj) ki kj - ) singles; - incr i'; - ) b; - | 0 -> - let i' = ref 0 in - List.iteri (fun ib i_beta -> - let ki = Determinant.of_spindeterminants i_alfa i_beta in - let _singles, doubles, _triples = degree_bb.(ib) in - List.iter (fun (j', j_beta) -> - let kj = Determinant.of_spindeterminants j_alfa j_beta in - update !i' (j' + !j) 0 (Determinant.degree_beta ki kj) ki kj - ) doubles; - incr i'; - ) b; - | _ -> (); - end; - j := !j + n_beta - ) a - end - | 3 -> begin - let j = ref 1 in - - let deg_a = Spindeterminant.degree i_alfa in - List.iter (fun j_alfa -> - let degree_a = deg_a j_alfa in - begin - match degree_a with - | 3 -> - let i' = ref 0 in - List.iteri (fun ib i_beta -> - let ki = Determinant.of_spindeterminants i_alfa i_beta in - let kj = Determinant.of_spindeterminants j_alfa i_beta in - update !i' (ib + !j) 3 0 ki kj; - incr i'; - ) b; - | 2 -> - let i' = ref 0 in - List.iteri (fun ib i_beta -> - let ki = Determinant.of_spindeterminants i_alfa i_beta in - let singles, _doubles, _triples = degree_bb.(ib) in - List.iter (fun (j', j_beta) -> - let kj = Determinant.of_spindeterminants j_alfa j_beta in - update !i' (j' + !j) 2 (Determinant.degree_beta ki kj) ki kj - ) singles; - incr i'; - ) b; - | 1 -> - let i' = ref 0 in - List.iteri (fun ib i_beta -> - let ki = Determinant.of_spindeterminants i_alfa i_beta in - let _singles, doubles, _triples = degree_bb.(ib) in - List.iter (fun (j', j_beta) -> - let kj = Determinant.of_spindeterminants j_alfa j_beta in - update !i' (j' + !j) 1 (Determinant.degree_beta ki kj) ki kj - ) doubles; - incr i'; - ) b; - | 0 -> - let i' = ref 0 in - List.iteri (fun ib i_beta -> - let ki = Determinant.of_spindeterminants i_alfa i_beta in - let _singles, _doubles, triples = degree_bb.(ib) in - List.iter (fun (j', j_beta) -> - let kj = Determinant.of_spindeterminants j_alfa j_beta in - update !i' (j' + !j) 0 (Determinant.degree_beta ki kj) ki kj - ) triples; - incr i'; - ) b; - | _ -> (); - end; - j := !j + n_beta - ) a - end - | _ -> assert false - end; - let r = - Array.map (fun l -> - List.rev l - |> Vector.sparse_of_assoc_list ndet - ) result - in (i,r) - in - - - let result = - Array.init ndet (fun _ -> Vector.sparse_of_assoc_list ndet []) - in - - - List.mapi (fun i i_alfa -> i*n_beta, i_alfa) a - |> Stream.of_list - |> Farm.run ~ordered:false ~f:task - |> Stream.iter (fun (k, r) -> - Array.iteri (fun j r_j -> result.(k+j) <- r_j) r; - Printf.eprintf "%8d / %8d\r%!" (k+Array.length r) ndet; - ) ; - Matrix.sparse_of_vector_array result - ) - - - -(* Create a matrix using the fact that the determinant space is made of - the outer product of spindeterminants. *) -let create_matrix_spin_computed ?(nmax=2) f det_space = - lazy ( - let ndet = Ds.size det_space in - let a, b = - match Ds.determinants det_space with - | Ds.Spin (a,b) -> (a,b) - | _ -> assert false - in - let n_beta = Array.length b in - - let h2 i_alfa j_alfa = - let deg_a = Spindeterminant.degree a.(i_alfa) a.(j_alfa) in - match deg_a with - | 2 -> - let ai, aj = a.(i_alfa), a.(j_alfa) in - (fun i_beta j_beta -> - if i_beta <> j_beta then 0. else - let deg_b = 0 in - let ki = Determinant.of_spindeterminants ai b.(i_beta) in - let kj = Determinant.of_spindeterminants aj b.(j_beta) in - f deg_a deg_b ki kj - ) - | 1 -> - let ai, aj = a.(i_alfa), a.(j_alfa) in - (fun i_beta j_beta -> - let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in - match deg_b with - | 0 | 1 -> - let ki = Determinant.of_spindeterminants ai b.(i_beta) in - let kj = Determinant.of_spindeterminants aj b.(j_beta) in - f deg_a deg_b ki kj - | _ -> 0. - ) - | 0 -> - let ai, aj = a.(i_alfa), a.(j_alfa) in - (fun i_beta j_beta -> - let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in - match deg_b with - | 0 | 1 | 2 -> - let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in - let ki = Determinant.of_spindeterminants ai b.(i_beta) in - let kj = Determinant.of_spindeterminants aj b.(j_beta) in - f deg_a deg_b ki kj - | _ -> 0. - ) - | _ -> (fun _ _ -> 0.) - in - - let h3 i_alfa j_alfa = - let deg_a = Spindeterminant.degree a.(i_alfa) a.(j_alfa) in - match deg_a with - | 3 -> - let ai, aj = a.(i_alfa), a.(j_alfa) in - (fun i_beta j_beta -> - if i_beta <> j_beta then 0. else - let deg_b = 0 in - let ki = Determinant.of_spindeterminants ai b.(i_beta) in - let kj = Determinant.of_spindeterminants aj b.(j_beta) in - f deg_a deg_b ki kj - ) - | 2 -> - let ai, aj = a.(i_alfa), a.(j_alfa) in - (fun i_beta j_beta -> - let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in - match deg_b with - | 0 | 1 -> - let ki = Determinant.of_spindeterminants ai b.(i_beta) in - let kj = Determinant.of_spindeterminants aj b.(j_beta) in - f deg_a deg_b ki kj - | _ -> 0. - ) - | 1 -> - let ai, aj = a.(i_alfa), a.(j_alfa) in - (fun i_beta j_beta -> - let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in - match deg_b with - | 0 | 1 | 2 -> - let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in - let ki = Determinant.of_spindeterminants ai b.(i_beta) in - let kj = Determinant.of_spindeterminants aj b.(j_beta) in - f deg_a deg_b ki kj - | _ -> 0. - ) - | 0 -> - let ai, aj = a.(i_alfa), a.(j_alfa) in - (fun i_beta j_beta -> - let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in - match deg_b with - | 0 | 1 | 2 | 3 -> - let deg_b = Spindeterminant.degree b.(i_beta) b.(j_beta) in - let ki = Determinant.of_spindeterminants ai b.(i_beta) in - let kj = Determinant.of_spindeterminants aj b.(j_beta) in - f deg_a deg_b ki kj - | _ -> 0. - ) - | _ -> (fun _ _ -> 0.) - in - - let i_prev = ref (-10) - and result = ref (fun _ -> 0.) - in - let h123 = ref (fun _ -> 0.) in - - let h = if nmax = 2 then h2 else h3 in - - let g i = - (* - i : index of the i-th determinant. 1 <= i <= ndet - i_prev : index of the i-th determinant in the previous function call. - 1 <= i_prev <= ndet - i_a : index of the i_a-th alpha determinant. 0 <= i_a < n_alfa - i_b : index of the i_b-th beta determinant. 0 <= i_b < n_beta - j0 : index - 1 of the first determinant with the same alfa component - 0 <= j0 < n_beta*(n_alfa-1) - j1 : index - 1 of the next determinant with the 1st beta determinant - n_beta <= j1 <= ndet - j_a : index of the j_a-th alpha determinant. 0 <= j_a < n_alfa - j_b : index of the j_b-th beta determinant. 0 <= j_b < n_beta - *) - if i <> !i_prev then - begin - i_prev := i; - let i_a = (i-1)/n_beta in - let h1 = h i_a in - let i_b = i - i_a*n_beta - 1 in - let j0 = ref (2*ndet) in - let j1 = ref (2*ndet) in - let j_a = ref 0 in - result := fun j -> - if (!j0 < j) && (j <= !j1) then - () - else - begin - if (!j1 < j) && (j <= !j1 + n_beta) then - begin - incr j_a; - j0 := !j1; - end - else - begin - j_a := (j-1)/n_beta; - j0 := !j_a * n_beta; - end; - j1 := !j0 + n_beta; - h123 := h1 !j_a i_b; - end; - let j_b = j - !j0 - 1 in - !h123 j_b - end; - !result - in - - Matrix.of_fun ndet ndet g - ) - - - -let make ?(n_states=1) ?(algo=`Direct) det_space = - - let mo_basis = Ds.mo_basis det_space in - - (* While in a sequential region, initiate the parallel - 4-idx transformation to avoid nested parallel jobs - *) - ignore @@ MOBasis.two_e_ints mo_basis; - - let e_shift = - let d0 = - Ds.determinant_stream det_space - |> Stream.next - in - h_ij_non_zero mo_basis 0 0 d0 d0 - in - - let m_H = - - let f = - match Ds.determinants det_space with - | Ds.Arbitrary _ -> create_matrix_arbitrary - | Ds.Spin _ -> - if algo = `Direct then - create_matrix_spin_computed ~nmax:2 - else - create_matrix_spin ~nmax:2 - in - f (fun deg_a deg_b ki kj -> - if deg_a + deg_b > 0 then - h_ij_non_zero mo_basis deg_a deg_b ki kj - else - h_ij_non_zero mo_basis 0 0 ki ki -. e_shift - ) det_space - in - - let m_S2 = - let f = - match Ds.determinants det_space with - | Ds.Arbitrary _ -> create_matrix_arbitrary - | Ds.Spin _ -> create_matrix_spin ~nmax:2 - in - f (fun _deg_a _deg_b ki kj -> CIMatrixElement.make_s2 ki kj) det_space - (*TODO*) - in - - let eigensystem = lazy ( - - let eigensystem_incore () = - let m_H = - Lazy.force m_H - in - let diagonal = - Parallel.broadcast (lazy ( - Vec.init (Matrix.dim1 m_H) (fun i -> Matrix.get m_H i i) - )) - in - let matrix_prod psi = - let result = - Matrix.mm ~transa:`T psi m_H - |> Matrix.transpose - in - Parallel.broadcast (lazy result) - in - let eigenvectors, eigenvalues = - let result = - Davidson.make ~threshold:1.e-6 ~n_states diagonal matrix_prod - in - Parallel.broadcast (lazy result) - in - let eigenvalues = Vec.map (fun x -> x +. e_shift) eigenvalues in - (Conventions.rephase @@ Util.remove_epsilons eigenvectors), eigenvalues - in - - let eigensystem_direct () = - let m_H = - Lazy.force m_H - in - let diagonal = - Parallel.broadcast (lazy ( - Vec.init (Matrix.dim1 m_H) (fun i -> Matrix.get m_H i i) - )) - in - let matrix_prod psi = - let result = - Matrix.parallel_mm ~transa:`T ~transb:`N psi m_H - |> Matrix.transpose - in - Parallel.broadcast (lazy result) - in - let eigenvectors, eigenvalues = - let result = - Davidson.make ~threshold:1.e-6 ~n_states diagonal matrix_prod - in - Parallel.broadcast (lazy result) - in - let eigenvalues = Vec.map (fun x -> x +. e_shift) eigenvalues in - (Conventions.rephase @@ Util.remove_epsilons eigenvectors), eigenvalues - in - - match algo with - | `Direct -> eigensystem_direct () - | `InCore -> eigensystem_incore () - ) - in - { det_space ; e_shift ; m_H ; m_S2 ; eigensystem ; n_states } - - - - -let second_order_sum { det_space ; m_H ; m_S2 ; eigensystem ; n_states } - list_holes list_particles ?(unique=true) is_internal - i_o1_alfa alfa_o2_i w_alfa psi0 = - - let list_holes = Array.of_list list_holes in - let list_particles = Array.of_list list_particles in - - let psi0 = - let stream = - Ds.determinant_stream det_space - in - Array.init (Ds.size det_space) (fun i -> - (Stream.next stream), (Mat.copy_row psi0 (i+1)) ) - in - - - - let symmetric = i_o1_alfa == alfa_o2_i in - - - let det_contribution i = - - let already_generated = - if unique then - (fun alfa -> - if is_internal alfa then - true - else - let rec aux = function - | -1 -> false - | j -> Determinant.degree (fst psi0.(j)) alfa <= 2 - || aux (j-1) - in - aux (i-1) - ) - else - is_internal - in - - let psi_filtered_idx = - let rec aux accu = function - | j when j < i -> List.rev accu - | j -> - if Determinant.degree (fst psi0.(i)) (fst psi0.(j)) < 4 - then - aux (j::accu) (j-1) - else - aux accu (j-1) - in aux [] (Array.length psi0 - 1) - in - - let psi_filtered = - List.rev_map (fun i -> psi0.(i)) psi_filtered_idx - |> List.rev - in - - let psi_h_alfa alfa = - List.fold_left (fun accu (det, coef) -> -(* Single state here *) - accu +. coef.{1} *. (i_o1_alfa det alfa)) 0. psi_filtered - in - - let alfa_h_psi alfa = - List.fold_left (fun accu (det, coef) -> -(* Single state here *) - accu +. coef.{1} *. (alfa_o2_i alfa det)) 0. psi_filtered - in - - let psi_h_alfa_alfa_h_psi alfa = - if symmetric then - let x = psi_h_alfa alfa in x *. x - else - (psi_h_alfa alfa) *. (alfa_h_psi alfa) - in - - let det_i = fst psi0.(i) in - let w_alfa = w_alfa det_i in - - let same_spin = - List.fold_left (fun accu spin -> - accu +. - Array.fold_left (fun accu particle -> - accu +. - Array.fold_left (fun accu hole -> - if hole = particle then accu else - let alfa = - Determinant.single_excitation spin hole particle det_i - in - if Determinant.is_none alfa then accu else - - let single = - if already_generated alfa then 0. else - w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa - in - - let double = - Array.fold_left (fun accu particle' -> - if particle' >= particle || particle' = hole then - accu - else - accu +. - Array.fold_left (fun accu hole' -> - if hole' = particle' || hole' = particle || hole' <= hole then - accu - else - let alfa = - Determinant.single_excitation - spin hole' particle' alfa - in - if Determinant.is_none alfa || - already_generated alfa then - accu - else - accu +. w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa - ) 0. list_holes - ) 0. list_particles - in - accu +. single +. double - ) 0. list_holes - ) 0. list_particles - ) 0. [ Spin.Alfa ; Spin.Beta ] - in - - let opposite_spin = - Array.fold_left (fun accu particle -> - accu +. - Array.fold_left (fun accu hole -> - if hole = particle then accu else - let alfa = - Determinant.single_excitation Spin.Alfa hole particle det_i - in - if Determinant.is_none alfa then accu else - - let double_ab = - Array.fold_left (fun accu particle' -> - accu +. - Array.fold_left (fun accu hole' -> - if hole' = particle' then accu else - let alfa = - Determinant.double_excitation - Spin.Alfa hole particle - Spin.Beta hole' particle' det_i - in - if Determinant.is_none alfa || - already_generated alfa then - accu - else - accu +. w_alfa alfa *. psi_h_alfa_alfa_h_psi alfa - ) 0. list_holes - ) 0. list_particles - in - - accu +. double_ab - ) 0. list_holes - ) 0. list_particles - in - same_spin +. opposite_spin - in - - Util.stream_range 0 (Array.length psi0 - 1) - |> Farm.run ~ordered:true ~f:det_contribution - |> Util.stream_to_list - - - -let second_order_sum2 { det_space ; m_H ; m_S2 ; eigensystem ; n_states } - list_holes list_particles i_o1_alfa e0 psi0 = - - let psi0 = - let stream = - Ds.determinant_stream det_space - in - Array.init (Ds.size det_space) (fun i -> - (Stream.next stream), (Mat.copy_row psi0 (i+1)) ) - in - - let determinants = - - Ds.determinants_array det_space - |> Array.to_list - |> List.concat_map (fun det_i -> - [ Spin.Alfa ; Spin.Beta ] - |> List.concat_map (fun spin -> - List.concat_map (fun particle -> - List.map (fun hole -> - [ [ Determinant.single_excitation spin hole particle det_i ] ; - List.concat_map (fun particle' -> - List.map (fun hole' -> - Determinant.double_excitation - spin hole particle - spin hole' particle' det_i - ) list_holes - ) list_particles - ; - List.concat_map (fun particle' -> - List.map (fun hole' -> - Determinant.double_excitation - spin hole particle - (Spin.other spin) hole' particle' det_i - ) list_holes - ) list_particles - ] - |> List.concat - ) list_holes - ) list_particles - ) - ) - |> List.concat - |> List.filter (fun alfa -> not (Determinant.is_none alfa)) - |> List.sort_uniq compare - in - - List.fold_left (fun accu alfa -> - let alfa_o2 = i_o1_alfa alfa in - let a_h_psi = - Array.fold_left (fun accu (det,ci) -> ci.{1} *. (alfa_o2 det)) 0. psi0 - in - accu +. (a_h_psi *. a_h_psi) /. (e0 -. (alfa_o2 alfa)) - ) 0. determinants - - - - -let is_internal det_space = - let mo_class = DeterminantSpace.mo_class det_space in - let numbits = Array.length @@ MOClass.mo_class_array mo_class in - let m l = - List.fold_left (fun accu i -> - let j = i-1 in - Bitstring.logor accu (Bitstring.shift_left_one numbits j) - ) (Bitstring.zero numbits) l - in - let active_mask = m (MOClass.active_mos mo_class) in - let occ_mask = m (MOClass.core_mos mo_class) in - let inactive_mask = m (MOClass.inactive_mos mo_class) in - let occ_mask = Bitstring.logor occ_mask inactive_mask in - let neg_active_mask = Bitstring.lognot active_mask in - fun a -> - let alfa = - Determinant.alfa a - |> Spindeterminant.bitstring - in - if Bitstring.logand neg_active_mask alfa <> occ_mask then - false - else - let beta = - Determinant.beta a - |> Spindeterminant.bitstring - in - Bitstring.logand neg_active_mask beta = occ_mask - - -let is_external det_space = - let mo_class = DeterminantSpace.mo_class det_space in - let numbits = Array.length @@ MOClass.mo_class_array mo_class in - let m l = - List.fold_left (fun accu i -> - let j = i-1 in - Bitstring.logor accu (Bitstring.shift_left_one numbits j) - ) (Bitstring.zero numbits) l - in - let inactive_mask = m (MOClass.inactive_mos mo_class) in - fun a -> - let alfa = - Determinant.alfa a - |> Spindeterminant.bitstring - in - let n_a = - Bitstring.(popcount @@ logand inactive_mask alfa) - in - match n_a with - | 0 | 1 | 2 -> - let beta = - Determinant.beta a - |> Spindeterminant.bitstring - in - n_a + Bitstring.(popcount @@ logand inactive_mask beta) < 3 - | _ -> false - - -let pt2_en ci = - - let mo_basis = Ds.mo_basis ci.det_space in - let psi0, e0 = Parallel.broadcast ci.eigensystem in - - let i_o1_alfa = h_ij mo_basis in - - let w_alfa det_i = - let one_e, two_e, _ = h_integrals mo_basis in - let fock_diag_alfa, fock_diag_beta = - Ds.fock_diag ci.det_space det_i - in - let h_aa alfa = - match Excitation.of_det det_i alfa with - | Excitation.Double (_, - {hole = h ; particle = p ; spin = s }, - {hole = h'; particle = p'; spin = s'}) -> - let fock_diag1 = - if s = Spin.Alfa then - fock_diag_alfa - else - fock_diag_beta - in - let fock_diag2 = - if s' = Spin.Alfa then - fock_diag_alfa - else - fock_diag_beta - in - fock_diag1.(0) -. fock_diag1.(h) - +. (fock_diag1.(p ) -. two_e h p h p s s) - -. (fock_diag2.(h') -. two_e h h' h h' s s' +. two_e p h' p h' s s') - +. (fock_diag2.(p') -. two_e h p' h p' s s' - +. two_e p p' p p' s s' -. two_e h' p' h' p' s' s') - | Excitation.Single (_, - {hole = h ; particle = p ; spin = s }) -> - let fock_diag = - if s = Spin.Alfa then - fock_diag_alfa - else - fock_diag_beta - in - fock_diag.(0) -. fock_diag.(h) - +. (fock_diag.(p) -. two_e h p h p s s) - |> ignore; - h_ij mo_basis alfa alfa - | _ -> e0.{1} -. 1.0 - in - let e0 = e0.{1} in - fun alfa -> - 1. /. (e0 -. h_aa alfa) - in - - let mo_class = mo_class ci in - let list_holes = List.concat - [ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ] - and list_particles = List.concat - [ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ] - in - - second_order_sum ci list_holes list_particles - (is_internal ci.det_space) i_o1_alfa i_o1_alfa w_alfa psi0 - |> List.fold_left (+.) 0. - - -let _pt2_en ci = - - let mo_basis = Ds.mo_basis ci.det_space in - let psi0, e0 = Parallel.broadcast ci.eigensystem in - - let i_o1_alfa = h_ij mo_basis in - - let mo_class = mo_class ci in - let list_holes = List.concat - [ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ] - and list_particles = List.concat - [ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ] - in - second_order_sum2 ci list_holes list_particles i_o1_alfa e0.{1} psi0 - - - -let pt2_mp ci = - - let mo_basis = Ds.mo_basis ci.det_space in - - let i_o1_alfa = h_ij mo_basis in - - let eps = MOBasis.mo_energies mo_basis in - let w_alfa det_i alfa= - match Excitation.of_det det_i alfa with - | Excitation.Single (_, { hole ; particle ; spin })-> - 1./.(eps.{hole} -. eps.{particle}) - | Excitation.Double (_, { hole=h ; particle=p ; spin=s }, - { hole=h'; particle=p'; spin=s'})-> - 1./.(eps.{h} +. eps.{h'} -. eps.{p} -. eps.{p'}) - | _ -> assert false - in - - let mo_class = mo_class ci in - let list_holes = List.concat - [ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ] - and list_particles = List.concat - [ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ] - in - - let psi0, _ = Parallel.broadcast ci.eigensystem in - second_order_sum ci list_holes list_particles - (is_internal ci.det_space) i_o1_alfa i_o1_alfa w_alfa psi0 - |> List.fold_left (+.) 0. - - -let variance ci = - - let mo_basis = Ds.mo_basis ci.det_space in - let psi0, _ = Parallel.broadcast ci.eigensystem in - - let i_o1_alfa = h_ij mo_basis in - - let w_alfa _ _ = 1. in - - let mo_class = mo_class ci in - let list_holes = List.concat - [ MOClass.inactive_mos mo_class ; MOClass.active_mos mo_class ] - and list_particles = List.concat - [ MOClass.active_mos mo_class ; MOClass.virtual_mos mo_class ] - in - - second_order_sum ci list_holes list_particles - (is_internal ci.det_space) i_o1_alfa i_o1_alfa w_alfa psi0 - |> List.fold_left (+.) 0. - - - - -let pt2_en_reference ci = - - let mo_basis = Ds.mo_basis ci.det_space in - let psi0, e0 = Parallel.broadcast ci.eigensystem in - - let aux_basis = mo_basis in - let ds = - DeterminantSpace.fci_of_mo_basis ~frozen_core:false aux_basis - in - - let det_stream = - let e = - let f = is_external ci.det_space in - function - | None -> false - | Some d -> f d - in - let stream = - DeterminantSpace.determinant_stream ds - in - let rec next i = - let det = - try - Some (Stream.next stream) - with Stream.Failure -> None - in - if det = None then - None - else - if e det then - det - else - (next [@tailcall]) i - in - Stream.from next - in - - let out_dets = - det_stream - |> stream_to_list - |> Array.of_list - in - - let in_dets = - DeterminantSpace.determinants_array ci.det_space - in - - let m_H_aux = - let h_aa = - Array.map (fun ki -> h_ij aux_basis ki ki) out_dets - in - Array.map (fun ki -> - Array.mapi (fun j kj -> - (h_ij aux_basis ki kj) /. (e0.{1} -. h_aa.(j)) - ) out_dets - ) in_dets - |> Mat.of_array - in - - let m_F_aux = - Array.map (fun ki -> - Array.map (fun kj -> - h_ij aux_basis ki kj - ) out_dets - ) in_dets - |> Mat.of_array - in - - let m_HF = - gemm m_H_aux m_F_aux ~transb:`T - in - (gemm ~transa:`T psi0 @@ gemm m_HF psi0).{1,1} - - - - diff --git a/CI/CIMatrixElement.ml b/CI/CIMatrixElement.ml deleted file mode 100644 index 40d5243..0000000 --- a/CI/CIMatrixElement.ml +++ /dev/null @@ -1,257 +0,0 @@ -open Lacaml.D - -module De = Determinant -module Ex = Excitation -module Sp = Spindeterminant - -type t = float list - - -let non_zero integrals degree_a degree_b ki kj = - let kia = De.alfa ki and kib = De.beta ki - and kja = De.alfa kj and kjb = De.beta kj - in - - let single h p spin same opposite = - let same_spin_mo_list = - Sp.to_list same - and opposite_spin_mo_list = - Sp.to_list opposite - in - fun one_e two_e -> - let same_spin = - List.fold_left (fun accu i -> accu +. two_e h i p i spin spin) 0. same_spin_mo_list - and opposite_spin = - List.fold_left (fun accu i -> accu +. two_e h i p i spin (Spin.other spin) ) 0. opposite_spin_mo_list - in (one_e h p spin) +. same_spin +. opposite_spin - in - - let diag_element = - let mo_a = Sp.to_list kia - and mo_b = Sp.to_list kib - in - fun one_e two_e -> - let one = - (List.fold_left (fun accu i -> accu +. one_e i i Spin.Alfa) 0. mo_a) - +. - (List.fold_left (fun accu i -> accu +. one_e i i Spin.Beta) 0. mo_b) - in - let two = - let rec aux_same spin accu = function - | [] -> accu - | i :: rest -> - let new_accu = - List.fold_left (fun accu j -> accu +. two_e i j i j spin spin) accu rest - in - (aux_same [@tailcall]) spin new_accu rest - in - let rec aux_opposite accu other = function - | [] -> accu - | i :: rest -> - let new_accu = - List.fold_left (fun accu j -> accu +. two_e i j i j Spin.Alfa Spin.Beta) accu other - in - (aux_opposite [@tailcall]) new_accu other rest - in - (aux_same Spin.Alfa 0. mo_a) +. (aux_same Spin.Beta 0. mo_b) +. - (aux_opposite 0. mo_a mo_b) - in - one +. two - in - - let result_2e = lazy ( - match degree_a, degree_b with - | 1, 1 -> (* alpha-beta double *) - begin - let ha, pa, phase_a = Ex.single_of_spindet kia kja in - let hb, pb, phase_b = Ex.single_of_spindet kib kjb in - match phase_a, phase_b with - | Phase.Pos, Phase.Pos - | Phase.Neg, Phase.Neg -> fun _ two_e -> two_e ha hb pa pb Spin.Alfa Spin.Beta - | Phase.Neg, Phase.Pos - | Phase.Pos, Phase.Neg -> fun _ two_e -> -. two_e ha hb pa pb Spin.Alfa Spin.Beta - end - - | 2, 0 -> (* alpha double *) - begin - let h1, p1, h2, p2, phase = Ex.double_of_spindet kia kja in - match phase with - | Phase.Pos -> fun _ two_e -> two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa - | Phase.Neg -> fun _ two_e -> -. two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa - end - - | 0, 2 -> (* beta double *) - begin - let h1, p1, h2, p2, phase = Ex.double_of_spindet kib kjb in - match phase with - | Phase.Pos -> fun _ two_e -> two_e h1 h2 p1 p2 Spin.Beta Spin.Beta - | Phase.Neg -> fun _ two_e -> -. two_e h1 h2 p1 p2 Spin.Beta Spin.Beta - end - - | 1, 0 -> (* alpha single *) - begin - let h, p, phase = Ex.single_of_spindet kia kja in - match phase with - | Phase.Pos -> fun one_e two_e -> single h p Spin.Alfa kia kib one_e two_e - | Phase.Neg -> fun one_e two_e -> -. single h p Spin.Alfa kia kib one_e two_e - end - - | 0, 1 -> (* beta single *) - begin - let h, p, phase = Ex.single_of_spindet kib kjb in - match phase with - | Phase.Pos -> fun one_e two_e -> single h p Spin.Beta kib kia one_e two_e - | Phase.Neg -> fun one_e two_e -> -. single h p Spin.Beta kib kia one_e two_e - end - - | 0, 0 -> (* diagonal element *) - diag_element - - | _ -> assert false - ) in - - let result_3e = lazy ( - match degree_a, degree_b with - | 1, 1 -> (* alpha-beta double *) - begin - let ha, pa, phase_a = Ex.single_of_spindet kia kja in - let hb, pb, phase_b = Ex.single_of_spindet kib kjb in - match phase_a, phase_b with - | Phase.Pos, Phase.Pos - | Phase.Neg, Phase.Neg -> fun _ two_e _ -> two_e ha hb pa pb Spin.Alfa Spin.Beta - | Phase.Neg, Phase.Pos - | Phase.Pos, Phase.Neg -> fun _ two_e _ -> -. two_e ha hb pa pb Spin.Alfa Spin.Beta - end - - | 2, 0 -> (* alpha double *) - begin - let h1, p1, h2, p2, phase = Ex.double_of_spindet kia kja in - match phase with - | Phase.Pos -> fun _ two_e _ -> two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa - | Phase.Neg -> fun _ two_e _ -> -. two_e h1 h2 p1 p2 Spin.Alfa Spin.Alfa - end - - | 0, 2 -> (* beta double *) - begin - let h1, p1, h2, p2, phase = Ex.double_of_spindet kib kjb in - match phase with - | Phase.Pos -> fun _ two_e _ -> two_e h1 h2 p1 p2 Spin.Beta Spin.Beta - | Phase.Neg -> fun _ two_e _ -> -. two_e h1 h2 p1 p2 Spin.Beta Spin.Beta - end - - | 1, 0 -> (* alpha single *) - begin - let h, p, phase = Ex.single_of_spindet kia kja in - match phase with - | Phase.Pos -> fun one_e two_e _ -> single h p Spin.Alfa kia kib one_e two_e - | Phase.Neg -> fun one_e two_e _ -> -. single h p Spin.Alfa kia kib one_e two_e - end - - | 0, 1 -> (* beta single *) - begin - let h, p, phase = Ex.single_of_spindet kib kjb in - match phase with - | Phase.Pos -> fun one_e two_e _ -> single h p Spin.Beta kib kia one_e two_e - | Phase.Neg -> fun one_e two_e _ -> -. single h p Spin.Beta kib kia one_e two_e - end - - | 0, 0 -> (* diagonal element *) - fun one_e two_e _ -> diag_element one_e two_e - - | 3, 0 -> (* alpha triple *) - begin - let h1, p1, h2, p2, h3, p3, phase = Ex.triple_of_spindet kia kja in - match phase with - | Phase.Pos -> fun _ _ three_e -> three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Alfa Spin.Alfa - | Phase.Neg -> fun _ _ three_e -> -. three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Alfa Spin.Alfa - end - - | 0, 3 -> (* beta triple *) - begin - let h1, p1, h2, p2, h3, p3, phase = Ex.triple_of_spindet kib kja in - match phase with - | Phase.Pos -> fun _ _ three_e -> three_e h1 h2 h3 p1 p2 p3 Spin.Beta Spin.Beta Spin.Beta - | Phase.Neg -> fun _ _ three_e -> -. three_e h1 h2 h3 p1 p2 p3 Spin.Beta Spin.Beta Spin.Beta - end - - | 2, 1 -> (* alpha2 beta triple *) - begin - let h1, p1, h2, p2, phase = Ex.double_of_spindet kia kja in - let h3, p3, phase' = Ex.single_of_spindet kib kjb in - match phase, phase' with - | Phase.Pos, Phase.Pos - | Phase.Neg, Phase.Neg -> - fun _ _ three_e -> three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Alfa Spin.Beta - | Phase.Neg, Phase.Pos - | Phase.Pos, Phase.Neg -> - fun _ _ three_e -> -. three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Alfa Spin.Beta - end - - | 1, 2 -> (* alpha beta2 triple *) - begin - let h1, p1, phase = Ex.single_of_spindet kia kja in - let h2, p2, h3, p3, phase' = Ex.double_of_spindet kib kjb in - match phase, phase' with - | Phase.Pos, Phase.Pos - | Phase.Neg, Phase.Neg -> - fun _ _ three_e -> three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Beta Spin.Beta - | Phase.Neg, Phase.Pos - | Phase.Pos, Phase.Neg -> - fun _ _ three_e -> -. three_e h1 h2 h3 p1 p2 p3 Spin.Alfa Spin.Beta Spin.Beta - end - - | _ -> fun _ _ _ -> 0. - ) in - - List.map (fun (one_e, two_e, x) -> - match x with - | None -> (Lazy.force result_2e) one_e two_e - | Some three_e -> (Lazy.force result_3e) one_e two_e three_e - ) integrals - - - -let make integrals ki kj = - let degree_a, degree_b = - De.degrees ki kj - in - if degree_a+degree_b > 2 then - List.map (fun _ -> 0.) integrals - else - non_zero integrals degree_a degree_b ki kj - - - - -let make_s2 ki kj = - let degree_a = De.degree_alfa ki kj in - let kia = De.alfa ki in - let kja = De.alfa kj in - if degree_a > 1 then 0. - else - let degree_b = De.degree_beta ki kj in - let kib = De.beta ki in - let kjb = De.beta kj in - match degree_a, degree_b with - | 1, 1 -> (* alpha-beta double *) - let ha, pa, phase_a = Ex.single_of_spindet kia kja in - let hb, pb, phase_b = Ex.single_of_spindet kib kjb in - if ha = pb && hb = pa then - begin - match phase_a, phase_b with - | Phase.Pos, Phase.Pos - | Phase.Neg, Phase.Neg -> -1. - | Phase.Neg, Phase.Pos - | Phase.Pos, Phase.Neg -> 1. - end - else 0. - | 0, 0 -> - let ba = Sp.bitstring kia and bb = Sp.bitstring kib in - let tmp = Bitstring.logxor ba bb in - let n_a = Bitstring.logand ba tmp |> Bitstring.popcount in - let n_b = Bitstring.logand bb tmp |> Bitstring.popcount in - let s_z = 0.5 *. float_of_int (n_a - n_b) in - float_of_int n_a +. s_z *. (s_z -. 1.) - | _ -> 0. - - diff --git a/CI/Determinant.ml b/CI/Determinant.ml deleted file mode 100644 index a35aba5..0000000 --- a/CI/Determinant.ml +++ /dev/null @@ -1,222 +0,0 @@ -type t = -{ - alfa : Spindeterminant.t ; - beta : Spindeterminant.t ; -} - -type hole = int -type particle = int - - - - -let alfa t = t.alfa - -let beta t = t.beta - -let vac n = - { - alfa = Spindeterminant.vac n; - beta = Spindeterminant.vac n; - } - -let phase t = - match Spindeterminant.(phase t.alfa, phase t.beta) with - | Phase.Pos, Phase.Pos - | Phase.Neg, Phase.Neg -> Phase.Pos - | _ -> Phase.Neg - - -let of_spindeterminants a b = - { - alfa = a ; - beta = b - } - - -let is_none t = Spindeterminant.(is_none t.alfa || is_none t.beta) - - -let negate_phase t = - { t with alfa = Spindeterminant.negate_phase t.alfa } - -let set_phase p t = - { alfa = Spindeterminant.set_phase p t.alfa ; - beta = Spindeterminant.set_phase Phase.Pos t.beta - } - - -let degree_alfa t t' = - Spindeterminant.degree t.alfa t'.alfa - -let degree_beta t t' = - Spindeterminant.degree t.beta t'.beta - -let degrees t t' = - degree_alfa t t', degree_beta t t' - - -let degree t t' = - (degree_alfa t t') + (degree_beta t t') - - -let of_lists n a b = - let alfa = Spindeterminant.of_list n a - and beta = Spindeterminant.of_list n b - in of_spindeterminants alfa beta - - -let to_lists t = - Spindeterminant.to_list t.alfa, - Spindeterminant.to_list t.beta - - -let creation spin p t = - match spin with - | Spin.Alfa -> { t with alfa = Spindeterminant.creation p t.alfa } - | Spin.Beta -> { t with beta = Spindeterminant.creation p t.beta } - - -let annihilation spin h t = - match spin with - | Spin.Alfa -> { t with alfa = Spindeterminant.annihilation h t.alfa } - | Spin.Beta -> { t with beta = Spindeterminant.annihilation h t.beta } - - -let single_excitation spin h p t = - assert (h <> p); - match spin with - | Spin.Alfa -> { t with alfa = Spindeterminant.single_excitation h p t.alfa } - | Spin.Beta -> { t with beta = Spindeterminant.single_excitation h p t.beta } - - -let double_excitation spin h p spin' h' p' t = - assert (h <> p); - assert (h' <> p'); - match spin, spin' with - | Spin.(Alfa, Beta) -> { alfa = Spindeterminant.single_excitation h p t.alfa ; - beta = Spindeterminant.single_excitation h' p' t.beta } - | Spin.(Beta, Alfa) -> { beta = Spindeterminant.single_excitation h p t.beta ; - alfa = Spindeterminant.single_excitation h' p' t.alfa } - | Spin.(Alfa, Alfa) -> { t with alfa = Spindeterminant.double_excitation h p h' p' t.alfa } - | Spin.(Beta, Beta) -> { t with beta = Spindeterminant.double_excitation h p h' p' t.beta } - - -let compare = compare - - -let pp n ppf t = - Format.fprintf ppf "@[@[phase:%a@]@;@[a:%a@]@;@[b:%a@]@]@." - Phase.pp (phase t) - (Spindeterminant.pp n) t.alfa - (Spindeterminant.pp n) t.beta - - - -let test_case () = - - let test_creation () = - let l_a = [ 1 ; 2 ; 3 ; 5 ; 64 ] - and l_b = [ 2 ; 3 ; 5 ; 65 ] in - let det = of_lists 66 l_a l_b in - let z_a = alfa det - and z_b = beta det in - Alcotest.(check (list int )) "alfa" (Spindeterminant.to_list z_a) l_a; - Alcotest.(check (list int )) "beta" (Spindeterminant.to_list z_b) l_b; - Alcotest.(check bool) "phase" (phase det = Phase.Pos) true; - in - - let test_phase () = - let l_a = [ 1 ; 2 ; 3 ; 64 ; 5 ] - and l_b = [ 2 ; 3 ; 5 ; 65 ] in - let det = of_lists 66 l_a l_b in - Alcotest.(check bool) "phase" (phase det = Phase.Neg) true; - let l_a = [ 1 ; 2 ; 3 ; 64 ; 5 ] - and l_b = [ 3 ; 2 ; 5 ; 65 ] in - let det = of_lists 66 l_a l_b in - Alcotest.(check bool) "phase" (phase det = Phase.Pos) true; - let l_a = [ 1 ; 3 ; 2 ; 64 ; 5 ] - and l_b = [ 3 ; 2 ; 5 ; 65 ] in - let det = of_lists 66 l_a l_b in - Alcotest.(check bool) "phase" (phase det = Phase.Neg) true; - let l_a = [ 1 ; 3 ; 2 ; 64 ; 5 ] - and l_b = [ 3 ; 2 ; 65 ; 5 ] in - let det = of_lists 66 l_a l_b in - Alcotest.(check bool) "phase" (phase det = Phase.Pos) true; - in - - let test_operators () = - let det = - let open Spin in - creation Alfa 1 @@ creation Alfa 3 @@ creation Alfa 2 @@ creation Alfa 5 @@ - creation Beta 1 @@ creation Beta 3 @@ creation Beta 4 @@ creation Beta 5 @@ vac 10 - in - Alcotest.(check bool) "creation 1" true - (det = of_lists 10 [ 1 ; 3 ; 2 ; 5 ] [1 ; 3 ; 4 ; 5 ] ); - - let det' = - single_excitation Spin.Alfa 3 6 det - in - Alcotest.(check bool) "single_exc 1" true - (det' = of_lists 10 [ 1 ; 6 ; 2 ; 5 ] [1 ; 3 ; 4 ; 5 ] ); - - let det' = - single_excitation Spin.Beta 3 6 det - in - Alcotest.(check bool) "single_exc 2" true - (det' = of_lists 10 [ 1 ; 3 ; 2 ; 5 ] [1 ; 6 ; 4 ; 5 ] ); - - let det' = - single_excitation Spin.Alfa 4 6 det - in - Alcotest.(check bool) "single_exc 3" true (is_none det'); - - let det' = - single_excitation Spin.Beta 1 5 det - in - Alcotest.(check bool) "single_exc 4" true (is_none det'); - - let det' = - double_excitation Spin.Alfa 3 6 Spin.Alfa 2 7 det - in - let det'' = of_lists 10 [ 1 ; 6 ; 7 ; 5 ] [1 ; 3 ; 4 ; 5 ] in - Alcotest.(check bool) "double_exc 1" true (det' = det''); - - let det' = - double_excitation Spin.Beta 3 6 Spin.Beta 5 7 det - in - Alcotest.(check bool) "double_exc 2" true - (det' = of_lists 10 [ 1 ; 3 ; 2 ; 5 ] [1 ; 6 ; 4 ; 7 ] ); - - let det' = - double_excitation Spin.Alfa 3 6 Spin.Beta 5 7 det - in - Alcotest.(check bool) "double_exc 3" true - (det' = of_lists 10 [ 1 ; 6 ; 2 ; 5 ] [1 ; 3 ; 4 ; 7 ] ); - - let det' = - double_excitation Spin.Beta 5 7 Spin.Alfa 3 6 det - in - Alcotest.(check bool) "double_exc 4" true - (det' = of_lists 10 [ 1 ; 6 ; 2 ; 5 ] [1 ; 3 ; 4 ; 7 ] ); - - let det' = - double_excitation Spin.Alfa 4 6 Spin.Alfa 2 7 det - in - Alcotest.(check bool) "double_exc 5" true (is_none det'); - - let det' = - double_excitation Spin.Beta 1 5 Spin.Alfa 2 7 det - in - Alcotest.(check bool) "double_exc 6" true (is_none det'); - - in - - [ - "Creation", `Quick, test_creation; - "Phase", `Quick, test_phase; - "Operators",`Quick, test_operators; - ] - - - diff --git a/CI/Determinant.mli b/CI/Determinant.mli deleted file mode 100644 index 90196ef..0000000 --- a/CI/Determinant.mli +++ /dev/null @@ -1,93 +0,0 @@ -(** A Slater determinant is expressed as a Waller-Hartree double determinant: -{% $$ -D(\mathbf{R}) = D_\alpha(\mathbf{R_\alpha}) \times D_\beta(\mathbf{R_\beta}) -$$ %} -The {% $\alpha$ %} and {% $\beta$ %} determinants are of type [Spindeterminant.t]. -*) - - -type t -type hole = int -type particle = int - -(** {1 Accessors} *) - -val alfa : t -> Spindeterminant.t -(** Get the {% $\alpha$ %} spin-determinant. *) - -val beta : t -> Spindeterminant.t -(** Get the {% $\beta$ %} spin-determinant. *) - -val phase : t -> Phase.t -(** Get the phase of the Slater determinant, the product of the phases of the - spin-determinants. -*) - -val is_none : t -> bool -(** Tests if a Determinant is [None]. *) - - -(** {1 Second quantization operators} *) - -val vac : int -> t -(** Vacuum state, [vac = Some ]{% $|\rangle$ %}. The integer parameter is the size of the - MO basis set. *) - -val creation : Spin.t -> particle -> t -> t -(** [creation spin p] is the creation operator {% $a^\dagger_p$ %}. *) - -val annihilation : Spin.t -> hole -> t -> t -(** [annihilation spin h] is the annihilation operator {% $a_h$ %}. *) - -val single_excitation : Spin.t -> hole -> particle -> t -> t -(** Single excitation operator {% $T_h^p = a^\dagger_p a_h$ %}. *) - -val double_excitation : Spin.t -> hole -> particle -> Spin.t -> hole -> particle -> t -> t -(** Double excitation operator {% $T_{hh'}^{pp'} = a^\dagger_p a^\dagger_{p'} a_{h'} a_h$ %}. *) - -val degree_alfa : t -> t -> int -(** Returns degree of excitation between two determinants in the {% $\alpha$ %} spin. *) - -val degree_beta : t -> t -> int -(** Returns degree of excitation between two determinants in the {% $\beta$ %} spin. *) - -val degrees : t -> t -> int*int -(** Returns degrees of excitation between two determinants in {% $\alpha$ %} and - {% $\beta$ %} spins as a pair. *) - -val degree : t -> t -> int -(** Returns degree of excitation between two determinants. *) - -val to_lists : t -> int list * int list -(** Converts a Slater determinant to a pair of lists of orbital indices. *) - - -(** {1 Creators} *) - -val of_spindeterminants : Spindeterminant.t -> Spindeterminant.t -> t -(** Creates a Slater determinant from an {% $\alpha$ %} and a {% $\beta$ %} - [Spindeterminant.t]. -*) - -val of_lists : int -> int list -> int list -> t -(** Creates a Slater determinant from a two lists of orbital indices. - The integer parameter is the size of the MO basis set. *) - -val negate_phase : t -> t -(** Returns the same determinant with the phase negated. *) - -val set_phase : Phase.t -> t -> t -(** Returns the same determinant with the phase set to [p]. *) - -val compare : t -> t -> int -(** Comparison function for sorting *) - - -(** {1 Printers} *) - -val pp : int -> Format.formatter -> t -> unit -(** First [int] is the number of MOs to print. *) - -(** {1 Unit tests} *) - -val test_case : unit -> (string * [> `Quick ] * (unit -> unit)) list diff --git a/CI/DeterminantSpace.ml b/CI/DeterminantSpace.ml deleted file mode 100644 index 10c1a6f..0000000 --- a/CI/DeterminantSpace.ml +++ /dev/null @@ -1,360 +0,0 @@ -(** Data structures for storing the determinant space. - -If the space is built as the outer product of all {% $\alpha$ %} and {% -$\beta$ %} determinants, the storage is of type [Spin]. It is sufficient -to have the arrays of {% $\alpha$ %} and {% $\beta$ %} spindeterminants. - -Otherwise, the space is of type [Arbitrary]. - -*) - -type arbitrary_space = - { - det : int array array ; - det_alfa : Spindeterminant.t array ; - det_beta : Spindeterminant.t array ; - index_start : int array; - } - - -type determinant_storage = - | Arbitrary of arbitrary_space - | Spin of (Spindeterminant.t array * Spindeterminant.t array) - - -type t = - { - n_alfa : int ; - n_beta : int ; - mo_class : MOClass.t ; - mo_basis : MOBasis.t ; - determinants : determinant_storage; - } - - -module Ss = SpindeterminantSpace - -let n_alfa t = t.n_alfa -let n_beta t = t.n_beta -let mo_class t = t.mo_class -let mo_basis t = t.mo_basis - -let active_mos t = - mo_class t - |> MOClass.active_mos - - -let inactive_mos t = - mo_class t - |> MOClass.inactive_mos - - -let virtual_mos t = - mo_class t - |> MOClass.inactive_mos - - -let mo_class_array t = - mo_class t - |> MOClass.mo_class_array - - -let size t = - match t.determinants with - | Spin (a,b) -> (Array.length a) * (Array.length b) - | Arbitrary a -> - let ndet_a = Array.length a.det_alfa in - a.index_start.(ndet_a) - - -let determinant_stream t = - match t.determinants with - | Arbitrary a -> - let det_beta = a.det_beta - and det_alfa = a.det_alfa - and det = a.det in - let n_alfa = Array.length det_alfa in - let alfa = ref det_alfa.(0) - and det_i_alfa = ref det.(0) in - let i_alfa = ref 0 - and k_beta = ref 0 - in - Stream.from (fun _ -> - if !i_alfa = n_alfa then None else - begin - let i_beta = (!det_i_alfa).(!k_beta) in - let beta = det_beta.(i_beta) in - let result = - Some (Determinant.of_spindeterminants (!alfa) beta) - in - incr k_beta; - if !k_beta = Array.length !det_i_alfa then - begin - k_beta := 0; - incr i_alfa; - if !i_alfa < n_alfa then - begin - alfa := det_alfa.(!i_alfa); - det_i_alfa := det.(!i_alfa) - end - end; - result - end - ) - - | Spin (a,b) -> - let na = Array.length a - and nb = Array.length b in - let i = ref 0 - and j = ref 0 in - Stream.from (fun k -> - if !j < nb then - let result = - Determinant.of_spindeterminants a.(!i) b.(!j) - in - incr i; - if !i = na then (i := 0 ; incr j); - Some result - else - None) - - -let determinants t = t.determinants - - -let determinants_array t = - let s = determinant_stream t in - Array.init (size t) (fun _ -> Stream.next s) - - -let determinant t i = - let alfa, beta = - match t.determinants with - | Arbitrary a -> - let i_alfa = - let index_start = a.index_start in - let rec loop i_alfa = - if index_start.(i_alfa) <= i then - (loop [@tailcall]) (i_alfa+1) - else i_alfa - in loop 0 - in - let i_beta = i - a.index_start.(i_alfa) in - let alfa = a.det_alfa.(i_alfa) in - let beta = a.det_beta.(i_beta) in - alfa, beta - - | Spin (a,b) -> - let nb = Array.length b in - let k = i / nb in - let j = i - k * nb in - a.(j), b.(k) - - in - Determinant.of_spindeterminants alfa beta - - - -let fock_diag det_space det = - - let alfa_list = - Determinant.alfa det - |> Spindeterminant.to_list - in - let beta_list = - Determinant.beta det - |> Spindeterminant.to_list - in - let mo_basis = mo_basis det_space in - let mo_num = MOBasis.size mo_basis in - let one_e_ints = MOBasis.one_e_ints mo_basis - and two_e_ints = MOBasis.two_e_ints mo_basis - in - let two_e i j k l = ERI.get_phys two_e_ints i j k l in - let build_array list1 list2 = - let result = Array.make (mo_num+1) 0. in - - (* Occupied *) - List.iter (fun i -> - let x = one_e_ints.{i,i} in - result.(i) <- result.(i) +. x; - result.(0) <- result.(0) +. x; - List.iter (fun j -> - if j <> i then - begin - let x = two_e i j i j -. two_e i j j i in - result.(i) <- result.(i) +. x; - result.(0) <- result.(0) +. 0.5 *. x; - end - ) list1; - List.iter (fun j -> - begin - let x = two_e i j i j in - result.(i) <- result.(i) +. x; - result.(0) <- result.(0) +. 0.5 *. x; - end - ) list2; - ) list1; - - (* Virtuals*) - List.iter (fun i -> - if result.(i) = 0. then - begin - let x = one_e_ints.{i,i} in - result.(i) <- result.(i) +. x; - List.iter (fun j -> - let x = two_e i j i j -. two_e i j j i in - result.(i) <- result.(i) +. x; - ) list1; - List.iter (fun j -> - begin - let x = two_e i j i j in - result.(i) <- result.(i) +. x; - end - ) list2; - end - ) (Util.list_range 1 mo_num); - result - in - let alfa, beta = - build_array alfa_list beta_list, - build_array beta_list alfa_list - in - let e = alfa.(0) +. beta.(0) in - alfa.(0) <- e; - beta.(0) <- e; - alfa, beta - - - -let spin_of_mo_basis mo_basis f = - - let s = MOBasis.simulation mo_basis in - let e = Simulation.electrons s in - let n_alfa = Electrons.n_alfa e - and n_beta = Electrons.n_beta e in - let det_a = f n_alfa - and det_b = f n_beta - in - let mo_class = Ss.mo_class det_a in - let determinants = - let det_alfa = Ss.spin_determinants det_a - and det_beta = Ss.spin_determinants det_b - in - let n_det_beta = Array.length det_beta in - let n_det_alfa = Array.length det_alfa in - - let ndet = n_det_alfa * n_det_beta in - if Parallel.master then - Format.printf "Number of determinants : %d %d %d\n%!" - n_det_alfa n_det_beta ndet; - Spin (det_alfa, det_beta) - in - { n_alfa ; n_beta ; mo_class ; mo_basis ; determinants } - - -let arbitrary_of_mo_basis mo_basis f = - - let s = MOBasis.simulation mo_basis in - let e = Simulation.electrons s in - let n_alfa = Electrons.n_alfa e - and n_beta = Electrons.n_beta e in - let det_a = f n_alfa - and det_b = f n_beta - in - let mo_class = Ss.mo_class det_a in - let determinants = - let det_alfa = Ss.spin_determinants det_a - and det_beta = Ss.spin_determinants det_b - in - let n_det_beta = Array.length det_beta in - let n_det_alfa = Array.length det_alfa in - - let det = Array.make n_det_alfa - (Array.init n_det_beta (fun i -> i)) - in - let index_start = Array.init (n_det_alfa+1) (fun i -> i*n_det_beta) in - let ndet = (index_start.(n_det_alfa)) in - - if Parallel.master then - Format.printf "Number of determinants : %d %d %d\n%!" - n_det_alfa n_det_beta ndet; - Arbitrary { - det_alfa ; det_beta ; det ; index_start - } - in - { n_alfa ; n_beta ; mo_class ; mo_basis ; determinants } - - - -let cas_of_mo_basis mo_basis ~frozen_core n m = - let f n_alfa = - Ss.cas_of_mo_basis mo_basis ~frozen_core n_alfa n m - in - spin_of_mo_basis mo_basis f - - -let fci_of_mo_basis mo_basis ~frozen_core = - let f n_alfa = - Ss.fci_of_mo_basis mo_basis ~frozen_core n_alfa - in - spin_of_mo_basis mo_basis f - - -let fci_f12_of_mo_basis mo_basis ~frozen_core mo_num = - let s = MOBasis.simulation mo_basis in - let e = Simulation.electrons s in - let n_alfa = Electrons.n_alfa e - and n_beta = Electrons.n_beta e in - let n_core = - if frozen_core then - (Nuclei.small_core @@ Simulation.nuclei @@ MOBasis.simulation mo_basis) / 2 - else 0 - in - let n, m = - (n_alfa + n_beta - n_core), - (mo_num - n_core) - in - let f n_alfa = - Ss.cas_of_mo_basis mo_basis ~frozen_core n_alfa n m - in - let r = - spin_of_mo_basis mo_basis f - in - { r with mo_class = - MOClass.to_list r.mo_class - |> List.rev_map (fun i -> - match i with - | MOClass.Virtual i when i > mo_num -> MOClass.Auxiliary i - | i -> i) - |> List.rev - |> MOClass.of_list } - - -let cas_f12_of_mo_basis mo_basis ~frozen_core n m mo_num = - let f n_alfa = - Ss.cas_of_mo_basis mo_basis ~frozen_core n_alfa n m - in - let r = - spin_of_mo_basis mo_basis f - in - { r with mo_class = - MOClass.to_list r.mo_class - |> List.rev_map (fun i -> - match i with - | MOClass.Virtual i when i > mo_num -> MOClass.Auxiliary i - | i -> i) - |> List.rev - |> MOClass.of_list - } - - - -let pp ppf t = - Format.fprintf ppf "@[[ "; - let i = ref 0 in - determinant_stream t - |> Stream.iter (fun d -> Format.fprintf ppf "@[@[%8d@]@;@[%a@]@]@;" !i - (Determinant.pp (MOBasis.size (mo_basis t))) d; incr i) ; - Format.fprintf ppf "]@]" - diff --git a/CI/DeterminantSpace.mli b/CI/DeterminantSpace.mli deleted file mode 100644 index 14afee7..0000000 --- a/CI/DeterminantSpace.mli +++ /dev/null @@ -1,74 +0,0 @@ -(** -The determinant space in which we solve the Schrodinger equation. -*) - -type t - -type arbitrary_space = - { - det : int array array ; - det_alfa : Spindeterminant.t array ; - det_beta : Spindeterminant.t array ; - index_start : int array; - } - - -type determinant_storage = - | Arbitrary of arbitrary_space - | Spin of (Spindeterminant.t array * Spindeterminant.t array) - - -(** {1 Accessors} *) - -val n_alfa : t -> int -(** Number of {% $\alpha$ %} electrons in the {% $\alpha$ %} MOs. *) - -val n_beta : t -> int -(** Number of {% $\beta$ %} electrons in the {% $\beta$ %} MOs. *) - -val mo_class : t -> MOClass.t -(** The MO classes used to generate the space. *) - -val mo_basis : t -> MOBasis.t -(** The MO basis on which the determinants are expanded. *) - -val determinants : t -> determinant_storage -(** All the determinants belonging to the space. *) - -val determinants_array : t -> Determinant.t array -(** All the determinants belonging to the space. *) - -val determinant_stream : t -> Determinant.t Stream.t -(** All the determinants belonging to the space, as a stream. *) - -val size : t -> int -(** Size of the determinant space *) - -val fock_diag : t -> Determinant.t -> float array * float array -(** Returns the diagonal of the {% $\alpha$ %} and {% $\beta$ %} Fock matrices. - The zero elements contain the energy of the determinant. -*) - - -val fci_of_mo_basis : MOBasis.t -> frozen_core:bool -> t -(** Creates a space of all possible ways to put [n_alfa] electrons in the {% $\alpha$ %} - [Active] MOs and [n_beta] electrons in the {% $\beta$ %} [Active] MOs. - All other MOs are untouched. -*) - -val cas_of_mo_basis : MOBasis.t -> frozen_core:bool -> int -> int -> t -(** Creates a CAS(n,m) space of determinants. *) - -val fci_f12_of_mo_basis : MOBasis.t -> frozen_core:bool -> int -> t -(** Creates the active space to perform a FCI-F12 with an - auxiliary basis set. *) - -val cas_f12_of_mo_basis : MOBasis.t -> frozen_core:bool -> int -> int -> int -> t -(** [cas_of_mo_basis mo_basis m n mo_num] Creates a CAS(n,m) space - of determinants with an auxiliary basis set defined as the MOs from - [mo_num+1] to [MOBasis.size mo_basis]. -*) - -(** {2 Printing} *) - -val pp : Format.formatter -> t -> unit diff --git a/CI/Excitation.ml b/CI/Excitation.ml deleted file mode 100644 index 75bcc60..0000000 --- a/CI/Excitation.ml +++ /dev/null @@ -1,205 +0,0 @@ -type single_exc = - { - hole : int ; - particle : int ; - spin : Spin.t ; - } - -type t = -| Identity of Phase.t -| Single of Phase.t * single_exc -| Double of Phase.t * single_exc * single_exc -| Triple of Phase.t * single_exc * single_exc * single_exc -| Multiple of Phase.t * single_exc list - - -let single_of_spindet t t' = - assert (Spindeterminant.degree t t' = 1); - let d = Spindeterminant.bitstring t - and d' = Spindeterminant.bitstring t' - in - let tmp = Bitstring.logxor d d' in - let shift_left_one = Bitstring.(shift_left_one (numbits tmp)) in - let hole_z = Bitstring.logand (Spindeterminant.bitstring t ) tmp - and particle_z = Bitstring.logand (Spindeterminant.bitstring t') tmp - in - let hole = 1 + Bitstring.trailing_zeros hole_z - and particle = 1 + Bitstring.trailing_zeros particle_z - in - (* Phase calculation *) - let low, high = - if particle > hole then hole, particle - else particle, hole - in - let mask = - let h = high-1 in - let l = low in - let mask_up = shift_left_one h |> Bitstring.minus_one - and mask_dn = Bitstring.plus_one @@ Bitstring.lognot (shift_left_one l) - in Bitstring.logand mask_up mask_dn - in - let phase = - Phase.add (Phase.add (Spindeterminant.phase t) (Spindeterminant.phase t')) - (Phase.of_nperm (Bitstring.popcount @@ Bitstring.logand d mask )) - in - (hole, particle, phase) - - -let single_of_det t t' = - assert Determinant.(beta t = beta t' || alfa t = alfa t'); - if Determinant.(beta t = beta t') then - let hole, particle, phase = - single_of_spindet (Determinant.alfa t) (Determinant.alfa t') - in - Single (phase, { hole ; particle ; spin=Spin.Alfa }) - else - let hole, particle, phase = - single_of_spindet (Determinant.beta t) (Determinant.beta t') - in - Single (phase, { hole ; particle ; spin=Spin.Beta }) - - -let multiple_of_spindet t t' = - let holes = Spindeterminant.holes_of t t' - and particles = Spindeterminant.particles_of t t' - in - let t'' = - List.fold_left (fun accu h -> Spindeterminant.annihilation h accu) t holes - in - let t'' = - List.fold_left (fun accu p -> Spindeterminant.creation p accu) t'' particles - in - assert (t' = t'' || t' = Spindeterminant.negate_phase t''); - let phase = - if Spindeterminant.phase t' = Spindeterminant.phase t'' then - Phase.Pos - else - Phase.Neg - in - (phase, List.rev @@ List.rev_map2 (fun hole particle -> (hole, particle)) holes (List.rev particles) ) - - -let double_of_spindet t t' = - match multiple_of_spindet t t' with - | (phase, (h1,p1)::(h2,p2)::[]) -> (h1, p1, h2, p2, phase) - | _ -> invalid_arg "t and t' are not doubly excited" - - -let triple_of_spindet t t' = - match multiple_of_spindet t t' with - | (phase, (h1,p1)::(h2,p2)::(h3,p3)::[]) -> (h1, p1, h2, p2, h3, p3, phase) - | _ -> invalid_arg "t and t' are not doubly excited" - - -let multiple_of_det t t' = - let pa, a = - multiple_of_spindet (Determinant.alfa t) (Determinant.alfa t') - and pb, b = - multiple_of_spindet (Determinant.beta t) (Determinant.beta t') - in - let phase = Phase.add pa pb in - Multiple (phase, List.concat [ - List.rev @@ List.rev_map (fun (hole, particle) -> { hole ; particle ; spin=Spin.Alfa }) a ; - List.rev @@ List.rev_map (fun (hole, particle) -> { hole ; particle ; spin=Spin.Beta }) b ]) - - -let double_of_det t t' = - match multiple_of_det t t' with - | Multiple (phase, [e1 ; e2]) -> Double (phase, e1, e2) - | _ -> assert false - - -let triple_of_det t t' = - match multiple_of_det t t' with - | Multiple (phase, [e1 ; e2 ; e3]) -> Triple (phase, e1, e2, e3) - | _ -> assert false - - -let of_det t t' = - match Determinant.degree t t' with - | 0 -> if Determinant.phase t = Determinant.phase t' then - Identity Phase.Pos - else - Identity Phase.Neg - | 1 -> single_of_det t t' - | 2 -> double_of_det t t' - | 3 -> triple_of_det t t' - | _ -> multiple_of_det t t' - -let pp_s_exc ppf t = - Format.fprintf ppf "@[T^{%s}_{%d->%d}@]" - (match t.spin with - | Spin.Alfa -> "\\alpha" - | Spin.Beta -> "\\beta " ) - t.hole t.particle - -let pp ppf t = - let phase, l = - match t with - | Identity p -> p, [] - | Single (p,x) -> p, x::[] - | Double (p,x,y) -> p, x::y::[] - | Triple (p,x,y,z) -> p, x::y::z::[] - | Multiple (p,l) -> p, l - in - Format.fprintf ppf "@[%c" - (match phase with - | Phase.Pos -> '+' - | Phase.Neg -> '-' ); - List.iter (fun x -> Format.fprintf ppf "@[T^{%s}_{%d->%d}@]" - (match x.spin with - | Spin.Alfa -> "\\alpha" - | Spin.Beta -> "\\beta " ) - x.hole x.particle) l; - Format.fprintf ppf "@]" - - -let test_case () = - - (* - let test_id () = - let l_a = [ 1 ; 2 ; 3 ; 5 ; 64 ] - and l_b = [ 2 ; 3 ; 5 ; 65 ] in - let det1 = Determinant.of_lists l_a l_b in - let det2 = Determinant.negate_phase det1 in - in - *) - - let test_single () = - let l_a = [ 1 ; 2 ; 3 ; 5 ; 64 ] - and l_b = [ 2 ; 3 ; 5 ; 65 ] in - let det1 = Determinant.of_lists 66 l_a l_b in - let det2 = Determinant.single_excitation Spin.Alfa 3 7 det1 in - let t = single_of_det det1 det2 in - Alcotest.(check bool) "single 1" true (t = Single (Phase.Pos, { hole=3 ; particle=7 ; spin=Spin.Alfa}) ); - let det2 = - Determinant.single_excitation Spin.Alfa 2 7 det1 - |> Determinant.negate_phase - in - let t = single_of_det det1 det2 in - Alcotest.(check bool) "single 2" true (t = Single (Phase.Neg, { hole=2 ; particle=7 ; spin=Spin.Alfa }) ); - let det2 = Determinant.single_excitation Spin.Beta 2 7 det1 in - let t = single_of_det det1 det2 in - Alcotest.(check bool) "single 3" true (t = Single (Phase.Pos, { hole=2 ; particle=7 ; spin=Spin.Beta}) ); - let det2 = Determinant.single_excitation Spin.Beta 3 256 det1 in - let t = single_of_det det1 det2 in - Alcotest.(check bool) "single 4" true (t = Single (Phase.Pos, { hole=3 ; particle=256 ; spin=Spin.Beta}) ); - in - - let test_double () = - let l_a = [ 1 ; 2 ; 3 ; 5 ; 64 ] - and l_b = [ 2 ; 3 ; 5 ; 65 ] in - let det1 = Determinant.of_lists 66 l_a l_b in - let det2 = Determinant.double_excitation Spin.Alfa 3 7 Spin.Alfa 2 6 det1 in - let t = double_of_det det1 det2 in - Alcotest.(check bool) "double 1" true - (t = Double (Phase.Neg, - { hole=2 ; particle=7 ; spin=Spin.Alfa}, - { hole=3 ; particle=6 ; spin=Spin.Alfa})); - in - [ - "Single", `Quick, test_single; - "Double", `Quick, test_double; - ] - - diff --git a/CI/F12CI.ml b/CI/F12CI.ml deleted file mode 100644 index 38a247d..0000000 --- a/CI/F12CI.ml +++ /dev/null @@ -1,204 +0,0 @@ -open Lacaml.D - -module Ds = DeterminantSpace -module De = Determinant -module Sp = Spindeterminant - -type t = - { - mo_basis : MOBasis.t ; - det_space : DeterminantSpace.t ; - ci : CI.t ; - hf12_integrals : HF12.t ; - eigensystem : (Mat.t * Vec.t) lazy_t; - } - -let ci t = t.ci -let mo_basis t = t.mo_basis -let det_space t = t.det_space -let mo_class t = Ds.mo_class @@ det_space t -let eigensystem t = Lazy.force t.eigensystem - - - - -let dressing_vector ~frozen_core hf12_integrals f12_amplitudes ci = - - if Parallel.master then - Printf.printf "Building dressing\n%!"; - let det_space = - ci.CI.det_space - in - - let { HF12. - simulation ; aux_basis ; - f_0 ; f_1 ; f_2 ; f_3 } = hf12_integrals - in - - let m_HF = - - let f = - match Ds.determinants det_space with - | Ds.Arbitrary _ -> CI.create_matrix_arbitrary - | Ds.Spin _ -> CI.create_matrix_spin_computed ~nmax:3 - in - f (fun deg_a deg_b ki kj -> - match deg_a + deg_b with - | 0 -> f_0 ki - | 1 -> f_1 ki kj - | 2 -> f_2 ki kj - | 3 -> f_3 ki kj - | _ -> assert false - ) det_space - in - - let m_HF = - Lazy.force m_HF - in - - let result = - Matrix.parallel_mm m_HF (Matrix.dense_of_mat f12_amplitudes) - in - - if Parallel.master then - Printf.printf "dressing done\n%!"; - - Parallel.broadcast (lazy result) - -let sum l f = List.fold_left (fun accu i -> accu +. f i) 0. l - - -let make ~simulation ?(threshold=1.e-12) ~frozen_core ~mo_basis ~aux_basis_filename ?(state=1) () = - - - let det_space = - DeterminantSpace.fci_of_mo_basis mo_basis ~frozen_core - in - - let ci = CI.make ~n_states:state det_space in - - let hf12_integrals = - HF12.make ~frozen_core ~simulation ~mo_basis ~aux_basis_filename () - in - - let ci_coef, ci_energy = - let x = Lazy.force ci.eigensystem in - Parallel.broadcast (lazy x) - in - - - let eigensystem = lazy ( - let m_H = - Lazy.force ci.CI.m_H - in - - - let rec iteration ~state psi = -(* -Format.printf "%a@." DeterminantSpace.pp_det_space @@ CI.det_space ci; -Format.printf "%a@." Matrix.pp_matrix @@ Matrix.dense_of_mat psi; -*) - let column_idx = iamax (Mat.to_col_vecs psi).(state-1) in - - let delta = - (* delta_i = {% $\sum_j c_j H_{ij}$ %} *) - dressing_vector ~frozen_core hf12_integrals psi ci - |> Matrix.to_mat - in - (* - Format.printf "%a@." Matrix.pp_matrix @@ Matrix.dense_of_mat delta; - *) - - - Printf.printf "Cmax : %e\n" psi.{column_idx,state}; - Printf.printf "Norm : %e\n" (sqrt (gemm ~transa:`T delta delta).{state,state}); - - let f = 1.0 /. psi.{column_idx,state} in - let delta_00 = - (* Delta_00 = {% $\sum_{j \ne x} delta_j c_j / c_x$ %} *) - f *. ( (gemm ~transa:`T delta psi).{state,state} -. - delta.{column_idx,state} *. psi.{column_idx,state} ) - in - Printf.printf "Delta_00 : %e %e\n" delta.{column_idx,state} delta_00; - - delta.{column_idx,state} <- delta.{column_idx,state} -. delta_00; - - - let eigenvectors, eigenvalues = - - let delta = lacpy delta in - Mat.scal f delta; - for k=1 to state-1 do - for i=1 to Mat.dim1 delta do - delta.{i,k} <- delta.{i,state} - done; - done; - let diagonal = - Vec.init (Matrix.dim1 m_H) (fun i -> - if i = column_idx then - Matrix.get m_H i i +. delta.{column_idx,state} - else - Matrix.get m_H i i - ) - in - - let matrix_prod c = - let w = - Matrix.mm ~transa:`T c m_H - |> Matrix.transpose - |> Matrix.to_mat - in - let c = Matrix.to_mat c in - - for k=1 to state do - for i=1 to (Mat.dim1 w) do - w.{i,k} <- w.{i,k} +. delta.{i,k} *. c.{column_idx, k} ; - w.{column_idx,k} <- w.{column_idx,k} +. delta.{i,k} *. c.{i,k}; - done; - w.{column_idx,k} <- w.{column_idx,k} -. - delta.{column_idx,k} *. c.{column_idx,k}; - done; - - Matrix.dense_of_mat w - in - - - Parallel.broadcast (lazy ( - Davidson.make ~threshold:1.e-10 ~guess:psi ~n_states:state diagonal matrix_prod - )) - - in - let eigenvectors = - Conventions.rephase @@ Util.remove_epsilons eigenvectors - in - - - Vec.iter (fun energy -> Printf.printf "%g\t" energy) eigenvalues; - print_newline (); - - let conv = - 1.0 -. abs_float ( dot - (Mat.to_col_vecs psi).(0) - (Mat.to_col_vecs eigenvectors).(0) ) - in - if Parallel.master then - Printf.printf "F12 Convergence : %e %f\n" conv (eigenvalues.{state} - +. Simulation.nuclear_repulsion simulation); - - if conv > threshold then - iteration ~state eigenvectors - else - let eigenvalues = - Vec.map (fun x -> x +. ci.CI.e_shift) eigenvalues - in - eigenvectors, eigenvalues - in - iteration ~state ci_coef - - ) - in - { mo_basis ; det_space ; ci ; hf12_integrals ; eigensystem } - - - - diff --git a/CI/Phase.ml b/CI/Phase.ml deleted file mode 100644 index 991c7fb..0000000 --- a/CI/Phase.ml +++ /dev/null @@ -1,31 +0,0 @@ -type t = -| Pos -| Neg - -let of_nperm nperm = - if (nperm land 1) = 1 then Neg - else Pos - -let to_nperm = function -| Pos -> 0 -| Neg -> 1 - -let add t t' = - match t, t' with - | Pos, Pos - | Neg, Neg -> Pos - | Pos, Neg - | Neg, Pos -> Neg - -let neg = function - | Pos -> Neg - | Neg -> Pos - -let add_nperm phase = function - | 0 -> phase - | nperm -> add phase (of_nperm nperm) - -let pp ppf = function - | Pos -> Format.fprintf ppf "@[+1@]" - | Neg -> Format.fprintf ppf "@[-1@]" - diff --git a/CI/Phase.mli b/CI/Phase.mli deleted file mode 100644 index ffa36c1..0000000 --- a/CI/Phase.mli +++ /dev/null @@ -1,22 +0,0 @@ -type t = -| Pos -| Neg - -val of_nperm : int -> t -(** Returns the phase obtained by a given number of permuations. *) - -val to_nperm : t -> int -(** Converts the phase to [1] or [0] permutations. *) - -val add : t -> t -> t -(** Add a given phase to an existing phase. *) - -val add_nperm : t -> int -> t -(** Add to an existing phase a given number of permutations. *) - -val neg : t -> t -(** Negate the phase. *) - -(** {1 Printers} *) - -val pp : Format.formatter -> t -> unit diff --git a/CI/Spindeterminant.ml b/CI/Spindeterminant.ml deleted file mode 100644 index 9391af6..0000000 --- a/CI/Spindeterminant.ml +++ /dev/null @@ -1,249 +0,0 @@ -type s = - { - bitstring : Bitstring.t; - phase : Phase.t ; - } - -type t = s option -type hole = int -type particle = int - -let phase = function - | Some s -> s.phase - | None -> Phase.Pos - - -let is_none = function - | None -> true - | _ -> false - - -let bitstring = function - | Some s -> s.bitstring - | None -> invalid_arg "Spindeterminant is None" - - -let vac n = - Some { bitstring = Bitstring.zero n; - phase = Phase.Pos; } - - -let creation p = function - | None -> None - | Some spindet -> - let i = pred p in - if Bitstring.testbit spindet.bitstring i then - None - else - begin - let numbits = Bitstring.numbits spindet.bitstring in - let x = Bitstring.shift_left_one numbits i in - let bitstring = Bitstring.logor spindet.bitstring x in - let mask = Bitstring.minus_one x in - let r = Bitstring.logand bitstring mask in - let phase = Phase.add_nperm spindet.phase (Bitstring.popcount r) in - Some { bitstring ; phase } - end - - -let annihilation h = function - | None -> None - | Some spindet -> - let i = pred h in - if not (Bitstring.testbit spindet.bitstring i) then - None - else - begin - let numbits = Bitstring.numbits spindet.bitstring in - let x = Bitstring.shift_left_one numbits i in - let mask = Bitstring.minus_one x in - let r = Bitstring.logand spindet.bitstring mask in - let phase = Phase.add_nperm spindet.phase (Bitstring.popcount r) in - let bitstring = Bitstring.logand spindet.bitstring (Bitstring.lognot x) in - Some { bitstring ; phase } - end - -let single_excitation_reference h p spindet = - creation p @@ annihilation h @@ spindet - -let single_excitation h p = - single_excitation_reference h p - - -let double_excitation_reference h' p' h p spindet = - creation p' @@ creation p @@ annihilation h @@ annihilation h' @@ spindet - -let double_excitation h' p' h p = - double_excitation_reference h' p' h p - - -let degree t t' = - Bitstring.hamdist (bitstring t) (bitstring t') / 2 - -let holes_of t t' = - Bitstring.logand (bitstring t) (Bitstring.logxor (bitstring t) (bitstring t')) - |> Bitstring.to_list - -let particles_of t t' = - Bitstring.logand (bitstring t') (Bitstring.logxor (bitstring t) (bitstring t')) - |> Bitstring.to_list - -let holes_particles_of t t' = - let x = Bitstring.logxor (bitstring t) (bitstring t') in - let holes = Bitstring.logand (bitstring t) x |> Bitstring.to_list - and particles = Bitstring.logand (bitstring t') x |> Bitstring.to_list - in - List.rev_map2 (fun h p -> (h,p)) holes particles - |> List.rev - - -let set_phase p = function - | Some t -> Some { t with phase = p } - | None -> None - -let negate_phase = function - | Some t -> Some { t with phase = Phase.neg t.phase } - | None -> None - - -let of_bitstring ?(phase=Phase.Pos) bitstring = - Some { bitstring ; phase } - -let of_list n l = - List.rev l - |> List.fold_left (fun accu p -> creation p accu) (vac n) - - -let to_list = function - | None -> [] - | Some spindet -> - let rec aux accu z = - if not (Bitstring.is_zero z) then - let element = ((Bitstring.trailing_zeros z)+1) in - (aux [@tailcall]) (element::accu) (Bitstring.logand z (Bitstring.minus_one z) ) - else List.rev accu - in aux [] spindet.bitstring - -let to_array t = - to_list t - |> Array.of_list - -let n_electrons = function - | Some t -> Bitstring.popcount t.bitstring - | None -> 0 - - -let pp n ppf = function - | None -> Format.fprintf ppf "@[None@]" - | Some s -> - Format.fprintf ppf "@[%a %a@]" Phase.pp s.phase Bitstring.pp - s.bitstring - - - - -(*-----------------------------------------------------------------------------------*) - - -let test_case () = - - let test_creation () = - let l_a = [ 1 ; 2 ; 3 ; 5 ] in - let det = of_list 10 l_a in - Alcotest.(check (list int )) "bitstring 1" l_a (to_list det); - Alcotest.(check bool) "phase 2" true (phase det = Phase.Pos); - let l_b = [ 1 ; 3 ; 2 ; 5 ] in - let det = of_list 10 l_b in - Alcotest.(check (list int )) "bitstring 2" l_a (to_list det); - Alcotest.(check bool) "phase 2" true (phase det = Phase.Neg); - in - - let test_a_operators () = - let det = - creation 5 @@ creation 2 @@ creation 2 @@ creation 1 @@ (vac 10) - in - Alcotest.(check bool) "none 1" true (is_none det); - - let det = - creation 5 @@ creation 3 @@ creation 2 @@ creation 1 @@ (vac 10) - in - let l_a = [ 1 ; 2 ; 3 ; 5 ] in - Alcotest.(check (list int )) "bitstring 1" l_a (to_list det); - Alcotest.(check bool) "phase 1" true (phase det = Phase.Pos); - - let det = - creation 1 @@ creation 3 @@ creation 2 @@ creation 5 @@ (vac 10) - in - Alcotest.(check (list int )) "bitstring 2" l_a (to_list det); - Alcotest.(check bool) "phase 2" true (phase det = Phase.Neg); - - let l_b = [ 1 ; 3 ; 2 ; 5 ] in - let det = of_list 10 l_b in - Alcotest.(check (list int )) "bitstring 3" l_a (to_list det); - Alcotest.(check bool) "phase 3" true (phase det = Phase.Neg); - - Alcotest.(check bool) "none 1" true (annihilation 4 det |> is_none); - - let det = - annihilation 1 det - in - Alcotest.(check (list int )) "bitstring 4" (List.tl l_a) (to_list det); - Alcotest.(check bool) "phase 4" true (phase det = Phase.Neg); - - let det = - annihilation 3 det - in - Alcotest.(check (list int )) "bitstring 5" [ 2 ; 5 ] (to_list det); - Alcotest.(check bool) "phase 5" true (phase det = Phase.Pos); - - let det = - annihilation 5 @@ annihilation 2 det - in - Alcotest.(check (list int )) "bitstring 6" [] (to_list det); - Alcotest.(check bool) "phase 6" true (phase det = Phase.Pos); - - in - - let test_exc_operators () = - let l_a = [ 1 ; 2 ; 3 ; 5 ] in - let det = of_list 10 l_a in - let l_b = [ 1 ; 7 ; 3 ; 5 ] in - let det2 = of_list 10 l_b in - Format.printf "%a@." (pp 7) det; - Format.printf "%a@." (pp 7) det2; - Format.printf "%a@." (pp 7) (single_excitation_reference 2 7 det); - Alcotest.(check bool) "single 1" true (single_excitation_reference 2 7 det = det2); - Alcotest.(check bool) "single 2" true (single_excitation 2 7 det = single_excitation_reference 2 7 det); - Alcotest.(check bool) "single 3" true (single_excitation_reference 4 7 det |> is_none); - Alcotest.(check bool) "single 4" true (single_excitation 4 7 det |> is_none); - - let l_c = [ 1 ; 7 ; 6 ; 5 ] in - let det3 = of_list 10 l_c in - Alcotest.(check bool) "double 1" true (double_excitation_reference 2 7 3 6 det = det3); - Alcotest.(check bool) "double 2" true (double_excitation 2 7 3 6 det = double_excitation_reference 2 7 3 6 det); - Alcotest.(check bool) "double 3" true (double_excitation_reference 4 7 3 6 det |> is_none); - Alcotest.(check bool) "double 4" true (double_excitation 4 7 3 6 det |> is_none); - in - - let test_exc_spindet () = - let l_a = [ 1 ; 2 ; 3 ; 5 ] in - let det = of_list 10 l_a in - let l_b = [ 1 ; 7 ; 3 ; 5 ] in - let det2 = of_list 10 l_b in - Alcotest.(check int) "single" 1 (degree det det2); - Alcotest.(check (list int)) "holes" [2] (holes_of det det2); - Alcotest.(check (list int)) "particles" [7] (particles_of det det2); - let l_b = [ 1 ; 7 ; 3 ; 6 ] in - let det2 = of_list 10 l_b in - Alcotest.(check int) "double" 2 (degree det det2); - Alcotest.(check (list int)) "holes" [2 ; 5] (holes_of det det2); - Alcotest.(check (list int)) "particles" [6 ; 7] (particles_of det det2); - in - [ - "Creation", `Quick, test_creation; - "Creation/Annihilation Operators", `Quick, test_a_operators; - "Excitation Operators", `Quick, test_exc_operators; - "Excitation of spindet", `Quick, test_exc_spindet; - ] - - diff --git a/CI/Spindeterminant.mli b/CI/Spindeterminant.mli deleted file mode 100644 index 3ba94b1..0000000 --- a/CI/Spindeterminant.mli +++ /dev/null @@ -1,94 +0,0 @@ -(** -A spin-determinant is one of the two determinants in the Waller-Hartree -double determinant representation of a Slater determinant. It is represented -as a bit string and a phase factor. -*) - -type t -type hole = int -type particle = int - -(** {1 Accessors}. *) - -val phase : t -> Phase.t -(** Phase factor. - @raise Invalid_argument if the spin-determinant is [None]. -*) - -val set_phase : Phase.t -> t -> t -(** Returns a spin-determinant with the phase set to [p]. *) - - -val bitstring : t -> Bitstring.t -(** Bit string. - @raise Invalid_argument if the spin-determinant is [None]. -*) - -val is_none : t -> bool -(** Tests if a spin-determinant is [None]. *) - -val negate_phase : t -> t -(** Returns a spin-determinant with the phase reversed. *) - - -(** {1 Second quantization operators} *) - -val vac : int -> t -(** Vacuum state, [vac = Some ]{% $|\rangle$ %}. The integer parameter contains the - number of orbitals in the basis set. *) - -val creation : particle -> t -> t -(** [creation p] is the creation operator {% $a^\dagger_p$ %}. *) - -val annihilation : hole -> t -> t -(** [annihilation h] is the annihilation operator {% $a_h$ %}. *) - -val single_excitation : hole -> particle -> t -> t -(** Single excitation operator {% $T_h^p = a^\dagger_p a_h$ %}. *) - -val double_excitation : hole -> particle -> hole -> particle -> t -> t -(** Double excitation operator {% $T_{hh'}^{pp'} = a^\dagger_p a^\dagger_{p'} a_{h'} a_h$ %}. *) - -val degree : t -> t -> int -(** Returns degree of excitation between two spin-determinants. *) - -val holes_of : t -> t -> int list -(** Returns the list of holes in the excitation from one determinant to another. *) - -val particles_of : t -> t -> int list -(** Returns the list of particles in the excitation from one determinant to another. *) - -val holes_particles_of : t -> t -> (int*int) list -(** Returns the list of pairs of holes/particles in the excitation from one determinant to -another. *) - -val n_electrons : t -> int -(** Returns the number of electrons in the determinant. *) - - -(** {1 Creation} *) - -val of_bitstring : ?phase:Phase.t -> Bitstring.t -> t -(** Creates from a bitstring and an optional phase.*) - -val of_list : int -> int list -> t -(** Builds a spin-determinant from a list of orbital indices. If the creation of the - spin-determinant is not possible because of Pauli's exclusion principle, a [None] - spin-determinant is returned. - The first integer is the size of the MO basis set. *) - -val to_list : t -> int list -(** Transforms a spin-determinant into a list of orbital indices. *) - -val to_array : t -> int array -(** Transforms a spin-determinant into an array of orbital indices. *) - -(** {1 Printers}. *) - -val pp : int -> Format.formatter -> t -> unit -(** First [int] is the number of MOs to print *) - - -(** {1 Unit testing} *) - -val test_case : unit -> (string * [> `Quick ] * (unit -> unit)) list diff --git a/CI/SpindeterminantSpace.ml b/CI/SpindeterminantSpace.ml deleted file mode 100644 index 7fff6cb..0000000 --- a/CI/SpindeterminantSpace.ml +++ /dev/null @@ -1,74 +0,0 @@ -type t = - { - elec_num : int; - mo_basis : MOBasis.t; - mo_class : MOClass.t; - spin_determinants : Spindeterminant.t array; - } - - -let spin_determinants t = t.spin_determinants -let elec_num t = t.elec_num -let mo_basis t = t.mo_basis -let mo_class t = t.mo_class -let size t = Array.length t.spin_determinants - -let fci_of_mo_basis ~frozen_core mo_basis elec_num = - let mo_num = MOBasis.size mo_basis in - let mo_class = MOClass.fci ~frozen_core mo_basis in - let m l = - List.fold_left (fun accu i -> let j = i-1 in - Bitstring.logor accu (Bitstring.shift_left_one mo_num j) - ) (Bitstring.zero mo_num) l - in - let occ_mask = m (MOClass.core_mos mo_class) - and active_mask = m (MOClass.active_mos mo_class) - in - let neg_active_mask = Bitstring.lognot active_mask in - (* Here we generate the FCI space and filter out unwanted determinants - with excitations involving the core electrons. This should be improved. *) - let spin_determinants = - Bitstring.permtutations elec_num mo_num - |> List.filter (fun b -> Bitstring.logand neg_active_mask b = occ_mask) - |> Array.of_list - |> Array.map (fun b -> Spindeterminant.of_bitstring b) - in - { elec_num ; mo_basis ; mo_class ; spin_determinants } - - -let cas_of_mo_basis mo_basis ~frozen_core elec_num n m = - let mo_num = MOBasis.size mo_basis in - let mo_class = MOClass.cas_sd ~frozen_core mo_basis n m in - let m l = - List.fold_left (fun accu i -> let j = i-1 in - Bitstring.logor accu (Bitstring.shift_left_one mo_num j) - ) (Bitstring.zero mo_num) l - in - let active_mask = m (MOClass.active_mos mo_class) in - let occ_mask = m (MOClass.core_mos mo_class) in - let inactive_mask = m (MOClass.inactive_mos mo_class) in - let occ_mask = Bitstring.logor occ_mask inactive_mask in - let neg_active_mask = Bitstring.lognot active_mask in - (* Here we generate the FCI space and filter out all the unwanted determinants. - This should be improved. *) - let spin_determinants = - Bitstring.permtutations elec_num mo_num - |> List.filter (fun b -> Bitstring.logand neg_active_mask b = occ_mask) - |> Array.of_list - |> Array.map (fun b -> Spindeterminant.of_bitstring b) - in - { elec_num ; mo_basis ; mo_class ; spin_determinants } - - - -let pp ppf t = - Format.fprintf ppf "@[ ["; - let pp = Spindeterminant.pp @@ MOBasis.size (mo_basis t) in - Array.iteri (fun i d -> - Format.fprintf ppf "@[@[%8d@] @[%a@]@]@;" i pp d) - (spin_determinants t) ; - Format.fprintf ppf "]@]" - - - - diff --git a/CI/SpindeterminantSpace.mli b/CI/SpindeterminantSpace.mli deleted file mode 100644 index be955ce..0000000 --- a/CI/SpindeterminantSpace.mli +++ /dev/null @@ -1,46 +0,0 @@ -(** -The space built with determinants made with same-spin spinorbitals. -*) - -type t - -(** {1 Accessors} *) - -val size : t -> int -(** Number of determinants in the space. *) - -val spin_determinants : t -> Spindeterminant.t array -(** All the spin-determinants belonging to the space. *) - -val elec_num : t -> int -(** Number of (same-spin) electrons occupying the MOs. *) - -val mo_class : t -> MOClass.t -(** The MO classes used to generate the space. *) - -val mo_basis : t -> MOBasis.t -(** The MO basis on which the determinants are expanded. *) - - -(** {1 Creation} *) - -val fci_of_mo_basis : frozen_core:bool -> MOBasis.t -> int -> t -(** Create a space of all possible ways to put [n_elec-ncore] electrons in the - [Active] MOs. All other MOs are untouched. -*) - -val cas_of_mo_basis : MOBasis.t -> frozen_core:bool -> int -> int -> int -> t -(** [cas_of_mo_basis mo_basis n_elec n m] creates a CAS(n,m) space of - [Active] MOs. The unoccupied MOs are [Virtual], and the occupied MOs - are [Core] and [Inactive]. -*) - - -(** {2 Printing} *) - -val pp : Format.formatter -> t -> unit - - - - - diff --git a/INSTALL.md b/INSTALL.md deleted file mode 100644 index 9140d3f..0000000 --- a/INSTALL.md +++ /dev/null @@ -1,84 +0,0 @@ -# Generic installation - -```bash -opam install ocamlbuild ocamlfind lacaml mpi getopt alcotest zarith -``` - - -# BLAS/Lapack - -Install OpenBLAS from your system package manager, for example: - -```bash -sudo apt-get install libopenblas-dev -``` - -# LaCAML - -LaCAML is the OCaml binding to the LAPACK library. - -```bash -opam install lacaml -``` - -To use MKL with LaCaml: - -```bash -export LACAML_LIBS="-L${MKLROOT}/lib/intel64 -Wl,--no-as-needed -lmkl_rt -lpthread -lm -ldl" -opam install lacaml -``` - -# MPI - -MPI is the Message Passing Interface, required for distributed parallelism. -For large MPI calculations, a version >= 4.09.0 of the compiler is required. - -```bash -opam install mpi -``` - -To use Intel MPI - -```bash -export MPI_INC_DIR=${I_MPI_ROOT}/include64/ -export MPI_LIB_DIR=${I_MPI_ROOT}/lib64/ -export MPI_BIN_PATH=${I_MPI_ROOT}/bin64/ -opam install mpi -``` - -# odoc-ltxhtml - -This plugin allows to embed equations in the documentation generated by Ocamldoc. - -Download the source code [here](https://github.com/scemama/odoc-ltxhtml). - -```bash -git clone https://github.com/scemama/odoc-ltxhtml -cd odoc-ltxhtml -make install -``` - -# Getopt - -Parsing of command line arguments (similar to GNU GetOpt) - -```bash -opam install getopt -``` - -# Alcotest - -Lightweight and colourful test framework - -```bash -opam install alcotest -``` - -# Zarith - -Implements arithmetic and logical operations over arbitrary-precision integer - -```bash -opam install zarith -``` - diff --git a/LICENSE b/LICENSE deleted file mode 100644 index 7781d85..0000000 --- a/LICENSE +++ /dev/null @@ -1,674 +0,0 @@ - GNU GENERAL PUBLIC LICENSE - Version 3, 29 June 2007 - - Copyright (C) 2007 Free Software Foundation, Inc. - Everyone is permitted to copy and distribute verbatim copies - of this license document, but changing it is not allowed. - - Preamble - - The GNU General Public License is a free, copyleft license for -software and other kinds of works. - - The licenses for most software and other practical works are designed -to take away your freedom to share and change the works. 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It is safest -to attach them to the start of each source file to most effectively -state the exclusion of warranty; and each file should have at least -the "copyright" line and a pointer to where the full notice is found. - - QCaml - Copyright (C) 2018 Anthony Scemama - - This program is free software: you can redistribute it and/or modify - it under the terms of the GNU General Public License as published by - the Free Software Foundation, either version 3 of the License, or - (at your option) any later version. - - This program is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - GNU General Public License for more details. - - You should have received a copy of the GNU General Public License - along with this program. If not, see . - -Also add information on how to contact you by electronic and paper mail. - - If the program does terminal interaction, make it output a short -notice like this when it starts in an interactive mode: - - QCaml Copyright (C) 2018 Anthony Scemama - This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. - This is free software, and you are welcome to redistribute it - under certain conditions; type `show c' for details. - -The hypothetical commands `show w' and `show c' should show the appropriate -parts of the General Public License. Of course, your program's commands -might be different; for a GUI interface, you would use an "about box". - - You should also get your employer (if you work as a programmer) or school, -if any, to sign a "copyright disclaimer" for the program, if necessary. -For more information on this, and how to apply and follow the GNU GPL, see -. - - The GNU General Public License does not permit incorporating your program -into proprietary programs. If your program is a subroutine library, you -may consider it more useful to permit linking proprietary applications with -the library. If this is what you want to do, use the GNU Lesser General -Public License instead of this License. But first, please read -. diff --git a/META b/META deleted file mode 100644 index daebbca..0000000 --- a/META +++ /dev/null @@ -1,3 +0,0 @@ -version = "%{version}%" -description = "Quantum Chamistry" -requires = "lacaml" diff --git a/MOBasis/.merlin b/MOBasis/.merlin deleted file mode 100644 index 2ba6169..0000000 --- a/MOBasis/.merlin +++ /dev/null @@ -1 +0,0 @@ -REC diff --git a/MOBasis/HF12.ml b/MOBasis/HF12.ml deleted file mode 100644 index 5ddf5af..0000000 --- a/MOBasis/HF12.ml +++ /dev/null @@ -1,1170 +0,0 @@ -(** %{ $ \langle ij | H F | kl \rangle $ %} integrals. *) - -open Lacaml.D - -module Fis = FourIdxStorage - - -type t = { - simulation : Simulation.t ; - aux_basis : MOBasis.t ; - f_0 : Determinant.t -> float ; - f_1 : Determinant.t -> Determinant.t -> float ; - f_2 : Determinant.t -> Determinant.t -> float ; - f_3 : Determinant.t -> Determinant.t -> float ; -} - - -let sum l f = Array.fold_left (fun accu i -> accu +. f i) 0. l - -let array_3_init d1 d2 d3 fx = - let f k = - let x = - Bigarray.(Array2.create Float64 fortran_layout d1 d2) - in - for j=1 to d2 do - for i=1 to d1 do - x.{i,j} <- fx i j k - done - done; - (k,x) - in - let result = - SharedMemory.create Bigarray.Float64 [| d1 ; d2 ; d3 |] - |> Bigarray.array3_of_genarray - in - Util.list_range 1 d3 - |> Stream.of_list - |> Farm.run ~f ~ordered:false - |> Stream.iter (fun (k,x) -> - for j=1 to d2 do - for i=1 to d1 do - result.{i,j,k} <- x.{i,j} - done - done) - ; - if Parallel.master then Printf.printf "Broadcast d3\n%!" ; - try Parallel.InterNode.broadcast (lazy result) - with Invalid_argument _ -> - begin - Printf.eprintf "Array too large.\n%!"; - failwith "Array too large" - end - -let array_4_init d1 d2 d3 d4 fx = - let f (k,l) = - let x = - Bigarray.(Array2.create Float64 fortran_layout d1 d2) - in - for j=1 to d2 do - for i=1 to d1 do - x.{i,j} <- fx i j k l - done - done; - (k,l,x) - in - let result = - SharedMemory.create Bigarray.Float64 [| d1;d2;d3;d4 |] - in - Util.list_range 1 d4 - |> List.rev_map (fun l -> - Util.list_range 1 d3 - |> List.rev_map (fun k -> (k,l)) ) - |> List.concat - |> List.rev - |> Stream.of_list - |> Farm.run ~f ~ordered:false - |> Stream.iter (fun (k,l,x) -> - for j=1 to d2 do - for i=1 to d1 do - result.{i,j,k,l} <- x.{i,j} - done - done) - ; - if Parallel.master then Printf.printf "Broadcast d4\n%!" ; - try Parallel.InterNode.broadcast (lazy result) - with Invalid_argument _ -> - begin - Printf.eprintf "Array too large... splitting.\n%!"; - let x = - Bigarray.(Array3.create Float64 fortran_layout d1 d2 d3) - in - for l=1 to d4 do - if Parallel.master then - begin - for k=1 to d3 do - for j=1 to d2 do - for i=1 to d1 do - x.{i,j,k} <- result.{i,j,k,l} - done - done - done; - ignore @@ Parallel.InterNode.broadcast (lazy x) - end - else - begin - ignore @@ Parallel.InterNode.broadcast (lazy x); - for k=1 to d3 do - for j=1 to d2 do - for i=1 to d1 do - result.{i,j,k,l} <- x.{i,j,k} - done - done - done - end - done; - result - end - -let array_5_init d1 d2 d3 d4 d5 fx = - let f (l,m) = - let x = - Bigarray.(Array3.create Float64 fortran_layout d1 d2 d3) - in - for k=1 to d3 do - for j=1 to d2 do - for i=1 to d1 do - x.{i,j,k} <- fx i j k l m - done - done - done; - (l,m,x) - in - let result = - SharedMemory.create Bigarray.Float64 [| d1;d2;d3;d4;d5 |] - in - Util.list_range 1 d5 - |> List.rev_map (fun m -> - Util.list_range 1 d4 - |> List.rev_map (fun l -> (l,m)) ) - |> List.concat - |> List.rev - |> Stream.of_list - |> Farm.run ~f ~ordered:false - |> Stream.iter (fun (l,m,x) -> - for k=1 to d3 do - for j=1 to d2 do - for i=1 to d1 do - result.{i,j,k,l,m} <- x.{i,j,k} - done - done - done) - ; - if Parallel.master then Printf.printf "Broadcast d5\n%!" ; - try - Parallel.InterNode.broadcast (lazy result) - with Invalid_argument _ -> - begin - Printf.eprintf "Array too large... splitting.\n%!"; - let x = - Bigarray.(Genarray.create Float64 fortran_layout [| d1; d2; d3; d4 |]) - in - for m=1 to d5 do - if Parallel.master then - begin - for l=1 to d4 do - for k=1 to d3 do - for j=1 to d2 do - for i=1 to d1 do - x.{i,j,k,l} <- result.{i,j,k,l,m} - done - done - done - done; - ignore @@ Parallel.InterNode.broadcast (lazy x) - end - else - begin - ignore @@ Parallel.InterNode.broadcast (lazy x); - for l=1 to d4 do - for k=1 to d3 do - for j=1 to d2 do - for i=1 to d1 do - result.{i,j,k,l,m} <- x.{i,j,k,l} - done - done - done - done - end - done; - result - end - - -let make ~frozen_core ~simulation ~mo_basis ~aux_basis_filename () = - - let f12 = Util.of_some @@ Simulation.f12 simulation in - let mo_num = MOBasis.size mo_basis in - - (* Add auxiliary basis set *) - let simulation = - let charge = Charge.to_int @@ Simulation.charge simulation - and multiplicity = Electrons.multiplicity @@ Simulation.electrons simulation - and nuclei = Simulation.nuclei simulation - in - let general_basis = - Basis.general_basis @@ Simulation.basis simulation - in - GeneralBasis.combine [ - general_basis ; GeneralBasis.read aux_basis_filename - ] - |> Basis.of_nuclei_and_general_basis ~f12 nuclei - |> Simulation.make ~charge ~multiplicity ~nuclei - in - - let aux_basis = - MOBasis.of_mo_basis simulation mo_basis - in - - let aux_num = MOBasis.size aux_basis in - - (* While in a sequential region, initiate the parallel - 4-idx transformation to avoid nested parallel jobs - *) - ignore @@ MOBasis.two_e_ints aux_basis; - ignore @@ MOBasis.f12_ints aux_basis; - - (* Compute the integrals *) - if Parallel.master then Printf.eprintf "Computing HF12 integrals\n%!"; - - let mos_cabs = - Util.list_range (mo_num+1) aux_num - |> Array.of_list - in - - let n_core = - if frozen_core then - (Nuclei.small_core @@ Simulation.nuclei @@ MOBasis.simulation mo_basis) / 2 - else 0 - in - - let mos_in = - Util.list_range (n_core+1) mo_num - |> Array.of_list - in - - let mos_a k = - Determinant.alfa k - |> Spindeterminant.to_list - |> List.filter (fun i -> i > n_core) - |> Array.of_list - in - - let mos_b k = - Determinant.beta k - |> Spindeterminant.to_list - |> List.filter (fun i -> i > n_core) - |> Array.of_list - in - - let h_one = - let h = - MOBasis.one_e_ints aux_basis - in fun i j _ -> h.{i,j} - in - - let h_two = - let two_e_ints = MOBasis.two_e_ints aux_basis in - let h2 i j k l (s:Spin.t) (s':Spin.t) = - if s' <> s then - ERI.get_phys two_e_ints i j k l - else - (ERI.get_phys two_e_ints i j k l) -. - (ERI.get_phys two_e_ints i j l k) - in - h2 - in - - let f_two = - let f12_ints = MOBasis.f12_ints aux_basis in - let f2 i j k l (s:Spin.t) (s':Spin.t) = - if s' <> s then - 0.375 *. F12.get_phys f12_ints i j k l +. - 0.125 *. F12.get_phys f12_ints i j l k - else - 0.25 *. ( - (F12.get_phys f12_ints i j k l) -. - (F12.get_phys f12_ints i j l k) ) - in - f2 - in - - let f_one = fun _ _ _ -> 0. in - - -(* - let s, s' = Spin.(Alfa, Beta) in - let m_3_Hschwarz_aa = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> let x = h_two a i j k s s in x *. x) - ) - in - let m_3_Hschwarz_ab = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> let x = h_two a i j k s s' in x *. x) - ) - in - let m_3_Fschwarz_aa = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> let x = f_two a i j k s s in x *. x) - ) - in - let m_3_Fschwarz_ab = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> let x = f_two a i j k s s' in x *. x) - ) - in - - let eps = 1.e-15 in - - let sum_schwarz i j k l m n s1 s2 s3 s4 = - if (s1 = s2 && m_3_Hschwarz_aa.{i,j,k} < eps ) || - (s1 <> s2 && m_3_Hschwarz_ab.{i,j,k} < eps ) || - (s3 = s4 && m_3_Fschwarz_aa.{l,m,n} < eps ) || - (s3 <> s4 && m_3_Fschwarz_ab.{l,m,n} < eps ) - then - 0. - else - Array.fold_left (fun accu a -> - accu +. h_two a i j k s1 s2 *. f_two a l m n s3 s4 - ) 0. mos_cabs - in -*) - - (* Pre-compute dressed integrals *) - if Parallel.master then Printf.printf "Computing m_0111_1H_1F\n%!" ; - let m_0111_1H_1F = - Vec.init mo_num (fun i -> - sum mos_cabs (fun a -> - h_one a i Spin.Alfa *. f_one a i Spin.Alfa )) - in - - if Parallel.master then Printf.printf "Computing m_0111_1H_2Fa\n%!" ; - let m_0111_1H_2Fa, m_0111_2Ha_2Fa = - - let m_0122_Haa = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two a k i j Spin.Alfa Spin.Alfa *. f_two a k i j Spin.Alfa Spin.Alfa - ) ) - in - - let m_0111_1H_2Fa = - Mat.init_cols mo_num mo_num (fun i j -> - sum mos_cabs (fun a -> - h_one a i Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Alfa +. - h_two a j i j Spin.Alfa Spin.Alfa *. f_one a i Spin.Alfa - ) +. - if i < j then 0. else - begin - sum mos_cabs (fun a -> - sum mos_cabs (fun b -> if b >= a then 0. else - h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b i j Spin.Alfa Spin.Alfa - ) - ) +. - sum mos_in (fun k -> m_0122_Haa.{i,j,k}) - end - ) - in - - let m_0111_2Ha_2Fa = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two a j i j Spin.Alfa Spin.Alfa *. - f_two a k i k Spin.Alfa Spin.Alfa - ) -. if i < j then 0. else m_0122_Haa.{i,j,k} - ) - in m_0111_1H_2Fa, m_0111_2Ha_2Fa - in - - if Parallel.master then Printf.printf "Computing m_0111_1H_2Fb\n%!" ; - let m_0111_1H_2Fb, m_0111_2Hb_2Fb = - let m_0122_Hab = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two a k i j Spin.Alfa Spin.Beta *. f_two a k i j Spin.Alfa Spin.Beta - ) ) - in - - let m_0111_1H_2Fb = - Mat.init_cols mo_num mo_num (fun i j -> - sum mos_cabs (fun a -> - h_one a i Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Beta +. - h_two a j i j Spin.Alfa Spin.Beta *. f_one a i Spin.Alfa +. - h_one a j Spin.Alfa *. f_two a i j i Spin.Alfa Spin.Beta +. - h_two a i j i Spin.Alfa Spin.Beta *. f_one a j Spin.Alfa - ) +. - sum mos_in (fun k -> m_0122_Hab.{i,j,k} +. m_0122_Hab.{j,i,k} ) +. - sum mos_cabs (fun b -> - sum mos_cabs (fun a -> - h_two a b i j Spin.Alfa Spin.Beta *. f_two a b i j Spin.Alfa Spin.Beta - ) - ) - ) - in - - let m_0111_2Hb_2Fb = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two a i k i Spin.Alfa Spin.Beta *. - f_two a j k j Spin.Alfa Spin.Beta +. - h_two a k i k Spin.Alfa Spin.Beta *. - f_two a j i j Spin.Alfa Spin.Alfa - ) -. m_0122_Hab.{k,i,j} - ) - in - m_0111_1H_2Fb, m_0111_2Hb_2Fb - in - - if Parallel.master then Printf.printf "Computing m_0111_2Ha_2Fb\n%!" ; - let m_0111_2Ha_2Fb = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two a j i j Spin.Alfa Spin.Alfa *. - f_two a k i k Spin.Alfa Spin.Beta - ) - ) - in - - let f_0 ki = - - let mos_i, mos_i' = mos_a ki, mos_b ki in - let same = (mos_i = mos_i') in - - (* Alpha *) - let a = - sum mos_i (fun i -> m_0111_1H_1F.{i}) - in - - let b = - if same then a else - sum mos_i' (fun i -> m_0111_1H_1F.{i}) - in - - let aa = - sum mos_i (fun j -> - sum mos_i (fun i -> m_0111_1H_2Fa.{i,j} )) - in - - let bb = - if same then aa else - sum mos_i' (fun j -> - sum mos_i' (fun i -> m_0111_1H_2Fa.{i,j} )) - in - - let ab = - sum mos_i' (fun j -> - sum mos_i (fun i -> m_0111_1H_2Fb.{i,j} )) - in - - let aaa = - sum mos_i (fun k -> - sum mos_i (fun j -> - sum mos_i (fun i -> m_0111_2Ha_2Fa.{i,j,k} ))) - in - - let bbb = - if same then aaa else - sum mos_i' (fun k -> - sum mos_i' (fun j -> - sum mos_i' (fun i -> m_0111_2Ha_2Fa.{i,j,k} ))) - in - - let baa = - sum mos_i' (fun k -> - sum mos_i (fun j -> - sum mos_i (fun i -> - m_0111_2Ha_2Fb.{i,j,k} +. m_0111_2Hb_2Fb.{i,j,k} - ))) - in - - let bba = - sum mos_i (fun k -> - sum mos_i' (fun j -> - sum mos_i' (fun i -> - m_0111_2Ha_2Fb.{i,j,k} +. m_0111_2Hb_2Fb.{j,i,k} - ))) - in - - a +. b +. aa +. bb +. ab +. aaa +. baa +. bba +. bbb - in - - if Parallel.master then Printf.printf "Computing m_1111_1H_1F\n%!" ; - let m_1111_1H_1F = - Mat.init_cols mo_num mo_num (fun i k -> - sum mos_cabs (fun a -> h_one a i Spin.Alfa *. f_one a k Spin.Alfa )) - in - - if Parallel.master then Printf.printf "Computing m_1111_2Ha_2Fa\n%!" ; - let m_1111_2Ha_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - if l=i then - sum mos_cabs (fun a -> - h_two a l j l Spin.Alfa Spin.Alfa *. - f_two a i j k Spin.Alfa Spin.Alfa ) - else - sum mos_cabs (fun a -> - h_two a j i j Spin.Alfa Spin.Alfa *. - f_two a l k l Spin.Alfa Spin.Alfa +. - h_two a l j l Spin.Alfa Spin.Alfa *. - f_two a i j k Spin.Alfa Spin.Alfa ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1111_2Hb_2Fa\n%!" ; - let m_1111_2Hb_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - if l=i then - sum mos_cabs (fun a -> - h_two a l j l Spin.Alfa Spin.Beta *. - f_two a i j k Spin.Alfa Spin.Beta ) - else - sum mos_cabs (fun a -> - h_two a j i j Spin.Alfa Spin.Beta *. - f_two a l k l Spin.Alfa Spin.Alfa +. - h_two a l j l Spin.Alfa Spin.Beta *. - f_two a i j k Spin.Alfa Spin.Beta ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1111_2Ha_2Fb\n%!" ; - let m_1111_2Ha_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - sum mos_cabs (fun a -> - h_two a j i j Spin.Alfa Spin.Alfa *. - f_two a l k l Spin.Alfa Spin.Beta +. - h_two a l j l Spin.Alfa Spin.Beta *. - f_two a i j k Spin.Alfa Spin.Alfa - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1111_2Hb_2Fb\n%!" ; - let m_1111_2Hb_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - sum mos_cabs (fun a -> - h_two a j i j Spin.Alfa Spin.Beta *. - f_two a l k l Spin.Alfa Spin.Beta +. - h_two a l j l Spin.Alfa Spin.Alfa *. - f_two a i j k Spin.Alfa Spin.Beta - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1121_2Ha_2Fa\n%!" ; - let m_1121_2Ha_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - sum mos_cabs (fun a -> - h_two a k j i Spin.Alfa Spin.Alfa *. - f_two a l j l Spin.Alfa Spin.Alfa - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1121_2Hb_2Fa\n%!" ; - let m_1121_2Hb_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - sum mos_cabs (fun a -> - h_two a k j i Spin.Alfa Spin.Beta *. - f_two a l j l Spin.Alfa Spin.Alfa - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1121_2Ha_2Fb\n%!" ; - let m_1121_2Ha_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - sum mos_cabs (fun a -> - h_two a k j i Spin.Alfa Spin.Alfa *. - f_two a l j l Spin.Alfa Spin.Beta - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1121_2Hb_2Fb\n%!" ; - let m_1121_2Hb_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - sum mos_cabs (fun a -> - h_two a k j i Spin.Alfa Spin.Beta *. - f_two a l j l Spin.Alfa Spin.Beta - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1122_va\n%!" ; - let m_1122_va = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - sum mos_cabs (fun a -> - h_two a l j i Spin.Alfa Spin.Alfa *. - f_two a l j k Spin.Alfa Spin.Alfa - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1111_1H_2Fa\n%!" ; - let m_1111_1H_2Fa = - array_3_init mo_num mo_num mo_num (fun j i k -> - sum mos_in (fun l -> m_1122_va.{l,j,i,k}) +. - sum mos_cabs (fun a -> - h_one a i Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Alfa +. - h_two a j i j Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +. - h_one a j Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa +. - h_two a k j i Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa +. - sum mos_cabs (fun b -> if b > a then 0. else - h_two b a j i Spin.Alfa Spin.Alfa *. - f_two b a j k Spin.Alfa Spin.Alfa ) - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1122_v2\n%!" ; - let m_1122_v2 = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - sum mos_cabs (fun a -> - h_two a l j i Spin.Alfa Spin.Beta *. - f_two a l j k Spin.Alfa Spin.Beta - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1122_v3\n%!" ; - let m_1122_v3 = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - sum mos_cabs (fun a -> - h_two a l i j Spin.Alfa Spin.Beta *. - f_two a l k j Spin.Alfa Spin.Beta - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1111_1H_2Fb\n%!" ; - let m_1111_1H_2Fb = - array_3_init mo_num mo_num mo_num (fun j i k -> - sum mos_in (fun l -> m_1122_v2.{l,j,i,k} +. m_1122_v3.{l,j,i,k}) +. - sum mos_cabs (fun a -> - h_one a i Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Beta +. - h_two a j i j Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +. - h_one a j Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta +. - h_two a k j i Spin.Alfa Spin.Beta *. f_one a j Spin.Beta +. - sum mos_cabs (fun b -> - h_two b a j i Spin.Alfa Spin.Beta *. - f_two b a j k Spin.Alfa Spin.Beta - ) - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_1122_oa\n%!" ; - let m_1122_oa = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - if l > j then - sum mos_cabs (fun a -> - h_two a k j l Spin.Alfa Spin.Alfa *. - f_two a i j l Spin.Alfa Spin.Alfa - ) - else 0. - ) - in - - if Parallel.master then Printf.printf "Computing m_1122_o\n%!" ; - let m_1122_o = - array_4_init mo_num mo_num mo_num mo_num (fun l j i k -> - sum mos_cabs (fun a -> - h_two a k j l Spin.Alfa Spin.Beta *. - f_two a i j l Spin.Alfa Spin.Beta - ) - ) - in - - let f_1 ki kj = - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - let mos_novirt, mos_novirt' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logor i j) - |> Array.of_list - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logor i j) - |> Array.of_list - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - let mos_ij, mos_ij' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logand i j) - |> Array.of_list - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logand i j) - |> Array.of_list - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - let mos_i, mos_i' = - match s with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - - let mos_j, mos_j' = - match s with - | Spin.Alfa -> mos_a kj, mos_b kj - | Spin.Beta -> mos_b kj, mos_a kj - in - - let result = - m_1111_1H_1F.{i,k} +. - sum mos_ij (fun j -> - m_1111_1H_2Fa.{j,i,k} - +. sum mos_i (fun l -> m_1111_2Ha_2Fa.{l,j,i,k}) - +. sum mos_i' (fun l -> m_1111_2Ha_2Fb.{l,j,i,k}) - +. sum mos_j (fun l -> m_1121_2Ha_2Fa.{l,j,i,k}) - +. sum mos_j' (fun l -> m_1121_2Ha_2Fb.{l,j,i,k}) - -. sum mos_novirt (fun l -> m_1122_va.{l,j,i,k}) - -. sum mos_ij (fun l -> m_1122_oa.{l,j,i,k} ) - ) +. - sum mos_ij' (fun j -> - m_1111_1H_2Fb.{j,i,k} - +. sum mos_i (fun l -> m_1111_2Hb_2Fa.{l,j,i,k}) - +. sum mos_i' (fun l -> m_1111_2Hb_2Fb.{l,j,i,k}) - +. sum mos_j (fun l -> m_1121_2Hb_2Fb.{l,j,i,k}) - +. sum mos_j' (fun l -> m_1121_2Hb_2Fa.{l,j,i,k}) - -. sum mos_novirt (fun l -> m_1122_v2.{l,j,i,k}) - -. sum mos_novirt' (fun l -> m_1122_v3.{l,j,i,k}) - -. sum mos_ij (fun l -> m_1122_o.{l,j,i,k}) - ) - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - in - - if Parallel.master then Printf.printf "Computing m_2112_1H_2Fa\n%!" ; - let m_2112_1H_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_one a i Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +. - h_one a j Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Alfa +. - h_two a l i j Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +. - h_two a k j i Spin.Alfa Spin.Alfa *. f_one a l Spin.Alfa ) +. - sum mos_cabs (fun a -> - sum mos_in (fun m -> -. h_two m a j i Spin.Alfa Spin.Alfa *. - f_two m a k l Spin.Alfa Spin.Alfa) ) +. - sum mos_cabs (fun a -> - sum mos_cabs (fun b -> if b >= a then 0. else - h_two b a j i Spin.Alfa Spin.Alfa *. f_two b a l k Spin.Alfa Spin.Alfa - ) - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2112_1H_2Fb\n%!" ; - let m_2112_1H_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_one a i Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +. - h_one a j Spin.Alfa *. f_two a i l k Spin.Alfa Spin.Beta +. - h_two a l i j Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +. - h_two a k j i Spin.Alfa Spin.Beta *. f_one a l Spin.Alfa ) +. - sum mos_cabs (fun a -> - sum mos_in (fun m -> - h_two m a j i Spin.Alfa Spin.Beta *. f_two m a l k Spin.Alfa Spin.Beta +. - h_two m a i j Spin.Alfa Spin.Beta *. f_two m a k l Spin.Alfa Spin.Beta ) ) +. - sum mos_cabs (fun a -> - sum mos_cabs (fun b -> - h_two b a j i Spin.Alfa Spin.Beta *. f_two b a l k Spin.Alfa Spin.Beta - ) - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2112_2Ha_2Fa\n%!" ; - let m_2112_2Ha_2Fa = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> - h_two a n i n Spin.Alfa Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +. - h_two a n j n Spin.Alfa Spin.Alfa *. f_two a i l k Spin.Alfa Spin.Alfa - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2112_2Hb_2Fa\n%!" ; - let m_2112_2Hb_2Fa = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> - h_two a n i n Spin.Alfa Spin.Beta *. f_two a j k l Spin.Alfa Spin.Alfa +. - h_two a n j n Spin.Alfa Spin.Beta *. f_two a i l k Spin.Alfa Spin.Alfa - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2112_2Ha_2Fb\n%!" ; - let m_2112_2Ha_2Fb = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> - h_two a n i n Spin.Alfa Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +. - h_two a n j n Spin.Alfa Spin.Beta *. f_two a i l k Spin.Alfa Spin.Beta - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2121_2Ha_2Fa\n%!" ; - let m_2121_2Ha_2Fa = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> - h_two a l i j Spin.Alfa Spin.Alfa *. f_two a n k n Spin.Alfa Spin.Alfa +. - h_two a k j i Spin.Alfa Spin.Alfa *. f_two a n l n Spin.Alfa Spin.Alfa - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2121_2Hb_2Fa\n%!" ; - let m_2121_2Hb_2Fa = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> - h_two a l i j Spin.Alfa Spin.Beta *. f_two a n k n Spin.Alfa Spin.Alfa +. - h_two a k j i Spin.Alfa Spin.Beta *. f_two a n l n Spin.Alfa Spin.Beta - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2121_2Ha_2Fb\n%!" ; - let m_2121_2Ha_2Fb = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> - h_two a l i j Spin.Alfa Spin.Alfa *. f_two a n k n Spin.Alfa Spin.Beta +. - h_two a k j i Spin.Alfa Spin.Alfa *. f_two a n l n Spin.Alfa Spin.Beta - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2122_2Ha_2Fa_ij\n%!" ; - let m_2122_2Ha_2Fa_ij = - let s = Spin.Alfa in - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> - h_two a k i n s s *. f_two a j l n s s - +. h_two a l i n s s *. f_two a j n k s s - -. h_two a k j n s s *. f_two a i l n s s - -. h_two a l j n s s *. f_two a i n k s s - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2122_2Hb_2Fb_ij\n%!" ; - let m_2122_2Hb_2Fb_ij = - let s, s' = Spin.(Alfa, Beta) in - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> - h_two a k n i s s *. f_two a j n l s s' - +. h_two a l n j s s' *. f_two a i n k s s - -. h_two a k j n s s' *. f_two a i l n s s' - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2122_2Hb_2Fb_ij2\n%!" ; - let m_2122_2Hb_2Fb_ij2 = - let s, s' = Spin.(Alfa, Beta) in - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> - -. h_two a l i n s s' *. f_two a j k n s s' +. - (if n < j then - h_two a k n i s s' *. f_two a j n l s' s' - +. h_two a l n j s' s' *. f_two a i n k s s' - else - -. h_two a k n i s s' *. f_two j a n l s' s' - -. h_two a l j n s' s' *. f_two i a k n s s' - ) - ) - ) - in - - if Parallel.master then Printf.printf "Computing m_2122_2Ha_2Fa_ij2\n%!" ; - let m_2122_2Ha_2Fa_ij2 = - let s, s' = Spin.(Alfa, Beta) in - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> h_two a k n i s s' *. f_two a j n l s s') +. - sum mos_cabs (fun a -> h_two a l n j s s' *. f_two a i n k s s') -. - sum mos_cabs (fun a -> h_two a l n i s s' *. f_two a j n k s s') -. - sum mos_cabs (fun a -> h_two a k n j s s' *. f_two a i n l s s') - ) - in - - if Parallel.master then Printf.printf "Computing m_2122_2Ha_2Fa_nv\n%!" ; - let m_2122_2Ha_2Fa_nv = - let s = Spin.Alfa in - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> h_two a n i j s s *. f_two a n l k s s ) ) - in - - if Parallel.master then Printf.printf "Computing m_2122_2Hb_2Fb_nv\n%!" ; - let m_2122_2Hb_2Fb_nv = - let s, s' = Spin.(Alfa, Beta) in - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> -. h_two a n i j s s' *. f_two a n k l s s' ) ) - in - - if Parallel.master then Printf.printf "Computing m_2122_2Hb_2Fb_nv2\n%!" ; - let m_2122_2Hb_2Fb_nv2 = - let s, s' = Spin.(Alfa, Beta) in - array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l -> - sum mos_cabs (fun a -> -. h_two a n j i s s' *. f_two a n l k s s' ) ) - in - - let f_2 ki kj = - let i, j, k, l, s, s', phase = - match Excitation.of_det ki kj with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - let mos_i, mos_i' = - match s with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - - let mos_j, mos_j' = - match s with - | Spin.Alfa -> mos_a kj, mos_b kj - | Spin.Beta -> mos_b kj, mos_a kj - in - - let mos_ij, mos_ij' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logand i j) - |> Array.of_list - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logand i j) - |> Array.of_list - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - let mos_novirt, mos_novirt' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logor i j) - |> Array.of_list - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logor i j) - |> Array.of_list - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - let result = - if s = s' then - m_2112_1H_2Fa.{i,j,k,l} +. - sum mos_i (fun n -> m_2112_2Ha_2Fa.{n,i,j,k,l} ) +. - sum mos_i' (fun n -> m_2112_2Hb_2Fa.{n,i,j,k,l} ) +. - sum mos_j (fun n -> m_2121_2Ha_2Fa.{n,i,j,k,l} ) +. - sum mos_j' (fun n -> m_2121_2Ha_2Fb.{n,i,j,k,l} ) +. - sum mos_ij (fun n -> m_2122_2Ha_2Fa_ij.{n,i,j,k,l} ) +. - sum mos_ij' (fun n -> m_2122_2Ha_2Fa_ij2.{n,i,j,k,l} ) +. - sum mos_novirt (fun n -> m_2122_2Ha_2Fa_nv.{n,i,j,k,l} ) - else - m_2112_1H_2Fb.{i,j,k,l} +. - sum mos_i (fun n -> m_2112_2Ha_2Fb.{n,i,j,k,l} ) +. - sum mos_i' (fun n -> m_2112_2Ha_2Fb.{n,j,i,l,k} ) +. - sum mos_j (fun n -> m_2121_2Hb_2Fa.{n,i,j,k,l} ) +. - sum mos_j' (fun n -> m_2121_2Hb_2Fa.{n,j,i,l,k} ) +. - sum mos_novirt'(fun n -> m_2122_2Hb_2Fb_nv.{n,i,j,k,l} ) +. - sum mos_novirt (fun n -> m_2122_2Hb_2Fb_nv2.{n,i,j,k,l} )+. - sum mos_ij (fun n -> m_2122_2Hb_2Fb_ij.{n,i,j,k,l} ) +. - sum mos_ij' (fun n -> m_2122_2Hb_2Fb_ij2.{n,i,j,k,l} ) - in - - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - in - - let ncabs = Array.length mos_cabs in - let tmp_h = Mat.make0 ncabs 9 in - let tmp_f = Mat.make0 ncabs 9 in - - let f_3 ki kj = - let i, j, m, k, l, n, s1, s2, s3, phase = - match Excitation.of_det ki kj with - | Excitation.(Triple (phase, - { hole=h1 ; particle=p1 ; spin=s1 }, - { hole=h2 ; particle=p2 ; spin=s2 }, - { hole=h3 ; particle=p3 ; spin=s3 }) ) -> - h1, h2, h3, p1, p2, p3, s1, s2, s3, phase - | _ -> assert false - in - - let result = - let open Spin in - match s1, s2, s3 with - | Alfa, Alfa, Alfa - | Beta, Beta, Beta -> - (* - sum mos_cabs (fun a -> h_two a k i j s1 s2 *. f_two a m n l s3 s3) - +. sum mos_cabs (fun a -> h_two a n i j s1 s2 *. f_two a m l k s2 s3) - -. sum mos_cabs (fun a -> h_two a l i j s1 s2 *. f_two a m n k s3 s3) - +. sum mos_cabs (fun a -> h_two a l i m s1 s3 *. f_two a j n k s3 s2) - -. sum mos_cabs (fun a -> h_two a n i m s1 s3 *. f_two a j l k s2 s2) - -. sum mos_cabs (fun a -> h_two a k i m s1 s3 *. f_two a j n l s3 s2) - +. sum mos_cabs (fun a -> h_two a n j m s2 s3 *. f_two a i l k s2 s1) - +. sum mos_cabs (fun a -> h_two a k j m s2 s3 *. f_two a i n l s3 s1) - -. sum mos_cabs (fun a -> h_two a l j m s2 s3 *. f_two a i n k s3 s1) - - sum_schwarz k i j m n l s1 s2 s3 s3 - +. sum_schwarz n i j m l k s1 s2 s2 s3 - -. sum_schwarz l i j m n k s1 s2 s3 s3 - +. sum_schwarz l i m j n k s1 s3 s3 s2 - -. sum_schwarz n i m j l k s1 s3 s2 s2 - -. sum_schwarz k i m j n l s1 s3 s3 s2 - +. sum_schwarz n j m i l k s2 s3 s2 s1 - +. sum_schwarz k j m i n l s2 s3 s3 s1 - -. sum_schwarz l j m i n k s2 s3 s3 s1 - *) - Array.iteri (fun idx a -> tmp_f.{idx+1,7} <- f_two a i l k s2 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,5} <- f_two a j l k s2 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,2} <- f_two a m l k s2 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,9} <- f_two a i n k s3 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,4} <- f_two a j n k s3 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,3} <- f_two a m n k s3 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,8} <- f_two a i n l s3 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,6} <- f_two a j n l s3 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,1} <- f_two a m n l s3 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,3} <- if tmp_f.{idx+1,3} = 0. then 0. else -. h_two a l i j s1 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,1} <- if tmp_f.{idx+1,1} = 0. then 0. else h_two a k i j s1 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,2} <- if tmp_f.{idx+1,2} = 0. then 0. else h_two a n i j s1 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,5} <- if tmp_f.{idx+1,5} = 0. then 0. else -. h_two a n i m s1 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,6} <- if tmp_f.{idx+1,6} = 0. then 0. else -. h_two a k i m s1 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,4} <- if tmp_f.{idx+1,4} = 0. then 0. else h_two a l i m s1 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,9} <- if tmp_f.{idx+1,9} = 0. then 0. else -. h_two a l j m s2 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,7} <- if tmp_f.{idx+1,7} = 0. then 0. else h_two a n j m s2 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,8} <- if tmp_f.{idx+1,8} = 0. then 0. else h_two a k j m s2 s3) mos_cabs; - dot (Mat.as_vec tmp_h) (Mat.as_vec tmp_f) - | Alfa, Alfa, Beta - | Beta, Beta, Alfa -> - (* - sum mos_cabs (fun a -> h_two a l i j s1 s2 *. f_two a m k n s1 s3) - -. sum mos_cabs (fun a -> h_two a k i j s1 s2 *. f_two a m l n s1 s3) - +. sum mos_cabs (fun a -> h_two a l m j s3 s2 *. f_two a i n k s3 s1) - -. sum mos_cabs (fun a -> h_two a k m j s3 s2 *. f_two a i n l s3 s1) - +. sum mos_cabs (fun a -> h_two a k m i s3 s1 *. f_two a j n l s3 s2) - -. sum mos_cabs (fun a -> h_two a l m i s3 s1 *. f_two a j n k s3 s2) - +. sum mos_cabs (fun a -> h_two a n j m s2 s3 *. f_two a i l k s2 s1) - -. sum mos_cabs (fun a -> h_two a n i m s1 s3 *. f_two a j l k s2 s2) - - sum_schwarz l i j m k n s1 s2 s1 s3 - -. sum_schwarz k i j m l n s1 s2 s1 s3 - +. sum_schwarz l m j i n k s3 s2 s3 s1 - -. sum_schwarz k m j i n l s3 s2 s3 s1 - +. sum_schwarz k m i j n l s3 s1 s3 s2 - -. sum_schwarz l m i j n k s3 s1 s3 s2 - +. sum_schwarz n j m i l k s2 s3 s2 s1 - -. sum_schwarz n i m j l k s1 s3 s2 s2 - *) - Array.iteri (fun idx a -> tmp_f.{idx+1,1} <- f_two a m k n s1 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,2} <- f_two a m l n s1 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,4} <- f_two a i n l s3 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,5} <- f_two a j n l s3 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,3} <- f_two a i n k s3 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,6} <- f_two a j n k s3 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,7} <- f_two a i l k s2 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,8} <- f_two a j l k s2 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,1} <- if tmp_f.{idx+1,1} = 0. then 0. else h_two a l i j s1 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,2} <- if tmp_f.{idx+1,2} = 0. then 0. else -. h_two a k i j s1 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,3} <- if tmp_f.{idx+1,3} = 0. then 0. else +. h_two a l m j s3 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,4} <- if tmp_f.{idx+1,4} = 0. then 0. else -. h_two a k m j s3 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,5} <- if tmp_f.{idx+1,5} = 0. then 0. else +. h_two a k m i s3 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,6} <- if tmp_f.{idx+1,6} = 0. then 0. else -. h_two a l m i s3 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,7} <- if tmp_f.{idx+1,7} = 0. then 0. else +. h_two a n j m s2 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,8} <- if tmp_f.{idx+1,8} = 0. then 0. else -. h_two a n i m s1 s3) mos_cabs; - dot ~n:(8*ncabs) (Mat.as_vec tmp_h) (Mat.as_vec tmp_f) - | Alfa, Beta, Beta - | Beta, Alfa, Alfa -> - (* - sum mos_cabs (fun a -> h_two a l i j s1 s2 *. f_two a m k n s1 s3) - -. sum mos_cabs (fun a -> h_two a n i j s1 s2 *. f_two a m k l s1 s2) - +. sum mos_cabs (fun a -> h_two a n i m s1 s3 *. f_two a j k l s1 s2) - +. sum mos_cabs (fun a -> h_two a n j m s2 s3 *. f_two a i l k s2 s1) - -. sum mos_cabs (fun a -> h_two a l i m s1 s3 *. f_two a j k n s1 s3) - -. sum mos_cabs (fun a -> h_two a l j m s2 s3 *. f_two a i n k s3 s1) - +. sum mos_cabs (fun a -> h_two a k m i s3 s1 *. f_two a j n l s3 s2) - -. sum mos_cabs (fun a -> h_two a k j i s2 s1 *. f_two a m n l s3 s2) - - sum_schwarz l i j m k n s1 s2 s1 s3 - -. sum_schwarz n i j m k l s1 s2 s1 s2 - +. sum_schwarz n i m j k l s1 s3 s1 s2 - +. sum_schwarz n j m i l k s2 s3 s2 s1 - -. sum_schwarz l i m j k n s1 s3 s1 s3 - -. sum_schwarz l j m i n k s2 s3 s3 s1 - +. sum_schwarz k m i j n l s3 s1 s3 s2 - -. sum_schwarz k j i m n l s2 s1 s3 s2 - *) - Array.iteri (fun idx a -> tmp_f.{idx+1,6} <- f_two a i n k s3 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,4} <- f_two a i l k s2 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,5} <- f_two a j k n s1 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,1} <- f_two a m k n s1 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,2} <- f_two a m k l s1 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,3} <- f_two a j k l s1 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,7} <- f_two a j n l s3 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_f.{idx+1,8} <- f_two a m n l s3 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,1} <- if tmp_f.{idx+1,1} = 0. then 0. else h_two a l i j s1 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,2} <- if tmp_f.{idx+1,2} = 0. then 0. else -. h_two a n i j s1 s2) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,3} <- if tmp_f.{idx+1,3} = 0. then 0. else +. h_two a n i m s1 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,4} <- if tmp_f.{idx+1,4} = 0. then 0. else +. h_two a n j m s2 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,5} <- if tmp_f.{idx+1,5} = 0. then 0. else -. h_two a l i m s1 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,6} <- if tmp_f.{idx+1,6} = 0. then 0. else -. h_two a l j m s2 s3) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,7} <- if tmp_f.{idx+1,7} = 0. then 0. else +. h_two a k m i s3 s1) mos_cabs; - Array.iteri (fun idx a -> tmp_h.{idx+1,8} <- if tmp_f.{idx+1,8} = 0. then 0. else -. h_two a k j i s2 s1) mos_cabs; - dot ~n:(8*ncabs) (Mat.as_vec tmp_h) (Mat.as_vec tmp_f) - | Beta, Alfa, Beta - | Alfa, Beta, Alfa -> assert false - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - in - - let result = - { simulation ; aux_basis ; - f_0 ; f_1 ; f_2 ; f_3 - } - in - result - - - diff --git a/MOBasis/Localisation.ml b/MOBasis/Localisation.ml deleted file mode 100644 index 150b30a..0000000 --- a/MOBasis/Localisation.ml +++ /dev/null @@ -1,1198 +0,0 @@ -(* Algorithme de localisation des orbitales *) - -(* SOMMAIRE *) - -(* 0. Paramètres du calcul *) - -(* I. Définition des types *) - -(* II : Définition des fonctions pour la localisation *) - - (* 1. Définitions de base nécessaire pour la suite *) - (* 2. Fonction de calcul de la matrice des angles selon la méthode de Edminston *) - (* 3. Fonction calcul de la matrice des angles selon la méthode de Boys façon Edminston = NON FONCTIONNELLE *) - (* 4. Fonction de calcul de la matrice des angles selon la méthode de Boys *) - (* 5. Pattern matching : calcul de alpha et du critere D *) - (* 6. Norme d'une matrice *) - (* 7. Détermination de alpha_max et ses indices i et j. - Si alpha max > pi/2 on soustrait pi/2 à la matrice des alphas de manière récursive - Si alpha max < pi/2 on ajoute pi/2 à la matrice des alphas de manière récursive *) - (* 8. Matrice de rotation 2 par 2 *) - (* 9. Matrice de rotation n par n avec un angle fixe *) - (* 10. Fonction d'extraction des 2 vecteurs propres i et j de la matrice des OMs pour les mettres dans la matrice Ksi (n par 2) - pour appliquer R afin d'effectuer la rotation des orbitales *) (* {1,2} -> 1ere ligne, 2e colonne *) - (* 11. Fonction de calcul de ksi~ (matrice n par 2), nouvelle matrice par application de la matrice de rotation dans laquelle - on obtient les deux orbitales que l'on va réinjecter dans la matrice Phi*) - (* 12. Fonction pour la création de matrice intermédiaire pour supprimer i j et ajouter i~ et j~ *) - (* 13. Matrice intérmédiaire où les orbitales i et j ont été supprimées et remplacées par des 0, par soustraction de la matrice Phi - par la matrice *) - -(* III. Localisation des OMs *) - - (* 1. Boucle de calcul de la nouvelle matrice des coefficient après n rotation d'orbitales *) - (* 2. Fonction de localisation *) - -(* IV : Fonctions pour la séparation et le rassemblement des matrices *) - - (* 1. Fonction de création d'une liste d'entier à partir d'un vecteur de float*) - (* 2. Fonction créant une liste à partir des éléments manquant d'une autre liste, dans l'intervalle [1 ; n_mo] *) - (* 3. Fonction de séparation d'une matrice en 2 sous matrice, la première matrice correspondant aux colonnes de la matrice dont le numéro est présent - dans la liste et la seconde à celles dont le numéro de colonne n'est pas présent dans la liste *) - (* 4. Liste des OMs occupées *) - (* 5. Liste des OMs de coeur *) - (* 6. Fonction de creation d'une liste des OMs pi virtuelles *) - (* 7. Fonction de rassemblement de 2 matrices *) - -(* V. Calcul *) - - (* 1. Séparation des OMs -> m_occ : OMs occupées; m_vir : OMs vacantes *) - (* 1.1 Liste des OMs pi virtuelles *) - (* 2. Application d'une légère rotation d'un angle fixé aux OMs pour améliorer la convergence *) - (* 3. Légende *) - (* 4. Rotation des orbitales : localise localisation new_X / "methode" / epsilon = 1. si <1 diminue l'angle des rotations / nb itération / critère de convergence *) - (* 4.1 Fonction de localisation de toutes les orbitales virtuelles sans separation *) - (* 4.2 Fonction de localisation en separant les orbitales pi et sigma *) - (* 4.3 Fonction de localisation en separant les orbitales pi et sigma et les 10 dernières sigma *) - (* 4.4 Fonction séparant les orbitales pi, la premiere et la seconde moitié des orbitales sigma *) - (* 5. Rassemblement des occupées et des virtuelles *) - (* 5.1 Rassemblement des orbitales occupées (coeur et non coeur) *) - (* 5.2 Pattern matching du type de separation des orbitales virtuelles et rassemblement des orbitales occupées et virtuelles *) - -(* VI. Analyse *) - - (* 1. Fonction de calcul de l'extension spatiale des orbitales *) - (* 2. Fonction de tri par ordre croissant d'une liste *) - (* 3. Fonction de tri par ordre croissant de l'extension spatiale des orbitales *) - (* 4. Moyenne/variance/ecart-type/mediane de l'extension spatiale des orbitales *) - (* 5. Fonction d'affichage *) - -let methode = "Boys_er";; (* Method for th orbitals localization *) -let iteration = 1_000_000;; (* Maximum number of iteration for each localization *) -let cc = 10e-6;; (* Convergence criterion *) -let pre_angle = 0.001;; (* Rotation of the matrix with a small angle to improve the convergence *) -let epsilon = 1.;; (* Rotation angle = angle /. epsilon, default value : epsilon = 1. *) - -let x_end = 1;; (* Choice of the x_end for the pi/sigma/end separation, size of the second matrix with the sigma orbitals *) -(* !!! WARNING : even if you don't use this localization method, 0 < x_end < total number of sigma orbitals. - If you don't use this method, use the default value, x_end = 1 WARNING !!! *) - -(* Choice of the separation type of orbitals *) - -(* For valence ones *) -type type_separation = - | Sigma_pi - | Occ_vir - | Custom of int list list - -let string_of_separation = function - | Sigma_pi -> "Sigma/pi" - | Occ_vir -> "Occ/Vir" - | Custom _ -> "Custom" - -open Lacaml.D - -(* I. Types definitions *) - -type alphaij = { - alpha_max : float; - indice_ii : int; - indice_jj : int; -} - -type alphad = { - m_alpha : Mat.t; - d : float; -} - -let localize mo_basis separation = - - let simulation = MOBasis.simulation mo_basis in - let n_occ = - let elec = Simulation.electrons simulation - in - Electrons.n_alfa elec - in - let ao_basis = MOBasis.ao_basis mo_basis in - let n_core = - (* - (Nuclei.small_core @@ Simulation.nuclei @@ MOBasis.simulation mo_basis) / 2 - *) - 0 - in - let charge = Simulation.charge simulation - |>Charge.to_int - in - - (* II : Definition of the fonctions for the localization *) - - (* 1. Basic definitions *) - let m_C = MOBasis.mo_coef mo_basis in - let n_ao = Mat.dim1 m_C in - let pi = acos(-1.) in - - (* 2. Function for Edminston-Ruedenberg localization*) - (* Coefficient matrix n_ao x n_mo -> n_mo x n_mo matrix with angle(rad) between orbitals, Edminston localization criterion *) - (* matrix -> matrix, float *) - let f_alpha_er m_C = - - let ee_ints = AOBasis.ee_ints ao_basis in - let n_mo = Mat.dim2 m_C in - - let m_b12 = Mat.init_cols n_mo n_mo (fun i j -> 0.) in - let m_a12 = Mat.init_cols n_mo n_mo (fun i j -> 0.) in - let v_d = Vec.init n_mo (fun i -> 0.) in - - (* Tableaux temporaires *) - let m_pqr = - Bigarray.(Array3.create Float64 fortran_layout n_ao n_ao n_ao) - in - let m_qr_i = Mat.create (n_ao*n_ao) n_mo in - let m_ri_j = Mat.create (n_ao*n_mo) n_mo in - let m_ij_k = Mat.create (n_mo*n_mo) n_mo in - - Array.iter (fun s -> - (* Grosse boucle externe sur s *) - Array.iter (fun r -> - Array.iter (fun q -> - Array.iter (fun p -> - m_pqr.{p,q,r} <- ERI.get_phys ee_ints p q r s - ) (Util.array_range 1 n_ao) - ) (Util.array_range 1 n_ao) - ) (Util.array_range 1 n_ao); - - (* Conversion d'un tableau a 3 indices en une matrice nao x nao^2 *) - let m_p_qr = - Bigarray.reshape (Bigarray.genarray_of_array3 m_pqr) [| n_ao ; n_ao*n_ao |] - |> Bigarray.array2_of_genarray - in - - let m_qr_i = - (* (qr,i) = = \sum_p

C_{pi} *) - gemm ~transa:`T ~c:m_qr_i m_p_qr m_C - in - - let m_q_ri = - (* Transformation de la matrice (qr,i) en (q,ri) *) - Bigarray.reshape_2 (Bigarray.genarray_of_array2 m_qr_i) n_ao (n_ao*n_mo) - in - - let m_ri_j = - (* (ri,j) = = \sum_q C_{bj} *) - gemm ~transa:`T ~c:m_ri_j m_q_ri m_C - in - - let m_r_ij = - (* Transformation de la matrice (ri,j) en (r,ij) *) - Bigarray.reshape_2 (Bigarray.genarray_of_array2 m_ri_j) n_ao (n_mo*n_mo) - in - - let m_ij_k = - (* (ij,k) = = \sum_r C_{rk} *) - gemm ~transa:`T ~c:m_ij_k m_r_ij m_C - in - - let m_ijk = - (* Transformation de la matrice (ei,j) en (e,ij) *) - Bigarray.reshape (Bigarray.genarray_of_array2 m_ij_k) [| n_mo ; n_mo ; n_mo |] - |> Bigarray.array3_of_genarray - in - - Array.iter (fun j -> - Array.iter (fun i -> - m_b12.{i,j} <- m_b12.{i,j} +. m_C.{s,j} *. (m_ijk.{i,i,i} -. m_ijk.{j,i,j}); - m_a12.{i,j} <- m_a12.{i,j} +. m_ijk.{i,i,j} *. m_C.{s,j} -. - 0.25 *. ( (m_ijk.{i,i,i} -. m_ijk.{j,i,j}) *. m_C.{s,i} +. - (m_ijk.{j,j,j} -. m_ijk.{i,j,i}) *. m_C.{s,j}) - ) (Util.array_range 1 n_mo); - v_d.{j} <- v_d.{j} +. m_ijk.{j,j,j} *. m_C.{s,j} - ) (Util.array_range 1 n_mo) - ) (Util.array_range 1 n_ao); - - (Mat.init_cols n_mo n_mo ( fun i j -> - if i= j - then 0. - else if asin( m_b12.{i,j} /. sqrt(m_b12.{i,j}**2. +. m_a12.{i,j}**2.)) > 0. - then 0.25 *. acos( -. m_a12.{i,j} /. sqrt(m_b12.{i,j}**2. +. m_a12.{i,j}**2.)) - else -. 0.25 *. acos( -. m_a12.{i,j} /. sqrt(m_b12.{i,j}**2. +. m_a12.{i,j}**2.))) - ,Vec.sum v_d) - - in - - (* 3. Function for the Boys localization like the Edminston-Ruedenberg localization *) - (* Coefficient matrix n_ao x n_mo -> n_mo x n_mo matrix with angle between orbitals, localization Boys like ER criterion *) - (* Matrix -> matrix, float *) - let f_alpha_boys_er m_C = - - let multipoles = AOBasis.multipole ao_basis in - let n_mo = Mat.dim2 m_C in - let x = - Multipole.matrix_x multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let y = - Multipole.matrix_y multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let z = - Multipole.matrix_z multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let m_b12= - Mat.init_cols n_mo n_mo ( fun i j -> - (x.{i,i} -. x.{j,j}) *. x.{i,j} +. - (y.{i,i} -. y.{j,j}) *. y.{i,j} +. - (z.{i,i} -. z.{j,j}) *. z.{i,j}) - in - let m_a12 = - Mat.init_cols n_mo n_mo ( fun i j -> - let x' = x.{i,i} -. x.{j,j} - and y' = y.{i,i} -. y.{j,j} - and z' = z.{i,i} -. z.{j,j} in - x.{i,j} *. x.{i,j} +. - y.{i,j} *. y.{i,j} +. - z.{i,j} *. z.{i,j} -. - 0.25 *. (x'*.x' +. y'*.y' +. z'*.z') - ) - in - (Mat.init_cols n_mo n_mo ( fun i j -> - if i=j - then 0. - else - let w = atan2 m_b12.{i,j} m_a12.{i,j} in - if w >= 0. - then 0.25 *. (pi -. w) - else -. 0.25 *. (pi +. w) - ) , 0.5 *. (Vec.sum @@ Vec.init n_mo ( fun i -> - x.{i,i} *. x.{i,i} +. - y.{i,i} *. y.{i,i} +. - z.{i,i} *. z.{i,i} ) ) - ) - in -(* 4. Function for the original Boys localization *) -(* Coefficient matrix n_ao x n_mo -> (n_mo x n_mo matrix with angle between orbitals, localization criterion *) -(* Matrix -> matrix, float *) - let f_theta_boys m_C = - let multipoles = AOBasis.multipole ao_basis in - let n_mo = Mat.dim2 m_C - in - let x = - Multipole.matrix_x multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let y = - Multipole.matrix_y multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let z = - Multipole.matrix_z multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let r2 = - Multipole.matrix_r2 multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let m_b_0 = - Mat.init_cols n_mo n_mo (fun i j -> - r2.{i,i} +. r2.{j,j} -. - (x.{i,i} *. x.{i,i} +. x.{j,j} *. x.{j,j} +. - y.{i,i} *. y.{i,i} +. y.{j,j} *. y.{j,j} +. - z.{i,i} *. z.{i,i} +. z.{j,j} *. z.{j,j} ) - ) - in - let m_beta = - Mat.init_cols n_mo n_mo (fun i j -> - let x' = (x.{i,i} -. x.{j,j}) - and y' = (y.{i,i} -. y.{j,j}) - and z' = (z.{i,i} -. z.{j,j}) - in - x'*.x' +. y'*.y' +. z'*.z' -. - 4. *. ( x.{i,j} *. x.{i,j} +. - y.{i,j} *. y.{i,j} +. - z.{i,j} *. z.{i,j} ) - ) - in - let m_gamma = - Mat.init_cols n_mo n_mo (fun i j -> - 4. *. ( x.{i,j} *. (x.{i,i} -. x.{j,j}) +. - y.{i,j} *. (y.{i,i} -. y.{j,j}) +. - z.{i,j} *. (z.{i,i} -. z.{j,j}) ) - ) - in - let m_theta = Mat.init_cols n_mo n_mo (fun i j -> - if i <> j then - 0.25 *. atan2 m_gamma.{i,j} m_beta.{i,j} - else 0. - ) - in - let m_critere_B = Mat.init_cols n_mo n_mo (fun i j -> - 0.5 *. (m_b_0.{i,j} +. 0.25 *. ((1. -. cos(4. *. m_theta.{i,j})) *. m_beta.{i,j} +. sin(4. *. m_theta.{i,j}) *. m_gamma.{i,j}))) - - in - m_theta, Vec.sum(Mat.as_vec m_critere_B) - in - - (* Function to compute the new angle after rotation between the 2 orbitals j1 and j2, by the Boys like ER localization *) - (* n_mo x n_mo matrix with angle between orbitals, index of the orbital j1, index of the orbital j2 -> n_mo x 2 matrix with the new angles between j1 and j2, new localization criterion *) - (* matrix, integer, integer -> matrix, float *) - let f2_alpha_boys_er m_C j1 j2= - let multipoles = AOBasis.multipole ao_basis in - let n_mo = Mat.dim2 m_C - in - let x = - Multipole.matrix_x multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let y = - Multipole.matrix_y multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let z = - Multipole.matrix_z multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - - let m_b12 = - Mat.init_cols n_mo 2 (fun i j -> - if j = 1 then - (x.{i,i} -. x.{j1,j1}) *. x.{i,j1} +. - (y.{i,i} -. y.{j1,j1}) *. y.{i,j1} +. - (z.{i,i} -. z.{j1,j1}) *. z.{i,j1} - else - (x.{i,i} -. x.{j2,j2}) *. x.{i,j2} +. - (y.{i,i} -. y.{j2,j2}) *. y.{i,j2} +. - (z.{i,i} -. z.{j2,j2}) *. z.{i,j2} - ) - in - - let m_a12 = - Mat.init_cols n_mo 2 (fun i j -> - if j = 1 then - - let x' = (x.{i,i} -. x.{j1,j1}) - and y' = (y.{i,i} -. y.{j1,j1}) - and z' = (z.{i,i} -. z.{j1,j1}) in - x.{i,j1} *. x.{i,j1} +. - y.{i,j1} *. y.{i,j1} +. - z.{i,j1} *. z.{i,j1} -. - 0.25 *. (x' *. x' +. y' *. y' +. z' *. z' ) - - else - - let x' = (x.{i,i} -. x.{j2,j2}) - and y' = (y.{i,i} -. y.{j2,j2}) - and z' = (z.{i,i} -. z.{j2,j2}) in - x.{i,j2} *. x.{i,j2} +. - y.{i,j2} *. y.{i,j2} +. - z.{i,j2} *. z.{i,j2} -. - 0.25 *. (x' *. x' +. y' *. y' +. z' *. z' ) - ) - in - - (Mat.init_cols n_mo 2 ( fun i j -> - if i=j1 && j=1 - then 0. - else if i = j2 && j=2 - then 0. - else - let x = atan2 m_b12.{i,j} m_a12.{i,j} in - if x >= 0. then 0.25 *. (pi -. x) - else -. 0.25 *. (pi +. x) - ), - Vec.sum @@ Vec.init n_mo ( fun i -> - x.{i,i} *. x.{i,i} +. - y.{i,i} *. y.{i,i} +. - z.{i,i} *. z.{i,i} ) - ) - in - - (* Function to compute the new angle after rotation between the 2 orbitals j1 and j2, by the Boys localization *) - (* n_mo x n_mo matrix with angles between orbitals, index of the orbital j1, index of the orbital j2 -> n_mo x 2 matrix with the new angles between j1 and j2, new localization criterion *) - (* matrix, integer, integer -> matrix, float *) - let f2_theta_boys m_C j1 j2 = - let multipoles = AOBasis.multipole ao_basis in - let n_mo = Mat.dim2 m_C - in - let x = - Multipole.matrix_x multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let y = - Multipole.matrix_y multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let z = - Multipole.matrix_z multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - let r2 = - Multipole.matrix_r2 multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:m_C - in - - let m_beta = - Mat.init_cols n_mo 2 (fun i j -> - if j = 1 then - - let x' = (x.{i,i} -. x.{j1,j1}) - and y' = (y.{i,i} -. y.{j1,j1}) - and z' = (z.{i,i} -. z.{j1,j1}) in - x' *. x' +. y' *. y' +. z' *. z' - -. 4. *. ( x.{i,j1} *. x.{i,j1} +. - y.{i,j1} *. y.{i,j1} +. - z.{i,j1} *. z.{i,j1} ) - else - - let x' = (x.{i,i} -. x.{j2,j2}) - and y' = (y.{i,i} -. y.{j2,j2}) - and z' = (z.{i,i} -. z.{j2,j2}) in - x' *. x' +. y' *. y' +. z' *. z' - -. 4. *. ( x.{i,j2} *. x.{i,j2} +. - y.{i,j2} *. y.{i,j2} +. - z.{i,j2} *. z.{i,j2} ) - ) - in - - let m_gamma = - let gamma g = Mat.init_cols n_mo 2 (fun i j -> - if j = 1 - then 4. *. g.{i,j1} *. (g.{i,i} -. g.{j1,j1}) - else 4. *. g.{i,j2} *. (g.{i,i} -. g.{j2,j2})) - in Mat.add (gamma x) (Mat.add (gamma y) (gamma z)) - in - - let m_theta = Mat.init_cols n_mo 2 (fun i j -> - if i=j1 && j=1 - then 0. - else if i = j2 && j=2 - then 0. - else +. 0.25 *. atan2 m_gamma.{i,j} m_beta.{i,j}) - in - let m_critere_B = Vec.init n_mo (fun i -> - r2.{i,i} -. x.{i,i}*.x.{i,i} -. y.{i,i}*.y.{i,i} -. z.{i,i}*.z.{i,i}) - - in m_theta, Vec.sum( m_critere_B) - in - - (* 5. Pattern matching : choice of the localization method *) - (* The method, coefficient matrix n_ao x n_mo -> n_mo x n_mo matrix with the angle between orbitals using previous function, localization criterion *) - (* string, matrix -> matrix, float *) - - let m_alpha_d methode m_C = - - let alpha methode = - match methode with - | "Boys_er" - | "BOYS_ER" - | "boys_er" -> let alpha_boys , d_boys = f_alpha_boys_er m_C in {m_alpha = alpha_boys; d = d_boys} - | "Boys" - | "boys" - | "BOYS" -> let theta_boys, b_boys = f_theta_boys m_C in {m_alpha = theta_boys; d = b_boys} - | "ER" - | "er" -> let alpha_er , d_er = f_alpha_er m_C in {m_alpha = alpha_er; d = d_er} - | _ -> invalid_arg "Unknown method, please enter Boys or ER" - - in - alpha methode - in - - (* 5. Pattern matching : choice of the localization method to compute the n_mo x 2 new angles and not the n_mo x n_mo angles, after the rotation of i and j orbitals *) - (* The method, coefficient matrix n_ao x n_mo, index of the orbital i , index of the orbital j -> n_mo x 2 matrix with the new angle between orbitals i and j using previous function, new localization criterion *) - (* string, matrix, integer, integer -> matrix, float *) - let f_speed_alpha methode m_C indice_i indice_j = - let alpha_speed methode = - - match methode with - | "Boys_er" - | "boys_er" -> let m_alpha, critere_D = f2_alpha_boys_er m_C indice_i indice_j in {m_alpha = m_alpha; d = critere_D} - | "BOYS" -> let m_alpha, critere_D = f2_theta_boys m_C indice_i indice_j in {m_alpha = m_alpha; d = critere_D} - | _ -> invalid_arg "Unknown method, please enter Boys or ER" - - in - alpha_speed methode - - in - (* 6. Norm of a matrix *) - (* Matrix -> float *) - let norm m = - sqrt (Mat.syrk_trace m) - in - - (* 7. Calculation of the max angle[-pi/.4 , pi/.4] and its indexes i and j in the matrix *) - (* n_mo x n_mo matrix with angles between orbitals, coefficient matrix n_ao x n_mo, max number of iteration -> max angle, line location, column location *) - (* matrix, matrix, integer -> float, integer, integer *) - let rec new_m_alpha m_alpha m_C n_rec_alpha= - - let pi_2 = 0.5 *. pi in - let n_mo = Mat.dim2 m_C in - let alpha_m = - if n_rec_alpha == 0 then - m_alpha - else - Mat.init_cols n_mo n_mo (fun i j -> - if m_alpha.{i,j} >= pi_2 then - m_alpha.{i,j} -. pi_2 - else if m_alpha.{i,j} <= -. pi_2 then - m_alpha.{i,j} +. pi_2 - else m_alpha.{i,j} - ) - in - - (* Location of the max angle in the matrix *) - (* angle matrix -> location of the max element *) - (* matrix -> integer *) - let max_element alpha_m = - Mat.as_vec alpha_m - |> iamax - in - - (* Indexes i and j of the max angle *) - (* -> integer, integer *) - let indice_ii, indice_jj = - let max = max_element alpha_m - in - (max - 1) mod n_mo +1, (max - 1) / n_mo +1 - in - - (* Value of the max angle *) - (* angle matrix -> value of the max angle*) - (* matrix -> float *) - let alpha alpha_m = - let i = indice_ii in - let j = indice_jj - in - alpha_m.{i,j} - in - let alpha_max = alpha alpha_m - - in - if alpha_max < pi_2 then - {alpha_max; indice_ii; indice_jj} - else - new_m_alpha alpha_m m_C (n_rec_alpha-1) - in - - (* 8. Rotation matrix 2x2 *) - (* angle -> 2x2 rotation matrix *) - (* float -> matrix *) - let f_R alpha = - [| [| cos alpha ; -. sin alpha |] ; - [| sin alpha ; cos alpha |] |] - |> Mat.of_array - in - - (* 9. Rotation matrix nxn *) - (* Coefficient matrix n_ao x n_mo, angle -> new coefficient matrix n_ao x n_mo after a rotation with a small angle *) - (* matrix, float -> matrix *) - let rotate m_C angle= - - let n_mo = Mat.dim2 m_C in - - (* Antisymmetrization of the matrix and diagonal terms = 0, X *) - (* angle -> Antisymmetric matrix with this angle and diagonal terms = 0 *) - (* float -> matrix *) - let m_angle angle= - - Mat.init_cols n_mo n_mo (fun i j -> - if i = j - then 0. - else if i>j - then -. angle - else angle) - in - - let m = m_angle angle in - - (* Square of the matrix X² *) - (* -> X . X *) - (* -> matrix*) - let mm = gemm m m in - - (* Diagonalization of X² *) - (* diag = vector that contains the eigenvalues (-tau²), mm contains the eigenvectors (W) *) - (* -> vector *) - let diag = syev ~vectors:true mm in - - (* -tau² to tau² *) - (* -> vector that contains the eigenvalues (tau²) *) - (* -> vector *) - let square_tau= Vec.abs diag in - - (* tau² to tau *) - (* -> vector that contains the eigenvalues tau *) - (* -> vector *) - let tau = Vec.sqrt square_tau in - - (* Calculation of cos tau from the vector tau *) - (* -> cos(tau) *) - (* -> float *) - let cos_tau = Vec.cos tau in - - (* Matrix cos tau *) - (* -> matrix with diagonal terms cos(tau) and 0 also *) - (* -> matrix *) - let m_cos_tau = - - Mat.init_cols n_mo n_mo (fun i j -> - if i=j - then cos_tau.{i} - else 0.) - in - - (* Calcul of sin(tau) from the vector tau *) - let sin_tau = Vec.sin tau in - - (* Matrix sin tau *) - (* -> matrix with diagonal terms sin(tau) and 0 also *) - (* -> matrix *) - let m_sin_tau = - - Mat.init_cols n_mo n_mo (fun i j -> - if i=j - then sin_tau.{i} - else 0.) - in - - (* Calculation of the vector tau^-1 *) - (* -> vector tau^-1 *) - (* -> vector *) - let tau_1 = - - Vec.init n_mo (fun i -> - if tau.{i}<= 0.001 - then 1. - else 1. /. tau.{i}) - in - (* Calculation of the matrix tau^⁻1 *) - (* -> matrix tau^-1 *) - (* -> matrix *) - let m_tau_1 = - - Mat.init_cols n_mo n_mo (fun i j -> - if i=j - then tau_1.{i} - else 0.) - in - - (* W cos(tau) Wt *) - (* -> matrix *) - let a = gemm mm @@ gemm ~transb:`T m_cos_tau mm in - - (* W tau^-1 sin(tau) Wt X *) - (* -> matrix *) - let b = gemm mm @@ gemm m_tau_1 @@ gemm m_sin_tau @@ gemm ~transa:`T mm m in - - (* Sum of a + b -> Rotation matrix *) - (* -> Rotation matrix *) - (* -> matrix *) - let m_r = Mat.add a b - in - gemm m_C m_r - in - - (* Function to extract 2 vectors i and j in a matrix *) - (* Coefficient matrix n_ao x n_mo, index of the orbital i, index of the orbital j -> n_mo x 2 matrix with the eigenvetors i and j*) - (* matrix, integer, integer -> matrix *) - let f_Ksi indice_i indice_j m_C = - let n_ao = Mat.dim1 m_C - - in - Mat.init_cols n_ao 2 (fun i j -> - if j=1 - then m_C.{i,indice_i} - else m_C.{i,indice_j} ) - in - - (* Function to apply a rotation with a 2x2 rotation matrix on a n_mo x 2 matrix that contains i and j *) - (* 2x2 rotation matrix, n_mo x 2 eigenvetors(i and j) matrix -> n_mo x 2 new eigenvetors(i~ and j~) after rotation *) - (* matrix, matrix -> matrix *) - let f_Ksi_tilde m_R m_Ksi = gemm m_Ksi m_R - in - - (* Function to create intermediate coefficient matrix in order to delete the i j orbitals and add i~ j~ in the coefficient matrix *) - (* n_mo x 2 matrix with k and l orbitals, index of k, index of l, n_ao x n_mo matrix coefficient -> matrix where all terms are equal to 0 except the k and l columns that contain the eigenvetors k and l *) - (* matrix, integer, integer, matrix -> matrix *) - let f_k mat indice_i indice_j m_C = - let n_mo = Mat.dim2 m_C in - let n_ao = Mat.dim1 m_C - - in - Mat.init_cols n_ao n_mo (fun i j -> - if j=indice_i - then mat.{i,1} - else if j=indice_j - then mat.{i,2} - else 0.) - in - - (* Function to create a intermediate angle matrix in order to delete all the previous angle between i and all the other orbitals, j and all the other orbitals. - And add the new angles between these orbitals *) - (* n_mo x 2 matrix with angles between k and all the other orbitals l and all the other orbitals, index of k, index of l, coefficent matrix n_ao x n_mo -> matrix where all terms are equal to 0 except the k and l lines and columns that contains the angles between the orbitals *) - (* matrix, integer, integer, matrix -> matrix *) - let f_k_angle mat indice_i indice_j m_C = - let n_mo = Mat.dim2 m_C - - in - Mat.init_cols n_mo n_mo (fun i j -> - if j=indice_i - then mat.{i,1} - else if j=indice_j - then mat.{i,2} - else if i = indice_i - then -. mat.{j,1} - else if i = indice_j - then -. mat.{j,2} - else 0.) - in - - (* Intermediate matrix where the i and j orbitals are equal to 0 *) - (* Coefficient matrix n_ao x n_mo, matrix where terms are equal to 0 except the k and l columns that contain the eigenvetors k and l *) - (* matrix, matrix -> matrix *) - let f_interm m_C mat = - - Mat.sub m_C mat - in - - (* Function to compute the new coefficient matrix after a rotation between 2 orbitals *) - (* coefficient matrix n_ao x n_mo, angle matrix, parameter -> new coefficient matrix n_ao x n_mo *) - let new_m_C m_C m_alpha epsilon = - - (* alphaij contains the max angle of the angle matrix and the indexes *) - let n_rec_alpha = 10 in - let alphaij = new_m_alpha m_alpha m_C n_rec_alpha in - - (* Value of the angle *) - let alpha = (alphaij.alpha_max) *. epsilon in - - (* Localtion of the max angle *) - let indice_i = alphaij.indice_ii in - let indice_j = alphaij.indice_jj in - - (* Rotation matrix *) - let m_R = f_R alpha in - - (* Matrix with i and j orbitals *) - let m_Ksi = f_Ksi indice_i indice_j m_C in - - (* Matrix with the new i~ and j~ orbitals *) - let m_Ksi_tilde = f_Ksi_tilde m_R m_Ksi in - - (* Matrix to delete the i and j orbitals in the coefficient matrix *) - let m_Psi = f_k m_Ksi indice_i indice_j m_C in - - (* Matrix to add the i~ and j~ orbitals in the coefficient matrix *) - let m_Psi_tilde = f_k m_Ksi_tilde indice_i indice_j m_C in - - (* Coefficient matrix without the i and j orbitals *) - let m_interm = f_interm m_C m_Psi - - in - (* Matrice after rotation, max angle, index i, index j *) - (Mat.add m_Psi_tilde m_interm, alpha, indice_i, indice_j) - in - - (* Function to compute the new angle matrix after one rotation between 2 orbitals *) - (* Previous angle matrix n_mo x n_mo, new coefficient matrix n_ao x n_mo, previous angle matrix, index of the orbital i, index of the orbital j -> new angle matrix, new localization criterion *) - (* matrix, matrix, matrix, integer, integer -> matrix, float *) - let m_alpha m_new_m_C prev_m_alpha indice_i indice_j = - - (* n_mo x 2 matrix that contains the new angles between i,j with the other orbitals *) - let speed_alphad = f_speed_alpha methode m_new_m_C indice_i indice_j in - - (* New localization criterion *) - let critere_D = speed_alphad.d in - - (* Previous angles *) - let ksi_angle = f_Ksi indice_i indice_j prev_m_alpha in - - (* New angles *) - let ksi_angle_tilde = speed_alphad.m_alpha in - - (* Matrix to delete the previous angles *) - let psi_angle = f_k_angle ksi_angle indice_i indice_j m_new_m_C in - - (* Matrix to add the new angles *) - let psi_tilde_angle = f_k_angle ksi_angle_tilde indice_i indice_j m_new_m_C in - - (* Matrix without the angles between i, j and the orbitals *) - let m_interm = f_interm prev_m_alpha psi_angle - - in - (* New angle matrix, new localization criterion *) - (Mat.add m_interm psi_tilde_angle, critere_D) - in - - - -(* III. Localization *) - - (* Loop to compute the new coefficient matrix avec n orbital rotations *) - (* Coefficeient matrix n_ao x n_mo, localization method, parameter, max number of iteration, previous localization criterion, previous angle matrix, convergence criterion -> new coefficient matrix after n orbital rotations *) - (* matrix, string, float, integer, float, matrix, float -> matrix *) - let rec localisation m_C methode epsilon n prev_critere_D prev_m_alpha cc = - - if n == 0 - then m_C - else - - (* New coefficient matrix after one rotation *) - let m_new_m_C, alpha_max, indice_i, indice_j = new_m_C m_C prev_m_alpha epsilon in - - (* New angle matrix after one rotation *) - let m_alpha, critere_D = m_alpha m_new_m_C prev_m_alpha indice_i indice_j in - - (* Matrix norm, angle average *) - - let norm_alpha = norm m_alpha in - let moyenne_alpha = norm_alpha /. (float_of_int((Mat.dim1 m_C)* (Mat.dim2 m_C))) in - let alpha = alpha_max /. epsilon in - - Printf.printf "%i %f %f %f %f\n%!" (iteration-n) critere_D alpha norm_alpha moyenne_alpha; - - (* Convergence criterion *) - if alpha_max**2. < cc**2. - then m_new_m_C - else localisation m_new_m_C methode epsilon (n-1) critere_D m_alpha cc - in - - (* 2. Localization function *) - let localise localisation m_C methode epsilon n cc = - - let alphad = m_alpha_d methode m_C in - let prev_m_alpha = alphad.m_alpha in - let prev_critere_D = 0. - in - localisation m_C methode epsilon n prev_critere_D prev_m_alpha cc - in - -(* IV : Functions to split and assemble matrix *) - - - (* Function to create a list from the missing elements of an other list*) - (* Coefficient matrix n_ao x n_mo, list -> list of missing element of the previous list *) - (* matrix, integer list -> integer list *) - let miss_elem mat lst = - - let n_mo = Mat.dim2 mat in - Util.list_range 1 n_mo - |> List.map (fun i -> - if List.mem i lst - then 0 - else i) - |> List.filter (fun x -> x > 0) - in - - (* Function to split a matrix in 2 matrix, the first matrix corresponds to the column number whose number is in the list, the second matrix corresponds to the column which are not in the list *) - (* Coefficient matrix n_ao x n_mo, list -> matrix, matrix *) - (* matrix, integer list -> matrix, matrix*) - let split_mat mat lst = - - let vec_of_mat = Mat.to_col_vecs mat in - let f a = vec_of_mat.(a-1) in - let vec_list_1 = List.map f lst in - let list_2 = miss_elem mat lst in - let vec_list_2 = List.map f list_2 - in - (Mat.of_col_vecs_list vec_list_1,Mat.of_col_vecs_list vec_list_2) - in - - - (* Function to create a list of pi MOs *) - (* Coefficient matrix n_ao x n_mo -> list of pi orbitals *) - (* matrix -> integer list *) - let list_pi mat = - let n_mo = Mat.dim2 mat in - let m_pi = Mat.init_cols n_ao (n_mo+1) ( fun i j -> - if j=1 && abs_float m_C.{i,j} < 1.e-8 - then 0. - else if j=1 - then abs_float m_C.{i,j} - else if abs_float mat.{i,j-1} < 1.e-8 - then 0. - else abs_float mat.{i,j-1}) - in - let vec = Mat.to_col_vecs m_pi in - (* TODO gemv *) - let vec_dot = Vec.init (Mat.dim2 mat) (fun i -> dot vec.(0) vec.(i)) in - let list_pi = - Util.list_range 1 (Mat.dim2 mat) - |> List.map (fun i -> if abs_float vec_dot.{i} = 0. then i else 0) - in - let rec remove x = function - | [] -> [] - | var :: tail -> if var = x - then remove x tail - else var :: (remove x tail) - in - remove 0 list_pi - in - - (* Function to assemble to matrix with the same number of line *) - (* Coefficient matrix n_ao x n, coefficient matrix n_ao x m -> Coefficient matrix n_ao x (n+m) *) - (* matrix, matrix -> matrix*) - let assemble mat_1 mat_2 = - - let v_mat_1 = Mat.to_col_vecs mat_1 in - let v_mat_2 = Mat.to_col_vecs mat_2 in - let m = Array.append v_mat_1 v_mat_2 - in - Mat.of_col_vecs m - in - -(* V. Calculation *) - - (* 1. Caption *) - let text = "Method : " ^ methode ^ "\nSeparation type : " - ^ (string_of_separation separation) - ^ "\nMax number of iterations : " ^ string_of_int(iteration) ^ "\ncc : " - ^ string_of_float(cc)^"\nepsilon : "^string_of_float(epsilon)^"\ncharge : " - ^ string_of_int(charge)^"\nRotation pre angle : "^string_of_float(pre_angle) - in - let caption = "Criterion max_angle norm_angle average_angle" - in - Printf.printf "%s\n" ""; - Printf.printf "%s\n" "Orbital localization"; - Printf.printf "%s\n" ""; - Printf.printf "%s\n" text; - Printf.printf "%s\n" ""; - Printf.printf "%s\n" caption; - Printf.printf "%s\n" ""; - - (* Localization function *) - (* Coefficient matrix n_ao x n_mo -> localized coefficient matrix n_ao x n_mo *) - (* matrix -> matrix *) - let f_localise mat = - - if Mat.dim2 mat = 0 - then Printf.printf "%s\n" "0 orbital, no localization"; - - let new_mat = - if Mat.dim2 mat = 0 - then mat - else rotate mat pre_angle - in - if Mat.dim2 mat = 0 - then new_mat - else localise localisation new_mat methode epsilon iteration cc - in - - - (* Localization function with n separations expressed as a list of lists of - orbital indices *) - let f_loc_list mat list_of_lists = - let vec_list = Mat.to_col_vecs mat in - list_of_lists - |> List.map (fun lst -> - lst - |> List.map (fun col -> vec_list.(col-1)) - |> Mat.of_col_vecs_list - |> f_localise - |> Mat.to_col_vecs_list - ) - |> List.concat - |> Mat.of_col_vecs_list - in - - let n_mo = Mat.dim2 m_C in - let list_full = Util.list_range 1 n_mo in - let list_core = Util.list_range 1 n_core in - let list_pi = list_pi m_C in - let list_sigma = List.filter (fun i -> not (List.mem i list_pi)) list_full in - let list_pi_occ = List.filter (fun i -> i > n_core && i <= n_occ) list_pi in - let list_sigma_occ = List.filter (fun i -> i > n_core && i <= n_occ) list_sigma in - let list_pi_vir = List.filter (fun i -> i > n_occ) list_pi in - let list_sigma_vir = List.filter (fun i -> i > n_occ) list_sigma in - let list_occ = Util.list_range (n_core+1) n_occ in - let list_vir = Util.list_range (n_occ+1) n_mo in - - Printf.printf "Orbital lists:"; - Printf.printf "\nCore: ["; - List.iter (fun i -> Printf.printf "%d," i) list_core; - Printf.printf "\b]\nOccupied: ["; - List.iter (fun i -> Printf.printf "%d," i) list_occ; - Printf.printf "\b]\nVirtual: ["; - List.iter (fun i -> Printf.printf "%d," i) list_vir; - Printf.printf "\b]\nSigma occ: ["; - List.iter (fun i -> Printf.printf "%d," i) list_sigma_occ; - Printf.printf "\b]\nPi occ: ["; - List.iter (fun i -> Printf.printf "%d," i) list_pi_occ; - Printf.printf "\b]\nSigma vir: ["; - List.iter (fun i -> Printf.printf "%d," i) list_sigma_vir; - Printf.printf "\b]\nPi vir: ["; - List.iter (fun i -> Printf.printf "%d," i) list_pi_vir; - Printf.printf "\b]\n\n"; - - (* Separation of the occupied and virtual MOs, valence and core MOs *) - let m_occ , m_vir = split_mat m_C list_occ in - let m_core, m_occu = split_mat m_occ list_core in - - let m_assemble_loc = - let list_of_lists = - match separation with - | Occ_vir -> [ list_core ; list_occ ; list_vir ] - | Sigma_pi -> [ list_core ; list_sigma_occ ; list_pi_occ ; list_pi_vir ; list_sigma_vir ] - | Custom l -> l - in - f_loc_list m_C list_of_lists - in - - let m_assemble_occ, m_assemble_vir = split_mat m_assemble_loc list_occ in - let m_assemble_core, m_assemble_occu = split_mat m_assemble_occ list_core in - - (* VI. Analysis *) - - (* Function to compute the spatial extent of MOs *) - (* Coefficient matrix n_ao x n_mo -> vector where the i th element is equal to the spatial extent of the i th orbital *) - (* Matrix -> vector *) - let distrib mat= - if Mat.dim1 mat = 0 - then Mat.as_vec mat - else - (let multipoles = AOBasis.multipole ao_basis in - let n_mo = Mat.dim2 mat in - let x = - Multipole.matrix_x multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:mat - in - let y = - Multipole.matrix_y multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:mat - in - let z = - Multipole.matrix_z multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:mat - in - let r2 = - Multipole.matrix_r2 multipoles - |> MOBasis.mo_matrix_of_ao_matrix ~mo_coef:mat - in - Vec.init n_mo (fun i -> - r2.{i,i} -. x.{i,i}*.x.{i,i} -. y.{i,i}*.y.{i,i} -. z.{i,i}*.z.{i,i})) - in - - (* Sorting function *) - (* tri insertion (<) list -> list in ascending order *) - (* parameter, list -> list *) - let rec insere comparaison elem liste = match liste with - | [] -> elem::[] - | tete::queue -> if comparaison elem tete - then elem :: liste - else tete :: insere comparaison elem queue - in - let rec tri_insertion comp = function - | [] -> [] - | tete::queue -> insere comp tete (tri_insertion comp queue) - in - - (* Sorting function to sort orbital spatial extent by ascending order *) - (* coefficient matrix n_ao x n_mo -> matrix n_ao x 2, first column corresponds to the spatial extent in function of the MOs number, the second column corresponds to the spatial extent in ascending order *) - (* matrix -> matrix *) - let m_distribution mat = - let vec_distrib= distrib mat in - let list_tri_distrib = tri_insertion (<) (Vec.to_list vec_distrib) in - let vec_tri_distrib = Vec.of_list list_tri_distrib - in - Mat.init_cols (Vec.dim vec_distrib) 2 (fun i j -> - if j=1 - then vec_distrib.{i} - else vec_tri_distrib.{i}) - - in - - (* Average/variance/standart deviation/median of spatial extent *) - (* Function to compute the average *) - let f_average mat = - if Mat.dim1 mat = 0 - then 0. - else Vec.sum (distrib mat) /. float_of_int(Vec.dim (distrib mat)) - in - - (* Function to compute the variance *) - let f_variance mat = - if (Vec.dim (distrib mat)) <= 1 - then 0. - else Vec.sum(Vec.init (Vec.dim (distrib mat)) (fun i -> - ((distrib mat).{i}-. (f_average mat))**2.)) /. float_of_int(Vec.dim (distrib mat) - 1) - in - - (* Function to compute the standard deviation *) - let f_stand_dev mat = - if (Vec.dim (distrib mat)) <= 1 - then 0. - else sqrt(abs_float(f_variance mat)) - in - - (* Fonction de calcul de la mediane *) - let f_median mat = - if (Vec.dim (distrib mat)) = 0 - then 0. - else - let vec_distrib= distrib mat in - let list_tri_distrib = tri_insertion (<) (Vec.to_list vec_distrib) in - let vec_tri_distrib = Vec.of_list list_tri_distrib - in - if (Vec.dim vec_distrib) mod 2 = 0 - then (vec_tri_distrib.{(Vec.dim vec_distrib)/2} +. vec_tri_distrib.{((Vec.dim vec_distrib)/2)+1}) /. 2. - else vec_tri_distrib.{int_of_float(float_of_int(Vec.dim vec_distrib)/. 2.) + 1} - in - (* Display function *) - (* Coefficient matrix n_ao x n_mo -> string *) - (* matrix -> string *) - let analyse mat = - let average = f_average mat in - let variance = f_variance mat in - let stand_dev = f_stand_dev mat in - let median = f_median mat - in - "Average : "^string_of_float(average)^"; Median : "^string_of_float(median)^"; Variance : "^string_of_float(variance)^"; Standard deviation : "^string_of_float(stand_dev) - in - - (* Display the numer of MOs *) - (* Coefficient matrix n_ao x n_mo -> string *) - (* matrix -> string *) - let n_orb mat = "Number of molecular orbitals : "^string_of_int(Mat.dim2 mat) in - - (* Display *) - Printf.printf "%s\n" ""; - Printf.printf "%s\n" (n_orb m_C); - Printf.printf "%s %i\n" "Number of pi orbitals : " (List.length list_pi ); - Printf.printf "%s %i\n" "Number of occupied pi orbitals : " (List.length list_pi_occ ); - Printf.printf "%s %i\n" "Number of virtual pi orbitals : " (List.length list_pi_vir ); - Printf.printf "%s %i\n" "Number of sigma orbitals : " (List.length list_sigma); - Printf.printf "%s %i\n" "Number of occupied sigma orbitals : " (List.length list_sigma_occ); - Printf.printf "%s %i\n" "Number of virtual sigma orbitals : " (List.length list_sigma_vir); - - Printf.printf "%s\n" ""; - - Printf.printf "%s %s\n" "All MOs before the localization" (analyse m_C); - Printf.printf "%s %s\n" "All MOs after the localization" (analyse m_assemble_loc); - Printf.printf "%s\n" ""; - Util.debug_matrix "Distribution of the spatial extent, before localization / sorting before localization / after localization / sorting after localization" - (assemble(m_distribution m_C) (m_distribution m_assemble_loc)); - - Printf.printf "%s\n" ""; - Printf.printf "%s %s\n" "Occupied orbitals : " (n_orb m_occ); - Printf.printf "%s %s\n" "Occupied orbitals before localization" (analyse m_occ); - Printf.printf "%s %s\n" "Occupied orbitals after localization" (analyse m_assemble_occ); - Printf.printf "%s\n" ""; - - Printf.printf "%s\n" ""; - Printf.printf "%s %s\n" "Core orbitals : " (n_orb m_core); - Printf.printf "%s %s\n" "Core orbitalses before localization : " (analyse m_core); - Printf.printf "%s %s\n" "Core orbitals after localization : " (analyse m_assemble_core); - Printf.printf "%s\n" ""; - - Printf.printf "%s\n" ""; - Printf.printf "%s %s\n" "Valence orbitals : " (n_orb m_occu); - Printf.printf "%s %s\n" "Valence orbitals before localization : " (analyse m_occu); - Printf.printf "%s %s\n" "Valence rbitals after localization : " (analyse m_assemble_occu); - Printf.printf "%s\n" ""; - - Printf.printf "%s\n" ""; - Printf.printf "%s %s\n" "Virtual orbitals : " (n_orb m_vir); - Printf.printf "%s %s\n" "Virtual orbitals before localization : " (analyse m_vir); - Printf.printf "%s %s\n" "Virtual orbitals after localization : " (analyse m_assemble_vir); - Printf.printf "%s\n" ""; - -m_assemble_loc - - diff --git a/MOBasis/MOBasis.ml b/MOBasis/MOBasis.ml deleted file mode 100644 index 5aaee9a..0000000 --- a/MOBasis/MOBasis.ml +++ /dev/null @@ -1,202 +0,0 @@ -open Lacaml.D -open Util -open Constants - -(** One-electron orthogonal basis set, corresponding to Molecular Orbitals. *) - -module HF = HartreeFock -module Si = Simulation - -type mo_type = - | RHF | ROHF | UHF | CASSCF | Projected - | Natural of string - | Localized of string - -type t = - { - simulation : Simulation.t; (* Simulation which produced the MOs *) - mo_type : mo_type; (* Kind of MOs (RHF, CASSCF, Localized...) *) - mo_occupation : Vec.t; (* Occupation numbers *) - mo_coef : Mat.t; (* Matrix of the MO coefficients in the AO basis *) - eN_ints : NucInt.t lazy_t; (* Electron-nucleus potential integrals *) - ee_ints : ERI.t lazy_t; (* Electron-electron potential integrals *) - f12_ints : F12.t lazy_t; (* F12 integrals *) - kin_ints : KinInt.t lazy_t; (* Kinetic energy integrals *) - one_e_ints : Mat.t lazy_t; (* Kinetic energy integrals *) - } - - -let size t = - Mat.dim2 t.mo_coef - -let simulation t = t.simulation -let mo_type t = t.mo_type -let ao_basis t = Si.ao_basis t.simulation -let mo_occupation t = t.mo_occupation -let mo_coef t = t.mo_coef -let eN_ints t = Lazy.force t.eN_ints -let ee_ints t = Lazy.force t.ee_ints -let kin_ints t = Lazy.force t.kin_ints -let two_e_ints t = Lazy.force t.ee_ints -let f12_ints t = Lazy.force t.f12_ints -let one_e_ints t = Lazy.force t.one_e_ints - - -let mo_energies t = - let m_C = mo_coef t in - let f = - let m_N = Mat.of_diag @@ mo_occupation t in - let m_P = x_o_xt m_N m_C in - match t.mo_type with - | RHF -> Fock.make_rhf ~density:m_P (ao_basis t) - | Projected - | ROHF -> (Mat.scal 0.5 m_P; - Fock.make_uhf ~density_same:m_P ~density_other:m_P (ao_basis t)) - | _ -> failwith "Not implemented" - in - let m_F0 = Fock.fock f in - xt_o_x m_F0 m_C - |> Mat.copy_diag - - -let mo_matrix_of_ao_matrix ~mo_coef ao_matrix = - xt_o_x ~x:mo_coef ~o:ao_matrix - - -let ao_matrix_of_mo_matrix ~mo_coef ~ao_overlap mo_matrix = - let sc = gemm ao_overlap mo_coef in - x_o_xt ~x:sc ~o:mo_matrix - - -let make ~simulation ~mo_type ~mo_occupation ~mo_coef () = - let ao_basis = - Si.ao_basis simulation - in - let eN_ints = lazy ( - AOBasis.eN_ints ao_basis - |> NucInt.matrix - |> mo_matrix_of_ao_matrix ~mo_coef - |> NucInt.of_matrix - ) - and kin_ints = lazy ( - AOBasis.kin_ints ao_basis - |> KinInt.matrix - |> mo_matrix_of_ao_matrix ~mo_coef - |> KinInt.of_matrix - ) - and ee_ints = lazy ( - AOBasis.ee_ints ao_basis - |> ERI.four_index_transform mo_coef - ) - and f12_ints = lazy ( - AOBasis.f12_ints ao_basis - |> F12.four_index_transform mo_coef - ) - in - let one_e_ints = lazy ( - Mat.add (NucInt.matrix @@ Lazy.force eN_ints) - (KinInt.matrix @@ Lazy.force kin_ints) ) - in - { simulation ; mo_type ; mo_occupation ; mo_coef ; - eN_ints ; ee_ints ; kin_ints ; one_e_ints ; - f12_ints } - - -let values t point = - let c = mo_coef t in - let a = AOBasis.values (Simulation.ao_basis t.simulation) point in - gemv ~trans:`T c a - -let of_hartree_fock hf = - let mo_coef = HF.eigenvectors hf in - let simulation = HF.simulation hf in - let mo_occupation = HF.occupation hf in - let mo_type = - match HF.kind hf with - | HartreeFock.RHF -> RHF - | HartreeFock.ROHF -> ROHF - | HartreeFock.UHF -> UHF - in - make ~simulation ~mo_type ~mo_occupation ~mo_coef () - - -let of_mo_basis simulation other = - - let mo_coef = - let basis = Simulation.ao_basis simulation in - let basis_other = ao_basis other in - let m_S = - Overlap.(matrix @@ of_basis_pair - (AOBasis.basis basis) - (AOBasis.basis basis_other) ) - in - let m_X = AOBasis.ortho basis in - (* Project other vectors in the current basis *) - let m_C = - gemm m_S @@ mo_coef other - in - (* Append dummy vectors to the input vectors *) - let result = - let vecs = Mat.to_col_vecs m_X in - Array.iteri (fun i v -> if (i < Array.length vecs) then vecs.(i) <- v) - (Mat.to_col_vecs m_C) ; - Mat.of_col_vecs vecs - in - (* Gram-Schmidt Orthonormalization *) - gemm m_X @@ (Util.qr_ortho @@ gemm ~transa:`T m_X result) - |> Util.remove_epsilons - |> Conventions.rephase - in - - let mo_occupation = - let occ = mo_occupation other in - Vec.init (Mat.dim2 mo_coef) (fun i -> - if (i <= Vec.dim occ) then occ.{i} - else 0.) - in - make ~simulation ~mo_type:Projected ~mo_occupation ~mo_coef () - - - - - -let pp ?(start=1) ?(finish=0) ppf t = - let open Lacaml.Io in - let rows = Mat.dim1 t.mo_coef - and cols = Mat.dim2 t.mo_coef - in - let finish = - match finish with - | 0 -> cols - | x -> x - in - - let rec aux first = - - if (first > finish) then () - else - begin - Format.fprintf ppf "@[@[@[%s@;" "Eigenvalues:"; - - Array.iteri (fun i x -> - if (i+1 >= first) && (i+1 <= first+4 ) then - Format.fprintf ppf "%12f@ " x) - (Vec.to_array @@ mo_energies t); - - Format.fprintf ppf "@]@;"; - Format.fprintf ppf "@[%a@]" - (Lacaml.Io.pp_lfmat - ~row_labels: - (Array.init rows (fun i -> Printf.sprintf "%d " (i + 1))) - ~col_labels: - (Array.init (min 5 (cols-first+1)) (fun i -> Printf.sprintf "-- %d --" (i + first) )) - ~print_right:false - ~print_foot:false - () ) (lacpy ~ac:first ~n:(min 5 (cols-first+1)) (t.mo_coef)) ; - Format.fprintf ppf "@]@;@;@]"; - (aux [@tailcall]) (first+5) - end - in - aux start - - diff --git a/MOBasis/MOBasis.mli b/MOBasis/MOBasis.mli deleted file mode 100644 index d918cfc..0000000 --- a/MOBasis/MOBasis.mli +++ /dev/null @@ -1,89 +0,0 @@ -(** Data structure to represent the molecular orbitals. - - The MO indices start from 1. - -*) - -open Lacaml.D - -type mo_type = - | RHF | ROHF | UHF | CASSCF | Projected - | Natural of string - | Localized of string - - -type t - -(** {1 Accessors} *) - -val simulation : t -> Simulation.t -(** Simulation which produced the MOs *) - -val mo_type : t -> mo_type -(** Kind of MOs (RHF, CASSCF, Localized...) *) - -val ao_basis : t -> AOBasis.t -(** Matrix of the MO coefficients in the AO basis *) - -val mo_occupation : t -> Vec.t -(** Occupation numbers *) - -val mo_coef : t -> Mat.t -(** Molecular orbitcal coefficients *) - -val eN_ints : t -> NucInt.t -(** Electron-nucleus potential integrals *) - -val ee_ints : t -> ERI.t -(** Electron-electron repulsion integrals *) - -val kin_ints : t -> KinInt.t -(** Kinetic energy integrals *) - -val one_e_ints : t -> Mat.t -(** One-electron integrals {% $\hat{T} + V$ %} *) - -val two_e_ints : t -> ERI.t -(** Electron-electron repulsion integrals *) - -val f12_ints : t -> F12.t -(** F12 integrals *) - -val size : t -> int -(** Number of molecular orbitals in the basis *) - -val mo_energies : t -> Vec.t -(** Fock MO energies *) - -val values : t -> Coordinate.t -> Vec.t -(** Values of the MOs evaluated at a given coordinate. *) - -(** {1 Creators} *) - -val make : simulation:Simulation.t -> - mo_type:mo_type -> - mo_occupation:Vec.t -> - mo_coef:Mat.t -> - unit -> t -(** Function to build a data structure representing the molecular orbitals. *) - -val of_hartree_fock : HartreeFock.t -> t -(** Build MOs from a Restricted Hartree-Fock calculation. *) - -val of_mo_basis : Simulation.t -> t -> t -(** Project the MOs of the other basis on the current one. *) - - -val mo_matrix_of_ao_matrix : mo_coef:Mat.t -> Mat.t -> Mat.t -(** Build a matrix in MO basis from a matrix in AO basis. *) - -val ao_matrix_of_mo_matrix : mo_coef:Mat.t -> ao_overlap:Mat.t -> Mat.t -> Mat.t -(** Build a matrix in AO basis from a matrix in MO basis. *) - - - -(** {1 Printers} *) - -val pp : ?start:int -> ?finish:int -> Format.formatter -> t -> unit - - diff --git a/MOBasis/MOClass.ml b/MOBasis/MOClass.ml deleted file mode 100644 index ef15c83..0000000 --- a/MOBasis/MOClass.ml +++ /dev/null @@ -1,140 +0,0 @@ -type mo_class = - | Core of int (* Always doubly occupied *) - | Inactive of int (* With 0,1 or 2 holes *) - | Active of int (* With 0,1 or 2 holes or particles *) - | Virtual of int (* With 0,1 or 2 particles *) - | Deleted of int (* Always unoccupied *) - | Auxiliary of int (* Auxiliary basis function *) - -type t = mo_class list - - -let pp_mo_class ppf = function - | Core i -> Format.fprintf ppf "@[Core %d@]" i - | Inactive i -> Format.fprintf ppf "@[Inactive %d@]" i - | Active i -> Format.fprintf ppf "@[Active %d@]" i - | Virtual i -> Format.fprintf ppf "@[Virtual %d@]" i - | Deleted i -> Format.fprintf ppf "@[Deleted %d@]" i - | Auxiliary i -> Format.fprintf ppf "@[Auxiliary %d@]" i - -let pp ppf t = - Format.fprintf ppf "@[[@,"; - let rec aux = function - | [] -> Format.fprintf ppf "]@]" - | x :: [] -> Format.fprintf ppf "%a@,]@]" pp_mo_class x - | x :: rest -> ( Format.fprintf ppf "%a@,;@," pp_mo_class x; aux rest ) - in - aux t - - - -let of_list t = t - -let to_list t = t - - -let core_mos t = - List.filter_map (fun x -> - match x with - | Core i -> Some i - | _ -> None) t - - -let inactive_mos t = - List.filter_map (fun x -> - match x with - | Inactive i -> Some i - | _ -> None ) t - - -let active_mos t = - List.filter_map (fun x -> - match x with - | Active i -> Some i - | _ -> None ) t - - -let virtual_mos t = - List.filter_map (fun x -> - match x with - | Virtual i -> Some i - | _ -> None ) t - - -let deleted_mos t = - List.filter_map (fun x -> - match x with - | Deleted i -> Some i - | _ -> None ) t - - -let auxiliary_mos t = - List.filter_map (fun x -> - match x with - | Auxiliary i -> Some i - | _ -> None ) t - - -let mo_class_array t = - let sze = List.length t + 1 in - let result = Array.make sze (Deleted 0) in - List.iter (fun c -> - match c with - | Core i -> result.(i) <- Core i - | Inactive i -> result.(i) <- Inactive i - | Active i -> result.(i) <- Active i - | Virtual i -> result.(i) <- Virtual i - | Deleted i -> result.(i) <- Deleted i - | Auxiliary i -> result.(i) <- Auxiliary i - ) t; - result - - -let fci ~frozen_core mo_basis = - let mo_num = MOBasis.size mo_basis in - let ncore = (Nuclei.small_core @@ Simulation.nuclei @@ MOBasis.simulation mo_basis) / 2 in - of_list ( - if frozen_core then - List.concat [ - Util.list_range 1 ncore - |> List.map (fun i -> Core i) ; - Util.list_range (ncore+1) mo_num - |> List.map (fun i -> Active i) - ] - else - Util.list_range 1 mo_num - |> List.map (fun i -> Active i) - ) - - -let cas_sd mo_basis ~frozen_core n m = - let mo_num = MOBasis.size mo_basis in - let n_alfa = MOBasis.simulation mo_basis |> Simulation.electrons |> Electrons.n_alfa in - let n_beta = MOBasis.simulation mo_basis |> Simulation.electrons |> Electrons.n_beta in - let n_unpaired = n_alfa - n_beta in - let n_alfa_in_cas = (n - n_unpaired)/2 + n_unpaired in - let last_inactive = n_alfa - n_alfa_in_cas in - let last_active = last_inactive + m in - let ncore = - if frozen_core then - (Nuclei.small_core @@ Simulation.nuclei @@ MOBasis.simulation mo_basis) / 2 - |> min last_inactive - else 0 - in - of_list ( - List.concat [ - if ncore > 0 then - Util.list_range 1 ncore - |> List.map (fun i -> Core i) - else - [] ; - Util.list_range (ncore+1) last_inactive - |> List.map (fun i -> Inactive i) ; - Util.list_range (last_inactive+1) last_active - |> List.map (fun i -> Active i) ; - Util.list_range (last_active+1) mo_num - |> List.map (fun i -> Virtual i) - ] - ) - - diff --git a/MOBasis/MOClass.mli b/MOBasis/MOClass.mli deleted file mode 100644 index 4c6e29f..0000000 --- a/MOBasis/MOClass.mli +++ /dev/null @@ -1,58 +0,0 @@ -(** CI Classes of MOs : active, inactive, etc *) - -type mo_class = - | Core of int (* Always doubly occupied *) - | Inactive of int (* With 0,1 or 2 holes *) - | Active of int (* With 0,1 or 2 holes or particles *) - | Virtual of int (* With 0,1 or 2 particles *) - | Deleted of int (* Always unoccupied *) - | Auxiliary of int (* Function of the auxiliary basis set *) - -type t - -(** Creation *) -val of_list : mo_class list -> t - -val to_list : t -> mo_class list - -val fci : frozen_core:bool -> MOBasis.t -> t -(** Creates the MO classes for FCI calculations : all [Active]. The - [n] lowest MOs are [Core] if [frozen_core = true]. -*) - -val cas_sd: MOBasis.t -> frozen_core:bool -> int -> int -> t -(** [cas_sd mo_basis n m ] creates the MO classes for CAS(n,m) + SD - calculations. lowest MOs are [Core], then all the next MOs are [Inactive], - then [Active], then [Virtual]. -*) - - -val core_mos : t -> int list -(** Returns a list containing the indices of the core MOs. *) - -val active_mos : t -> int list -(** Returns a list containing the indices of the active MOs. *) - -val virtual_mos : t -> int list -(** Returns a list containing the indices of the virtual MOs. *) - -val inactive_mos : t -> int list -(** Returns a list containing the indices of the inactive MOs. *) - -val deleted_mos : t -> int list -(** Returns a list containing the indices of the deleted MOs. *) - -val auxiliary_mos : t -> int list -(** Returns a list containing the indices of the auxiliary MOs. *) - -val mo_class_array : t -> mo_class array -(** Returns an array [a] such that [a.(i)] returns the class of MO [i]. - As the MO indices start from [1], the array has an extra zero entry - that should be ignored. *) - -(** {2 Printers} *) - -val pp_mo_class : Format.formatter -> mo_class -> unit - -val pp : Format.formatter -> t -> unit - diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..448d954 --- /dev/null +++ b/Makefile @@ -0,0 +1,23 @@ +# Frontend to dune. + +.PHONY: default build install uninstall test clean + +default: build + +build: + dune build + +test: + dune runtest -f + +install: + dune install + +uninstall: + dune uninstall + +clean: + dune clean +# Optionally, remove all files/folders ignored by git as defined +# in .gitignore (-X). + git clean -dfXq diff --git a/Makefile.include b/Makefile.include deleted file mode 100644 index 86b4787..0000000 --- a/Makefile.include +++ /dev/null @@ -1,65 +0,0 @@ -.NOPARALLEL: - -LIBS= -PKGS= -OCAMLBUILD=ocamlbuild -j 0 -cflags $(ocamlcflags) -lflags $(ocamllflags) $(ocamldocflags) -ocamlopt $(ocamloptflags) $(mpi) - -MLLFILES=$(filter-out $(wildcard _build/*), $(wildcard */*.mll) $(wildcard *.mll)) Utils/math_functions.c -MLYFILES=$(filter-out $(wildcard _build/*), $(wildcard */*.mly) $(wildcard *.mly)) -MLFILES= $(filter-out $(wildcard Parallel_*/*) $(wildcard _build/*), $(wildcard */*.ml) $(wildcard *.ml) ) -MLIFILES=$(filter-out $(wildcard Parallel_*/*) $(wildcard _build/*), $(wildcard */*.mli) $(wildcard *.mli) ) - -ALL_NATIVE=$(patsubst %.ml,%.native,$(wildcard run_*.ml)) -ALL_BYTE=$(patsubst %.ml,%.byte,$(wildcard run_*.ml)) -ALL_EXE=$(ALL_BYTE) $(ALL_NATIVE) lib - -.PHONY: default doc - - -default: $(ALL_EXE) - -tests: run_tests.native - -lib: _build/Utils/Util.cma - -_build/Utils/Util.cma: _build/Utils/Util.cmo _build/Utils/math_functions.o - ocamlmklib -o _build/Utils/Util _build/Utils/Util.cmo _build/Utils/math_functions.o - -QCaml.odocl: $(MLIFILES) - ls $(MLIFILES) | sed "s/\.mli//" > QCaml.odocl - -doc: QCaml.odocl - $(OCAMLBUILD) QCaml.docdir/index.html -use-ocamlfind $(PKGS) - -%.inferred.mli: $(MLFILES) - $(OCAMLBUILD) $*.inferred.mli -use-ocamlfind $(PKGS) - mv _build/$*.inferred.mli . - -%.byte: $(MLFILES) $(MLIFILES) $(MLLFILES) $(MLYFILES) - rm -f -- $* - $(OCAMLBUILD) $*.byte -use-ocamlfind $(PKGS) - -%.native: $(MLFILES) $(MLIFILES) $(MLLFILES) $(MLYFILES) - rm -f -- $* - $(OCAMLBUILD) $*.native -use-ocamlfind $(PKGS) - ln -s $*.native $* - -%.p.native: $(MLFILES) $(MLIFILES) $(MLLFILES) $(MLYFILES) - rm -f -- $* - $(OCAMLBUILD) $*.p.native -use-ocamlfind $(PKGS) - -%.p.byte: $(MLFILES) $(MLIFILES) $(MLLFILES) $(MLYFILES) - rm -f -- $* - $(OCAMLBUILD) -ocamlc ocamlcp $*.byte -use-ocamlfind $(PKGS) - -clean: - rm -f QCaml.odocl *.byte *.native && $(OCAMLBUILD) -clean - -debug: run_integrals.native - ./debug.sh - -install: $(ALL_NATIVE) - cp run_hartree_fock.native $(bin)/run_hartree_fock - -uninstall: - rm -f $(bin)/run_hartree_fock diff --git a/Notebooks/F12_fast.ipynb b/Notebooks/F12_fast.ipynb deleted file mode 100644 index 8e47f32..0000000 --- a/Notebooks/F12_fast.ipynb +++ /dev/null @@ -1,8123 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Test of F12 matrix elements" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "heading_collapsed": true - }, - "source": [ - "## Initialization" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "ExecuteTime": { - "end_time": "2020-03-30T10:15:59.908500Z", - "start_time": "2020-03-30T10:15:58.731Z" - }, - "hidden": true, - "init_cell": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val png_image : string -> unit = \n" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "- : unit = ()\n", - "Findlib has been successfully loaded. Additional directives:\n", - " #require \"package\";; to load a package\n", - " #list;; to list the available packages\n", - " #camlp4o;; to load camlp4 (standard syntax)\n", - " #camlp4r;; to load camlp4 (revised syntax)\n", - " #predicates \"p,q,...\";; to set these predicates\n", - " Topfind.reset();; to force that packages will be reloaded\n", - " #thread;; to enable threads\n", - "\n", - "- : unit = ()\n" - ] - }, - { - "data": { - "text/plain": [ - "val png_image : string -> Jupyter_notebook.display_id = \n" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let png_image = print_endline ;;\n", - "\n", - "(* --------- *)\n", - "\n", - "#cd \"/home/scemama/QCaml\";;\n", - "#use \"topfind\";;\n", - "#require \"jupyter.notebook\";;\n", - "\n", - "let png_image name = \n", - " Jupyter_notebook.display_file ~base64:true \"image/png\" (\"Notebooks/images/\"^name)\n", - ";;\n", - "\n", - "#require \"lacaml.top\";;\n", - "#require \"alcotest\";;\n", - "#require \"str\";;\n", - "#require \"bigarray\";;\n", - "#require \"zarith\";;\n", - "#require \"getopt\";;\n", - "#directory \"_build\";;\n", - "#directory \"_build/Basis\";;\n", - "#directory \"_build/CI\";;\n", - "#directory \"_build/MOBasis\";;\n", - "#directory \"_build/Nuclei\";;\n", - "#directory \"_build/Parallel\";;\n", - "#directory \"_build/Perturbation\";;\n", - "#directory \"_build/SCF\";;\n", - "#directory \"_build/Utils\";;" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "### Modules" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": { - "ExecuteTime": { - "end_time": "2020-03-30T10:16:00.033900Z", - "start_time": "2020-03-30T10:15:58.750Z" - }, - "hidden": true, - "init_cell": true - }, - "outputs": [], - "source": [ - "#load \"Constants.cmo\";;\n", - "#load_rec \"Util.cma\";;\n", - "#load_rec \"Matrix.cmo\";;\n", - "#load_rec \"Simulation.cmo\";;\n", - "#load_rec \"Spindeterminant.cmo\";;\n", - "#load_rec \"Determinant.cmo\";;\n", - "#load_rec \"HartreeFock.cmo\";;\n", - "#load_rec \"MOBasis.cmo\";;\n", - "#load_rec \"F12CI.cmo\";;" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "### Printers" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": { - "ExecuteTime": { - "end_time": "2020-03-30T10:16:00.095400Z", - "start_time": "2020-03-30T10:15:58.760Z" - }, - "hidden": true, - "init_cell": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val pp_mo : Format.formatter -> MOBasis.t -> unit = \n" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "#install_printer AngularMomentum.pp_string ;;\n", - "#install_printer Basis.pp ;;\n", - "#install_printer Charge.pp ;;\n", - "#install_printer Coordinate.pp ;;\n", - "#install_printer Vector.pp;;\n", - "#install_printer Matrix.pp;;\n", - "#install_printer Util.pp_float_2darray;;\n", - "#install_printer Util.pp_float_array;;\n", - "#install_printer Util.pp_matrix;;\n", - "#install_printer HartreeFock.pp ;;\n", - "#install_printer Fock.pp ;;\n", - "#install_printer MOClass.pp ;;\n", - "let pp_mo ppf t = MOBasis.pp ~start:1 ~finish:0 ppf t ;;\n", - "#install_printer pp_mo;;\n", - "(*\n", - "#install_printer DeterminantSpace.pp;;\n", - "*)\n", - "#install_printer SpindeterminantSpace.pp;;\n", - "#install_printer Bitstring.pp;;\n", - "\n", - "(* --------- *)\n", - "\n", - "open Lacaml.D\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "heading_collapsed": true - }, - "source": [ - "## Run" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "### Simulation\n" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": { - "ExecuteTime": { - "end_time": "2020-03-30T10:16:00.287500Z", - "start_time": "2020-03-30T10:15:58.769Z" - }, - "hidden": true, - "init_cell": true, - "scrolled": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val basis_filename : string = \"/home/scemama/qp2/data/basis/6-31g\"\n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val aux_basis_filename : string = \"/home/scemama/qp2/data/basis/cc-pvdz\"\n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val nuclei : Nuclei.t = [|(Element.C, 0.0000 0.0000 0.0000)|]\n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val frozen_core : bool = false\n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val multiplicity : int = 1\n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val state : int = 1\n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val f12 : F12factor.t =\n", - " {F12factor.expo_s = 1.;\n", - " gaussian =\n", - " {GaussianOperator.coef_g =\n", - " [ -0.314400 -0.303700 -0.168100 -0.098110 -0.060240 -0.037260 ];\n", - " expo_g =\n", - " [ 0.220900 1.004000 3.622000 12.160000 45.870000 254.400000 ];\n", - " expo_g_inv =\n", - " [ 4.526935 0.996016 0.276091 0.082237 0.021801 0.003931 ]}}\n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val basis : Basis.t =\n", - " \n", - " Atomic Basis set\n", - " ----------------\n", - "\n", - "-----------------------------------------------------------------------\n", - " # Angular Coordinates (Bohr) Exponents Coefficients\n", - " Momentum X Y Z\n", - "-----------------------------------------------------------------------\n", - " 1-3 S 0.0000 0.0000 0.0000 3.04752488e+03 1.83473713e-03\n", - " 4.57369518e+02 1.40373228e-02\n", - " 1.03948685e+02 6.88426223e-02\n", - " 2.92101553e+01 2.32184443e-01\n", - " 9.28666296e+00 4.67941348e-01\n", - " 3.16392696e+00 3.62311985e-01\n", - " \n", - " 7.86827235e+00 -1.19332420e-01\n", - " 1.88128854e+00 -1.60854152e-01\n", - " 5.44249258e-01 1.14345644e+00\n", - " \n", - " 1.68714478e-01 1.00000000e+00\n", - " \n", - " \n", - "-----------------------------------------------------------------------\n", - " 4-9 P 0.0000 0.0000 0.0000 7.86827235e+00 6.89990666e-02\n", - " 1.88128854e+00 3.16423961e-01\n", - " 5.44249258e-01 7.44308291e-01\n", - " \n", - " 1.68714478e-01 1.00000000e+00\n", - " \n", - " \n", - "-----------------------------------------------------------------------\n", - "\n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val aux_basis : Basis.t =\n", - " \n", - " Atomic Basis set\n", - " ----------------\n", - "\n", - "-----------------------------------------------------------------------\n", - " # Angular Coordinates (Bohr) Exponents Coefficients\n", - " Momentum X Y Z\n", - "-----------------------------------------------------------------------\n", - " 1-6 S 0.0000 0.0000 0.0000 3.04752488e+03 1.83473713e-03\n", - " 4.57369518e+02 1.40373228e-02\n", - " 1.03948685e+02 6.88426223e-02\n", - " 2.92101553e+01 2.32184443e-01\n", - " 9.28666296e+00 4.67941348e-01\n", - " 3.16392696e+00 3.62311985e-01\n", - " \n", - " 7.86827235e+00 -1.19332420e-01\n", - " 1.88128854e+00 -1.60854152e-01\n", - " 5.44249258e-01 1.14345644e+00\n", - " \n", - " 1.68714478e-01 1.00000000e+00\n", - " \n", - " 6.66500000e+03 6.92000000e-04\n", - " 1.00000000e+03 5.32900000e-03\n", - " 2.28000000e+02 2.70770000e-02\n", - " 6.47100000e+01 1.01718000e-01\n", - " 2.10600000e+01 2.74740000e-01\n", - " 7.49500000e+00 4.48564000e-01\n", - " 2.79700000e+00 2.85074000e-01\n", - " 5.21500000e-01 1.52040000e-02\n", - " 1.59600000e-01 -3.19100000e-03\n", - " \n", - " 6.66500000e+03 -1.46000000e-04\n", - " 1.00000000e+03 -1.15400000e-03\n", - " 2.28000000e+02 -5.72500000e-03\n", - " 6.47100000e+01 -2.33120000e-02\n", - " 2.10600000e+01 -6.39550000e-02\n", - " 7.49500000e+00 -1.49981000e-01\n", - " 2.79700000e+00 -1.27262000e-01\n", - " 5.21500000e-01 5.44529000e-01\n", - " 1.59600000e-01 5.80496000e-01\n", - " \n", - " 1.59600000e-01 1.00000000e+00\n", - " \n", - " \n", - "-----------------------------------------------------------------------\n", - " 4-15 P 0.0000 0.0000 0.0000 7.86827235e+00 6.89990666e-02\n", - " 1.88128854e+00 3.16423961e-01\n", - " 5.44249258e-01 7.44308291e-01\n", - " \n", - " 1.68714478e-01 1.00000000e+00\n", - " \n", - " 9.43900000e+00 3.81090000e-02\n", - " 2.00200000e+00 2.09480000e-01\n", - " 5.45600000e-01 5.08557000e-01\n", - " 1.51700000e-01 4.68842000e-01\n", - " \n", - " 1.51700000e-01 1.00000000e+00\n", - " \n", - " \n", - "-----------------------------------------------------------------------\n", - " 19-24 D 0.0000 0.0000 0.0000 5.50000000e-01 1.00000000e+00\n", - " \n", - " \n", - "-----------------------------------------------------------------------\n", - "\n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val charge : int = 0\n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val simulation : Simulation.t = \n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let basis_filename = \"/home/scemama/qp2/data/basis/6-31g\" \n", - "let aux_basis_filename = \"/home/scemama/qp2/data/basis/cc-pvdz\" \n", - "let nuclei = Nuclei.of_zmt_string \"c\" \n", - "let frozen_core = false\n", - "let multiplicity = 1\n", - "let state = 1\n", - "\n", - "let f12 = F12factor.gaussian_geminal 1.0 \n", - "let basis = Basis.of_nuclei_and_basis_filenames ~f12 ~nuclei [basis_filename] \n", - "let aux_basis = Basis.of_nuclei_and_basis_filenames ~nuclei (basis_filename :: aux_basis_filename :: []) \n", - "let charge = 0 \n", - "\n", - "\n", - "let simulation =\n", - " Simulation.make \n", - " ~charge ~multiplicity ~nuclei\n", - " ~cartesian:true\n", - " basis\n" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "ExecuteTime": { - "end_time": "2020-03-30T10:16:00.298200Z", - "start_time": "2020-03-30T10:15:58.778Z" - }, - "hidden": true, - "init_cell": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val n_elec_alfa : int = 3\n", - "val n_elec_beta : int = 3\n", - "val n_elec : int = 6\n" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let n_elec_alfa, n_elec_beta, n_elec = \n", - " let e = Simulation.electrons simulation in\n", - " Electrons.(n_alfa e, n_beta e, n_elec e)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "### Hartree-Fock" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "ExecuteTime": { - "end_time": "2020-03-30T10:16:00.474000Z", - "start_time": "2020-03-30T10:15:58.786Z" - }, - "hidden": true, - "init_cell": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "15 significant shell pairs computed in 0.030632 seconds\n", - "1\n", - "2\n", - "3\n", - "6\n", - "Computed ERIs in 0.141639 seconds\n", - "MOs =\n", - "\n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0.995189 -0.236456 -0 -0 0\n", - " 2 0.0272807 0.573253 -0 -0 0\n", - " 3 -0.00753288 0.50151 -0 -6.64951E-16 0\n", - " ... ... ... ... ...\n", - " 7 -0 -0 -0.0346136 -0.103467 0.874392\n", - " 8 -0 6.53154E-16 0.374215 -0.0232294 0.0788015\n", - " 9 -0 7.4731E-16 0.00656013 0.779165 0.118461\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 0 0.0649867 -0 -0\n", - " 2 -1.35345E-15 -1.62901 -0 -0\n", - " 3 7.04525E-16 1.63955 -0 -0\n", - " ... ... ... ...\n", - " 7 -0.106576 -0 0.122185 -0.823344\n", - " 8 1.15222 -0 0.0274317 -0.074201\n", - " 9 0.0201988 -0 -0.920122 -0.111546\n", - " \n" - ] - }, - { - "data": { - "text/plain": [ - "val hf : HartreeFock.t = \n", - "======================================================================\n", - " Restricted Hartree-Fock \n", - "======================================================================\n", - "\n", - " ------------------------------------------------------------\n", - " # HF energy Convergence HOMO-LUMO\n", - " ------------------------------------------------------------\n", - " 1 -36.54848150 7.4861e-01 0.2723\n", - " ------------------------------------------------------------\n", - "\n", - "\n", - " ============================================================\n", - " One-electron energy -52.6699343629\n", - " Kinetic 42.4526846308\n", - " Potential -95.1226189937\n", - " -------------------------------------------------------- \n", - " Two-electron energy 16.1214528647\n", - " Coulomb 21.8535626014\n", - " Exchange -5.7321097367\n", - " -------------------------------------------------------- \n", - " HF HOMO 0.8237527941\n", - " HF LUMO 8.2337246898\n", - " HF LUMO-LUMO 7.4099718957\n", - " -------------------------------------------------------- \n", - " Electronic energy -36.5484814981\n", - " Nuclear repulsion 0.0000000000\n", - " Hartree-Fock energy -36.5484814981\n", - " ============================================================\n", - " \n", - "\n" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mo_basis : MOBasis.t =\n", - " Eigenvalues: -11.127416 -0.632049 -0.269831 0.131526 0.151773 \n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0.995189 -0.236456 -0 -0 0\n", - " 2 0.0272807 0.573253 -0 -0 0\n", - " 3 -0.00753288 0.50151 -0 -6.64951E-16 0\n", - " ... ... ... ... ...\n", - " 7 -0 -0 -0.0346136 -0.103467 0.874392\n", - " 8 -0 6.53154E-16 0.374215 -0.0232294 0.0788015\n", - " 9 -0 7.4731E-16 0.00656013 0.779165 0.118461\n", - " \n", - " Eigenvalues: 0.786913 0.828232 0.869410 0.849164 \n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 0 0.0649867 -0 -0\n", - " 2 -1.35345E-15 -1.62901 -0 -0\n", - " 3 7.04525E-16 1.63955 -0 -0\n", - " ... ... ... ...\n", - " 7 -0.106576 -0 0.122185 -0.823344\n", - " 8 1.15222 -0 0.0274317 -0.074201\n", - " 9 0.0201988 -0 -0.920122 -0.111546\n", - " \n", - " \n" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let hf = HartreeFock.make ~guess:`Hcore ~max_scf:1 simulation ;;\n", - "\n", - "let mo_basis = MOBasis.of_hartree_fock hf" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "heading_collapsed": true - }, - "source": [ - "# FCI-F12" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "## Common functions" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "ExecuteTime": { - "end_time": "2020-03-30T10:16:00.507100Z", - "start_time": "2020-03-30T10:15:58.791Z" - }, - "hidden": true, - "init_cell": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val f12 : F12factor.t =\n", - " {F12factor.expo_s = 1.;\n", - " gaussian =\n", - " {GaussianOperator.coef_g =\n", - " [ -0.314400 -0.303700 -0.168100 -0.098110 -0.060240 -0.037260 ];\n", - " expo_g =\n", - " [ 0.220900 1.004000 3.622000 12.160000 45.870000 254.400000 ];\n", - " expo_g_inv =\n", - " [ 4.526935 0.996016 0.276091 0.082237 0.021801 0.003931 ]}}\n" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mo_num : int = 9\n" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val pp_spindet : Format.formatter -> Spindeterminant.t -> unit = \n" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val pp_det : Format.formatter -> Determinant.t -> unit = \n" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let f12 = Util.of_some @@ Simulation.f12 simulation \n", - "\n", - "let mo_num = MOBasis.size mo_basis \n", - "\n", - "let pp_spindet = Spindeterminant.pp mo_num\n", - "\n", - "let pp_det = Determinant.pp mo_num\n", - "\n", - ";;\n", - "\n", - "#install_printer pp_spindet ;;\n", - "#install_printer pp_det ;;\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "ExecuteTime": { - "end_time": "2020-03-30T10:16:03.181400Z", - "start_time": "2020-03-30T10:15:58.799Z" - }, - "hidden": true, - "init_cell": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val simulation_aux : Simulation.t = \n" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "66 significant shell pairs computed in 0.170052 seconds\n", - "1\n", - "2\n", - "3\n", - "6\n", - "9\n", - "10\n", - "11\n", - "12\n", - "15\n", - "18\n", - "Computed ERIs in 3.375684 seconds\n" - ] - }, - { - "data": { - "text/plain": [ - "val aux_basis : MOBasis.t =\n", - " Eigenvalues: -11.127416 -0.632049 -0.269831 0.131526 0.151773 \n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0.995189 -0.236456 -6.99905E-13 3.74871E-12 -1.80137E-11\n", - " 2 0.0272807 0.573253 1.6881E-12 1.54414E-12 2.46497E-12\n", - " 3 -0.00753288 0.50151 2.32851E-13 4.16589E-13 1.21024E-12\n", - " ... ... ... ... ...\n", - " 22 0 0 -0 0 0\n", - " 23 0 0 -0 0 0\n", - " 24 0 0 -0 0 0\n", - " \n", - " Eigenvalues: 0.786913 0.828232 0.869410 0.849164 1.480837 \n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 -- -- 10 --\n", - " 1 2.65719E-12 0.0649867 3.37785E-12 1.73781E-11 0\n", - " 2 2.11976E-13 -1.62901 3.37812E-13 3.5811E-12 0\n", - " 3 -1.352E-13 1.63955 -1.27564E-13 -8.81657E-13 0\n", - " ... ... ... ... ...\n", - " 22 0 0 0 0 -0.866025\n", - " 23 0 0 0 0 0\n", - " 24 0 0 0 0 0\n", - " \n", - " Eigenvalues: 1.033846 1.027840 1.023514 1.247024 25.958539 \n", - " -- 11 -- -- 12 -- -- 13 -- -- 14 -- -- 15 --\n", - " 1 -3.09588E-10 2.21922E-10 -9.52402E-10 3.79632 -6.98298E-09\n", - " 2 1.67373E-10 1.08424E-10 1.58507E-10 -10.5897 1.20079E-09\n", - " 3 3.96217E-11 1.2302E-11 6.11965E-11 53.7881 5.40421E-10\n", - " ... ... ... ... ...\n", - " 22 -0 0 0 -0 -0\n", - " 23 1.4274E-14 0 0 -0 2.39877E-13\n", - " 24 -1.04644E-14 -1.17777E-14 0 -0 -0\n", - " \n", - " Eigenvalues: 25.891758 25.895674 18.767112 377.619959 1.478100 \n", - " -- 16 -- -- 17 -- -- 18 -- -- 19 -- -- 20 --\n", - " 1 9.02237E-09 -1.52394E-08 27.2935 436.547 1.14358E-12\n", - " 2 1.49437E-09 4.31003E-09 -127.494 -10.9671 -4.3086E-14\n", - " 3 -2.24755E-10 1.44203E-09 -21.2025 -23.8199 -6.40841E-14\n", - " ... ... ... ... ...\n", - " 22 1.08099E-13 1.08791E-13 -0 0 -0.210667\n", - " 23 1.28809E-13 0 -0 0 0.86485\n", - " 24 -2.16198E-13 -2.17582E-13 -0 0 0.421334\n", - " \n", - " Eigenvalues: 1.480427 1.470884 1.461621 \n", - " -- 21 -- -- 22 -- -- 23 --\n", - " 1 -7.95748E-13 1.61942E-12 5.76543E-10\n", - " 2 2.98909E-14 -6.0852E-14 -2.17012E-11\n", - " 3 4.43594E-14 -9.03033E-14 -3.22277E-11\n", - " ... ... ...\n", - " 22 -0.188927 0.412218 -0.00158824\n", - " 23 0.10621 0.490651 -0.00399134\n", - " 24 0.377853 -0.824436 0.00317648\n", - " \n", - " \n" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val aux_num : int = 23\n" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let simulation_aux = \n", - " let charge = Charge.to_int @@ Simulation.charge simulation \n", - " and multiplicity = Electrons.multiplicity @@ Simulation.electrons simulation\n", - " and nuclei = Simulation.nuclei simulation\n", - " in\n", - " let general_basis = \n", - " Basis.general_basis @@ Simulation.basis simulation\n", - " in\n", - " GeneralBasis.combine [\n", - " general_basis ; GeneralBasis.read aux_basis_filename\n", - " ]\n", - " |> Basis.of_nuclei_and_general_basis ~f12 nuclei\n", - " |> Simulation.make ~charge ~multiplicity ~nuclei \n", - "\n", - "\n", - "let aux_basis = \n", - " MOBasis.of_mo_basis simulation_aux mo_basis\n", - "\n", - "let aux_num = \n", - " MOBasis.size aux_basis\n" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "ExecuteTime": { - "end_time": "2020-03-30T10:16:41.349200Z", - "start_time": "2020-03-30T10:15:58.806Z" - }, - "hidden": true, - "init_cell": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "66 significant shell pairs computed in 2.944168 seconds\n", - "1\n", - "2\n", - "3\n", - "6\n", - "9\n", - "10\n", - "11\n", - "12\n", - "15\n", - "18\n", - "Computed ERIs in 47.577040 seconds\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "4-idx transformation \n", - "23 / 23\n", - "4-idx transformation \n", - "23 / 23\n" - ] - } - ], - "source": [ - "let () = ignore @@ MOBasis.f12_ints aux_basis\n", - "let () = ignore @@ MOBasis.two_e_ints aux_basis" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "## Integral-based functions" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "\\begin{equation}\n", - "\\langle I | \\hat{H} | J \\rangle = \\begin{cases}\n", - "\\sum_i h_{ii} + \\frac{1}{2} \\sum_{ij} \\langle ij || ij \\rangle \\text{ when } |J\\rangle = |I\\rangle \\\\\n", - "h_{ik} + \\sum_{j} \\langle ij || kj \\rangle \\text{ when } |J\\rangle = \\hat{T}_i^k |I\\rangle \\\\\n", - "\\langle ij || kl \\rangle \\text{ when } |J\\rangle = \\hat{T}_{ij}^{kl} |I\\rangle \\\\\n", - "\\end{cases}\n", - "\\end{equation}\n", - "\n", - "\n", - "\\begin{equation}\n", - "\\langle I | \\hat{F} | J \\rangle = \\begin{cases}\n", - "\\sum_i f_{ii} + \\frac{1}{2} \\sum_{ij} \\langle ij || ij \\rangle \\text{ when } |J\\rangle = |I\\rangle \\\\\n", - "f_{ik} + \\sum_{j} \\langle ij || kj \\rangle \\text{ when } |J\\rangle = \\hat{T}_i^k |I\\rangle \\\\\n", - "\\langle ij || kl \\rangle \\text{ when } |J\\rangle = \\hat{T}_{ij}^{kl} |I\\rangle \\\\\n", - "\\end{cases}\n", - "\\end{equation}" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val cancel_singles : bool = false\n" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mos_cabs : int list =\n", - " [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]\n" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mos_abs : int list =\n", - " [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21;\n", - " 22; 23]\n" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mos_in : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9]\n" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mos_a : Determinant.t -> int list = \n" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mos_b : Determinant.t -> int list = \n" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let cancel_singles = false \n", - "\n", - "let mos_cabs = \n", - " Util.list_range (mo_num+1) aux_num\n", - " \n", - "let mos_abs = \n", - " Util.list_range 1 aux_num\n", - " \n", - "let mos_in = \n", - " Util.list_range 1 mo_num\n", - "\n", - "let mos_a k =\n", - " Determinant.alfa k\n", - " |> Spindeterminant.to_list\n", - " \n", - "let mos_b k =\n", - " Determinant.beta k\n", - " |> Spindeterminant.to_list\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "### H integrals" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val h_one : int -> int -> '_weak1 -> float = \n" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val h_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = \n" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let h_one =\n", - " let h = \n", - " MOBasis.one_e_ints aux_basis\n", - " in fun i j _ -> h.{i,j}\n", - " \n", - "let h_two = \n", - " let two_e_ints = MOBasis.two_e_ints aux_basis in\n", - " let h2 i j k l (s:Spin.t) (s':Spin.t) =\n", - " if s' <> s then\n", - " ERI.get_phys two_e_ints i j k l\n", - " else\n", - " (ERI.get_phys two_e_ints i j k l) -. \n", - " (ERI.get_phys two_e_ints i j l k)\n", - " in\n", - " h2\n", - "\n", - " \n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "### F12 integrals" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val f_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = \n" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val f_one : 'a -> 'b -> 'c -> float = \n" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let f_two = \n", - " let two_e_ints = MOBasis.f12_ints aux_basis in\n", - " let f2 i j k l (s:Spin.t) (s':Spin.t) =\n", - " if s' <> s then\n", - " 0.5 *. F12.get_phys two_e_ints i j k l\n", - " else\n", - " 0.5 *. (\n", - " (F12.get_phys two_e_ints i j k l) -. \n", - " (F12.get_phys two_e_ints i j l k) )\n", - " in\n", - " let f3 i j k l (s:Spin.t) (s':Spin.t) = \n", - " if (i=k && j<>l) || (j=l && i<>k) then\n", - " 0.\n", - " else\n", - " f2 i j k l s s'\n", - " in\n", - " if cancel_singles then f3 else f2\n", - "\n", - "let f_one = fun _ _ _ -> 0.\n", - "\n", - "(*\n", - "let f_two = h_two\n", - "\n", - "let f_one = h_one\n", - "*)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "## Determinant-based functions" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "### Integrals" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val f12_integrals :\n", - " 'a ->\n", - " ('b -> 'c -> 'd -> float) *\n", - " (int -> int -> int -> int -> Spin.t -> Spin.t -> float) * 'e option = \n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val h_ij : MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n", - " \n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val f_ij : 'a -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n", - " \n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val hf_ij :\n", - " MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float list =\n", - " \n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let f12_integrals mo_basis =\n", - " ( f_one, f_two, None )\n", - "\n", - "let h_ij mo_basis ki kj =\n", - " let integrals =\n", - " List.map (fun f -> f mo_basis)\n", - " [ CI.h_integrals ]\n", - " in\n", - " CIMatrixElement.make integrals ki kj \n", - " |> List.hd\n", - "\n", - "\n", - "let f_ij mo_basis ki kj =\n", - " let integrals =\n", - " List.map (fun f -> f mo_basis)\n", - " [ f12_integrals ]\n", - " in\n", - " CIMatrixElement.make integrals ki kj \n", - " |> List.hd \n", - "\n", - "\n", - "let hf_ij mo_basis ki kj =\n", - " let integrals =\n", - " List.map (fun f -> f mo_basis)\n", - " [ CI.h_integrals ; f12_integrals ]\n", - " in\n", - " CIMatrixElement.make integrals ki kj\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "### Determinant space" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val is_a_double : DeterminantSpace.t -> Determinant.t -> bool = \n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let is_a_double det_space =\n", - " let mo_class = DeterminantSpace.mo_class det_space in\n", - " let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n", - " let m l =\n", - " List.fold_left (fun accu i ->\n", - " let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n", - " ) (Bitstring.zero mo_num) l\n", - " in\n", - " let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n", - " fun k -> \n", - " let alfa =\n", - " Determinant.alfa k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let beta =\n", - " Determinant.beta k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let a = Bitstring.logand aux_mask alfa\n", - " and b = Bitstring.logand aux_mask beta\n", - " in\n", - " match Bitstring.popcount a + Bitstring.popcount b with\n", - " | 2 | 1 -> true\n", - " | 0 | _ -> false\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of determinants : 84 84 7056\n" - ] - }, - { - "data": { - "text/plain": [ - "val in_space : DeterminantSpace.t = \n" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of determinants : 1771 1771 3136441\n" - ] - }, - { - "data": { - "text/plain": [ - "val aux_space : DeterminantSpace.t = \n" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val det_space_in : unit -> Determinant.t Stream.t = \n" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val det_space_out : unit -> (Determinant.t * Determinant.t) Stream.t = \n" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let in_space = \n", - " DeterminantSpace.fci_f12_of_mo_basis aux_basis ~frozen_core mo_num\n", - " \n", - "let aux_space = \n", - " DeterminantSpace.fci_of_mo_basis aux_basis ~frozen_core \n", - "\n", - "let det_space_in () =\n", - " DeterminantSpace.determinant_stream in_space\n", - "\n", - "let det_space_out () =\n", - " let s = \n", - " DeterminantSpace.determinant_stream aux_space\n", - " in\n", - " Stream.from (fun _ ->\n", - " try\n", - " let is_a_double = is_a_double in_space in\n", - " let rec result () =\n", - " let ki = Stream.next s in\n", - " if is_a_double ki then\n", - " Some (ki,ki)\n", - " else\n", - " result ()\n", - " in\n", - " result ()\n", - " with Stream.Failure -> None\n", - " )\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": { - "hidden": true, - "scrolled": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val ci : CI.t =\n", - " {CI.e_shift = -37.5503734698766749; det_space = ; m_H = ;\n", - " m_S2 = ; eigensystem = ; n_states = 1}\n" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " 1 0.0000000000 4.27876562e-01\n", - " 2 -0.0892428622 1.30475694e-01\n", - " 3 -0.0992140908 8.74622552e-02\n", - " 4 -0.1022422166 2.82063810e-02\n", - " 5 -0.1043598897 3.75067379e-02\n", - " 6 -0.1065557159 4.71900677e-02\n", - " 7 -0.1080257508 1.17050850e-02\n", - " 8 -0.1082438353 4.19578665e-03\n", - " 0 -0.1082636845 1.74312819e-03\n", - " 1 -0.1082673418 7.12907013e-04\n", - " 2 -0.1082677387 3.29773623e-04\n", - " 3 -0.1082678068 1.62017164e-04\n", - " 4 -0.1082678363 1.97376384e-04\n", - " 5 -0.1082678767 1.65667212e-04\n", - " 6 -0.1082678966 1.24231166e-04\n", - " 7 -0.1082679014 1.06697750e-05\n", - " 8 -0.1082679016 5.05286931e-06\n", - " 0 -0.1082679016 2.52890819e-06\n" - ] - }, - { - "data": { - "text/plain": [ - "val ci_coef : Lacaml.D.Mat.t =\n", - " \n", - "\n", - " -- 1 --\n", - " 1 -0.780949\n", - " 2 -0\n", - " 3 -0\n", - " ...\n", - " 7054 -0\n", - " 7055 -0\n", - " 7056 -3.12865E-06\n", - " \n", - "val ci_energy : Lacaml.D.Vec.t =\n", - " R1 R2 R3\n", - " -37.6586 -36.7238 -36.2286\n" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " 1 -0.1082679016 4.37907116e-07\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let ci = CI.make ~n_states:state in_space\n", - "\n", - "let ci_coef, ci_energy = Lazy.force ci.eigensystem \n", - "\n", - "let _ = print_newline () \n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "Permutation operator $p_{12}$ that generates a new determinant with electrons 1 and 2 swapped." - ] - }, - { - "cell_type": "raw", - "metadata": { - "hidden": true - }, - "source": [ - "let p12 det_space =\n", - " let mo_class = DeterminantSpace.mo_class det_space in\n", - " let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n", - " let m l =\n", - " List.fold_left (fun accu i ->\n", - " let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n", - " ) (Bitstring.zero mo_num) l\n", - " in\n", - " let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n", - " let not_aux_mask =\n", - " Bitstring.(shift_left_one mo_num (mo_num-1) |> minus_one |> logxor aux_mask)\n", - " in\n", - " fun k ->\n", - " let alfa =\n", - " Determinant.alfa k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let beta =\n", - " Determinant.beta k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let a = Bitstring.logand aux_mask alfa\n", - " and b = Bitstring.logand aux_mask beta\n", - " in\n", - " match Bitstring.popcount a, Bitstring.popcount b with\n", - " | 2, 0 \n", - " | 0, 2 -> Some (Determinant.negate_phase k)\n", - " | 1, 1 -> Some (Determinant.of_spindeterminants\n", - " (Spindeterminant.of_bitstring @@\n", - " Bitstring.(logor b (logand not_aux_mask alfa)) )\n", - " (Spindeterminant.of_bitstring @@\n", - " Bitstring.(logor a (logand not_aux_mask beta))\n", - " ) )\n", - " | 1, 0 \n", - " | 0, 1 -> Some k\n", - " | _ -> None\n", - " \n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "## Matrices $\\langle I | H | \\alpha \\rangle$ and $\\langle I | F | \\alpha \\rangle$ " - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": { - "hidden": true, - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val randomize : bool = false\n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val out_list : (Determinant.t * Determinant.t) list =\n", - " [(phase:+1\n", - " a:+1 ++-------+------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 ++-------+------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - " a:+1 +-+------+------------------------------------------------------\n", - 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" b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 ---+--+--+------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - " a:+1 ----+-+--+------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 ----+-+--+------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - " a:+1 -----++--+------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 -----++--+------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - 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");\n", - "(phase:+1\n", - " a:+1 ---+---+-+------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 ---+---+-+------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - " a:+1 ----+--+-+------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 ----+--+-+------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - " a:+1 -----+-+-+------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 -----+-+-+------------------------------------------------------\n", - 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",\n", - "phase:+1\n", - "a:+1 ----+---++------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - " a:+1 -----+--++------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 -----+--++------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - " a:+1 ------+-++------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 ------+-++------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - " a:+1 -------+++------------------------------------------------------\n", - 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"b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 -+---++---------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 --+--++---------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ---+-++---------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ----+++---------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-----+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+----+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 -++----+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+---+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 -+-+---+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 --++---+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +---+--+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 -+--+--+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 --+-+--+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ---++--+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +----+-+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 -+---+-+--------------------------------------------------------\n", - "b:+1 -+++------------------------------------------------------------\n", - ";\n", - "...|]\n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let randomize = false\n", - "\n", - "let out_list =\n", - " Util.stream_to_list (det_space_out ())\n", - " \n", - "let in_list =\n", - " Util.stream_to_list (det_space_in ())\n", - " \n", - "let det_a = Array.of_list out_list\n", - " |> Array.map (fun (i,_) -> i)\n", - "\n", - "let det_I =\n", - " if randomize then\n", - " let n = 123456789 in\n", - " in_list\n", - " |> List.map (fun k -> (Random.int n, k))\n", - " |> List.sort compare\n", - " |> List.map (fun (_,k) -> k)\n", - " |> Array.of_list\n", - " else\n", - " Array.of_list in_list\n" - ] - }, - { - "cell_type": "raw", - "metadata": { - "hidden": true, - "raw_mimetype": "text/markdown" - }, - "source": [ - "let m_H_aux, m_F_aux = \n", - " \n", - " let rec col_vecs_list accu_H accu_F = function\n", - " | [] -> \n", - " List.rev accu_H, \n", - " List.rev accu_F \n", - " | (ki, ki') :: rest when ki = ki' ->\n", - " begin\n", - " let h, f = \n", - " List.map (fun kj ->\n", - " match hf_ij aux_basis kj ki with\n", - " | [ a ; b ] -> a, b\n", - " | _ -> assert false ) in_list\n", - " |> List.split\n", - " in\n", - " let h = Vec.of_list h in\n", - " let f = Vec.of_list f in\n", - " scal 0.5 f; (* Specific to He singlet *)\n", - " col_vecs_list (h::accu_H) (f::accu_F) rest\n", - " end\n", - " | (ki, ki') :: rest ->\n", - " begin\n", - " assert false;\n", - " end\n", - " in\n", - " let h, f = \n", - " col_vecs_list [] [] out_list\n", - " in\n", - " Mat.of_col_vecs_list h,\n", - " Mat.of_col_vecs_list f" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "Function to generate all intermediate external determinants $|\\alpha \\rangle$ between $|I\\rangle$ and $|J\\rangle$, with a positive phase factor.\n", - "\n", - "* `exc` is the degree of excitation between $|I\\rangle$ and $|J\\rangle$" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val generate_alphas :\n", - " Determinant.t -> Determinant.t -> int -> Determinant.t list = \n" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val compute_HaaF :\n", - " CIMatrixElement.De.t ->\n", - " CIMatrixElement.De.t list -> CIMatrixElement.De.t -> float = \n" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let generate_alphas ki kj exc =\n", - " (* Check input excitation degree *)\n", - " let d = Determinant.degree ki kj in\n", - " if d <> exc then\n", - " Printf.sprintf \"Invalid excitation degree. Expected %d and found %d.\" exc d\n", - " |> failwith;\n", - " \n", - " (* Generate single excitations *)\n", - " let all_singles ki =\n", - " let mos_a, mos_b = Determinant.to_lists ki in\n", - " [ List.map (fun hole -> \n", - " List.map (fun particle ->\n", - " if hole = particle then None else\n", - " Some (Determinant.single_excitation Spin.Alfa hole particle ki)\n", - " ) mos_abs\n", - " ) mos_a\n", - " ;\n", - " List.map (fun hole -> \n", - " List.map (fun particle ->\n", - " if hole = particle then None else\n", - " Some (Determinant.single_excitation Spin.Beta hole particle ki)\n", - " ) mos_abs\n", - " ) mos_b \n", - " ]\n", - " |> List.concat\n", - " |> List.concat\n", - " |> Util.list_some\n", - " |> List.filter (fun x -> Determinant.is_none x = false)\n", - " |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n", - " in\n", - " \n", - " (* Generate double excitations *)\n", - " let all_doubles ki =\n", - " let mos_a, mos_b = Determinant.to_lists ki in\n", - " [ List.map (fun hole -> (* Alpha-Alpha *)\n", - " List.map (fun particle ->\n", - " List.map (fun hole' -> \n", - " List.map (fun particle' ->\n", - " if hole = particle || hole' = particle' then None else\n", - " if hole' > hole && particle' < particle then\n", - " Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki)\n", - " else None\n", - " ) mos_abs\n", - " ) mos_a \n", - " ) mos_abs\n", - " ) mos_a\n", - " ; \n", - " List.map (fun hole -> (* Beta-Beta *)\n", - " List.map (fun particle ->\n", - " List.map (fun hole' -> \n", - " List.map (fun particle' ->\n", - " if hole' > hole && particle' < particle && hole <> particle && hole' <> particle' then\n", - " Some (Determinant.double_excitation Spin.Beta hole particle Spin.Beta hole' particle' ki)\n", - " else None\n", - " ) mos_abs\n", - " ) mos_b \n", - " ) mos_abs\n", - " ) mos_b\n", - " ;\n", - " List.map (fun hole -> (* Alpha-Beta *)\n", - " List.map (fun particle ->\n", - " List.map (fun hole' -> \n", - " List.map (fun particle' ->\n", - " if hole = particle || hole' = particle' then None else\n", - " Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Beta hole' particle' ki)\n", - " ) mos_abs\n", - " ) mos_b \n", - " ) mos_abs\n", - " ) mos_a\n", - " ]\n", - " |> List.concat\n", - " |> List.concat\n", - " |> List.concat\n", - " |> List.concat\n", - " |> Util.list_some\n", - " |> List.filter (fun x -> Determinant.is_none x = false)\n", - " |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n", - " in\n", - "\n", - " (* Generate left and right excitations *)\n", - " let al = List.concat [ all_singles ki ; all_doubles ki ] in\n", - " let ar = List.concat [ all_singles kj ; all_doubles kj ] in\n", - " \n", - " let mo_class = DeterminantSpace.mo_class in_space in\n", - " let m l =\n", - " List.fold_left (fun accu i ->\n", - " let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n", - " ) (Bitstring.zero mo_num) l\n", - " in\n", - " let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n", - " let good_cabs k = \n", - " let alfa =\n", - " Determinant.alfa k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let beta =\n", - " Determinant.beta k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let a = Bitstring.logand aux_mask alfa\n", - " and b = Bitstring.logand aux_mask beta\n", - " in\n", - " match Bitstring.popcount a + Bitstring.popcount b with\n", - " | 1 | 2 -> true\n", - " | _ -> false\n", - " in\n", - " \n", - " (* Merge lists in a set of unique determinants *)\n", - " List.concat [ al; ar ]\n", - " |> List.sort_uniq compare\n", - " \n", - " (* Filter out all determinants with incorrect numbers of electrons in the CABS *)\n", - " |> List.filter good_cabs \n", - " \n", - " \n", - "let compute_HaaF ki alphas kj =\n", - " List.fold_left (fun accu alpha -> accu\n", - " +. h_ij aux_basis ki alpha\n", - " *. f_ij aux_basis alpha kj\n", - " ) 0. alphas\n" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val check :\n", - " int ->\n", - " (CIMatrixElement.De.t -> CIMatrixElement.De.t -> float) -> int -> unit =\n", - " \n" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val sum : 'a list -> ('a -> float) -> float = \n" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let check n integral_value exc =\n", - " let cpudet, cpuint = ref 0., ref 0. in\n", - " let det_list =\n", - " match n with\n", - " | 0 -> det_I\n", - " | n -> Array.sub det_I 0 n\n", - " in\n", - " let result =\n", - " Printf.printf \"Checking ... \\n%!\";\n", - " let percent = ref 0 in\n", - " let task (i,ki) =\n", - " (let p = (10 * (i+1))/(Array.length det_list) in\n", - " if p <> !percent then\n", - " ( percent := p ; Printf.printf \" - %3d %%\\n%!\" (p*10) ));\n", - " Array.mapi (fun j kj -> \n", - " if i > j || Determinant.degree ki kj <> exc then\n", - " (0,0,0.,0.)\n", - " else\n", - " begin\n", - " let alphas = generate_alphas ki kj exc in\n", - " let det_value =\n", - " let t0 = Unix.gettimeofday () in\n", - " let result = compute_HaaF ki alphas kj in\n", - " cpudet := !cpudet +. Unix.gettimeofday () -. t0;\n", - " result\n", - " in\n", - " let int_value = \n", - " let t0 = Unix.gettimeofday () in\n", - " let result = integral_value ki kj in\n", - " cpuint := !cpuint +. Unix.gettimeofday () -. t0;\n", - " result\n", - " in\n", - "(* Printf.printf \"%d %d %e %e\\n%!\" i j det_value int_value; *)\n", - " (i,j,det_value,int_value)\n", - " end\n", - " ) det_list\n", - " in\n", - " det_list\n", - " |> Array.mapi (fun i ki -> (i,ki))\n", - " |> Array.to_list\n", - " |> Stream.of_list\n", - " |> Farm.run ~f:task\n", - " |> Util.stream_to_list\n", - " |> Array.concat\n", - " in\n", - " let i,j,d,v = \n", - " let rec aux k imax jmax emax dmax vmax = \n", - " if k = -1 then\n", - " imax, jmax, dmax, vmax\n", - " else\n", - " let i, j, d, v = result.(k) in\n", - " let e = abs_float (d -. v) in\n", - " if e >= emax then\n", - " aux (k-1) i j e d v\n", - " else\n", - " aux (k-1) imax jmax emax dmax vmax\n", - " in\n", - " aux (Array.length result - 1) 0 0 0. 0. 0.\n", - " in\n", - " let error = abs_float (d -. v) in\n", - " if error < epsilon_float then\n", - " (*\n", - " Printf.printf \"OK: %e\\n%!\" error\n", - " *)\n", - " Printf.printf \"OK: (%d, %d) | %e %e | %e | cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n", - " else\n", - " Printf.printf \"Failed: (%d, %d) | %e %e | %e | cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n", - "\n", - " \n", - "let sum l f = List.fold_left (fun accu i -> accu +. f i) 0. l" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val array_3_init :\n", - " int ->\n", - " int ->\n", - " int ->\n", - " (int -> int -> int -> float) ->\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val array_4_init :\n", - " int ->\n", - " int ->\n", - " int ->\n", - " int ->\n", - " (int -> int -> int -> int -> float) ->\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val array_5_init :\n", - " int ->\n", - " int ->\n", - " int ->\n", - " int ->\n", - " int ->\n", - " (int -> int -> int -> int -> int -> float) ->\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let array_3_init d1 d2 d3 f =\n", - " let result = \n", - " Bigarray.(Array3.create Float64 fortran_layout) d1 d2 d3\n", - " in\n", - " for k=1 to d3 do\n", - " for j=1 to d2 do\n", - " for i=1 to d1 do\n", - " result.{i,j,k} <- f i j k\n", - " done\n", - " done\n", - " done;\n", - " result\n", - "\n", - "\n", - "let array_4_init d1 d2 d3 d4 f =\n", - " let result = \n", - " Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4 |]\n", - " in\n", - " for l=1 to d4 do\n", - " for k=1 to d3 do\n", - " for j=1 to d2 do\n", - " for i=1 to d1 do\n", - " result.{i,j,k,l} <- f i j k l\n", - " done\n", - " done\n", - " done\n", - " done;\n", - " result\n", - "\n", - "\n", - "let array_5_init d1 d2 d3 d4 d5 f =\n", - " let result = \n", - " Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4;d5 |]\n", - " in\n", - " for m=1 to d5 do\n", - " for l=1 to d4 do\n", - " for k=1 to d3 do\n", - " for j=1 to d2 do\n", - " for i=1 to d1 do\n", - " result.{i,j,k,l,m} <- f i j k l m\n", - " done\n", - " done\n", - " done\n", - " done\n", - " done;\n", - " result\n", - "\n", - "(* ----- *)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "******" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "heading_collapsed": true - }, - "source": [ - "# 1. 0 " - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val m_0111_1H_1F : Lacaml.D.vec = R1 R2 R3 R7 R8 R9\n", - " 0 0 0 ... 0 0 0\n" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_1H_2Fa : Lacaml.D.mat =\n", - " \n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0 4.14783E-05 0.000191898 5.819E-05 3.17034E-05\n", - " 2 0.00285395 0 0.00130169 0.000700753 0.000516776\n", - " 3 0.0048103 0.000752348 0 0.00113768 0.000719116\n", - " ... ... ... ... ...\n", - " 7 -0.00384068 -0.00136624 -0.00343863 -0.00255958 -0.00227812\n", - " 8 0.0164152 0.0118156 0.0104307 0.00609247 0.00526221\n", - " 9 0.0169861 0.0119274 0.010345 0.00631195 0.00505777\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 0.000201004 -1.30762E-06 0.000334712 0.000361198\n", - " 2 0.000232139 -0.00168234 0.00083308 0.00101706\n", - " 3 -0.00387497 0.000450355 0.00302132 0.00343988\n", - " ... ... ... ...\n", - " 7 -0.00166296 0 0.00138345 0.00154153\n", - " 8 0.00316903 0.00287547 0 0.0177299\n", - " 9 0.0026978 0.00232342 0.00673081 0\n", - " \n", - "val m_0111_2Ha_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_1H_2Fb : Lacaml.D.mat =\n", - " \n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0.00296502 0.00298831 0.00488797 0.000118822 -0.000472343\n", - " 2 0.00298831 -0.00136007 -0.00413131 -0.0063196 -0.00598212\n", - " 3 0.00488797 -0.00413131 -0.00712707 -0.00508589 -0.00503032\n", - " ... ... ... ... ...\n", - " 7 -0.00407169 -0.00213075 -0.0040668 -0.00417519 -0.00370227\n", - " 8 0.0160284 0.0113906 0.0122954 0.00422564 0.00433285\n", - " 9 0.0166196 0.0110531 0.0122398 0.00511694 0.0023468\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 0.0112593 -0.00407169 0.0160284 0.0166196\n", - " 2 0.00920231 -0.00213075 0.0113906 0.0110531\n", - " 3 0.00825183 -0.0040668 0.0122954 0.0122398\n", - " ... ... ... ...\n", - " 7 0.0043954 -0.00205631 0.0045038 0.00403087\n", - " 8 0.0150589 0.0045038 0.0198249 0.0230215\n", - " 9 0.0158986 0.00403087 0.0230215 0.0220599\n", - " \n", - "val m_0111_2Hb_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_2Ha_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val integral_value : Determinant.t -> 'a -> float = \n" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "Failed: (5594, 5594) | -2.621269e-01 -2.621269e-01 | 9.992007e-16 | cpu : 605.920079 0.214178\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let m_0111_1H_1F = \n", - " Vec.init mo_num (fun i -> \n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_one a i Spin.Alfa ))\n", - "\n", - "let m_0111_1H_2Fa, m_0111_2Ha_2Fa =\n", - "\n", - " let m_0122_Haa = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a k Spin.Alfa Spin.Alfa *. f_two a k i j Spin.Alfa Spin.Alfa\n", - " ) )\n", - " in \n", - " \n", - " let m_0111_1H_2Fa = \n", - " Mat.init_cols mo_num mo_num (fun i j ->\n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Alfa +.\n", - " h_two i j a j Spin.Alfa Spin.Alfa *. f_one a i Spin.Alfa\n", - " ) +.\n", - " if i < j then 0. else\n", - " begin\n", - " sum mos_cabs (fun a ->\n", - " sum mos_cabs (fun b -> if b >= a then 0. else\n", - " h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b i j Spin.Alfa Spin.Alfa\n", - " )\n", - " ) +.\n", - " sum mos_in (fun k -> m_0122_Haa.{i,j,k}) \n", - " end\n", - " )\n", - " in\n", - " \n", - " let m_0111_2Ha_2Fa =\n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Alfa *.\n", - " f_two a k i k Spin.Alfa Spin.Alfa \n", - " ) -. if i < j then 0. else m_0122_Haa.{i,j,k}\n", - " )\n", - " in m_0111_1H_2Fa, m_0111_2Ha_2Fa\n", - "\n", - "\n", - " \n", - "let m_0111_1H_2Fb, m_0111_2Hb_2Fb =\n", - " let m_0122_Hab = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a k Spin.Alfa Spin.Beta *. f_two a k i j Spin.Alfa Spin.Beta\n", - " ) )\n", - " in\n", - " \n", - " let m_0111_1H_2Fb = \n", - " Mat.init_cols mo_num mo_num (fun i j ->\n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Beta +. \n", - " h_two i j a j Spin.Alfa Spin.Beta *. f_one a i Spin.Alfa +.\n", - " h_one j a Spin.Alfa *. f_two a i j i Spin.Alfa Spin.Beta +. \n", - " h_two j i a i Spin.Alfa Spin.Beta *. f_one a j Spin.Alfa\n", - " ) +.\n", - " sum mos_in (fun k -> m_0122_Hab.{i,j,k} +. m_0122_Hab.{j,i,k} ) +.\n", - " sum mos_cabs (fun a ->\n", - " sum mos_cabs (fun b ->\n", - " h_two i j a b Spin.Alfa Spin.Beta *. f_two a b i j Spin.Alfa Spin.Beta\n", - " )\n", - " )\n", - " )\n", - " in \n", - " \n", - " let m_0111_2Hb_2Fb =\n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two k i a i Spin.Alfa Spin.Beta *.\n", - " f_two a j k j Spin.Alfa Spin.Beta +.\n", - " h_two i k a k Spin.Alfa Spin.Beta *.\n", - " f_two a j i j Spin.Alfa Spin.Alfa \n", - " ) -. m_0122_Hab.{k,i,j}\n", - " )\n", - " in\n", - " m_0111_1H_2Fb, m_0111_2Hb_2Fb\n", - " \n", - "\n", - "let m_0111_2Ha_2Fb =\n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Alfa *.\n", - " f_two a k i k Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "\n", - "\n", - "let integral_value ki kj = \n", - "\n", - " let mos_i, mos_i' = mos_a ki, mos_b ki in\n", - " let same = (mos_i = mos_i') in\n", - " \n", - " (* Alpha *)\n", - " let a = \n", - " sum mos_i (fun i -> m_0111_1H_1F.{i}) \n", - " in\n", - " \n", - " let b = \n", - " if same then a else\n", - " sum mos_i' (fun i -> m_0111_1H_1F.{i})\n", - " in\n", - " \n", - " let aa = \n", - " sum mos_i (fun j ->\n", - " sum mos_i (fun i -> m_0111_1H_2Fa.{i,j} ))\n", - " in\n", - " \n", - " let bb = \n", - " if same then aa else\n", - " sum mos_i' (fun j ->\n", - " sum mos_i' (fun i -> m_0111_1H_2Fa.{i,j} ))\n", - " in\n", - " \n", - " let ab = \n", - " sum mos_i' (fun j ->\n", - " sum mos_i (fun i -> m_0111_1H_2Fb.{i,j} )) \n", - " in\n", - " \n", - " let aaa = \n", - " sum mos_i (fun k ->\n", - " sum mos_i (fun j ->\n", - " sum mos_i (fun i -> m_0111_2Ha_2Fa.{i,j,k} ))) \n", - " in\n", - " \n", - " let bbb = \n", - " if same then aaa else\n", - " sum mos_i' (fun k ->\n", - " sum mos_i' (fun j ->\n", - " sum mos_i' (fun i -> m_0111_2Ha_2Fa.{i,j,k} )))\n", - " in\n", - " \n", - " let baa = \n", - " sum mos_i' (fun k ->\n", - " sum mos_i (fun j ->\n", - " sum mos_i (fun i ->\n", - " m_0111_2Ha_2Fb.{i,j,k} +. m_0111_2Hb_2Fb.{i,j,k}\n", - " )))\n", - " in\n", - " \n", - " let bba = \n", - " sum mos_i (fun k ->\n", - " sum mos_i' (fun j ->\n", - " sum mos_i' (fun i ->\n", - " m_0111_2Ha_2Fb.{i,j,k} +. m_0111_2Hb_2Fb.{j,i,k} \n", - " ))) \n", - " in\n", - "\n", - " a +. b +. aa +. bb +. ab +. aaa +. baa +. bba +. bbb\n", - " \n", - " \n", - "let _ =\n", - " check 0 integral_value 0 \n", - " \n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "heading_collapsed": true - }, - "source": [ - "# 2. 1" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": { - "hidden": true, - "scrolled": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val m_1111_1H_1F : Lacaml.D.mat =\n", - " \n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0 0 0 0 0\n", - " 2 0 0 0 0 0\n", - " 3 0 0 0 0 0\n", - " ... ... ... ... ...\n", - " 7 0 0 0 0 0\n", - " 8 0 0 0 0 0\n", - " 9 0 0 0 0 0\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 0 0 0 0\n", - " 2 0 0 0 0\n", - " 3 0 0 0 0\n", - " ... ... ... ...\n", - " 7 0 0 0 0\n", - " 8 0 0 0 0\n", - " 9 0 0 0 0\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1111_2Ha_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1111_2Hb_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1111_2Ha_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1111_2Hb_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1121_2Ha_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1121_2Hb_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1121_2Ha_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1121_2Hb_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1122_va :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1111_1H_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1122_v2 :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1122_v3 :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1111_1H_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1122_oa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_1122_o :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val integral_value : Determinant.t -> Determinant.t -> float = \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "OK: (1, 35) | 1.340491e-02 1.340491e-02 | 2.775558e-17 | cpu : 79.129396 0.030664\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let m_1111_1H_1F = \n", - " Mat.init_cols mo_num mo_num (fun i k -> \n", - " sum mos_cabs (fun a -> h_one i a Spin.Alfa *. f_one a k Spin.Alfa ))\n", - "\n", - "\n", - " \n", - "\n", - "let m_1111_2Ha_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " if l=i then\n", - " sum mos_cabs (fun a ->\n", - " h_two j l a l Spin.Alfa Spin.Alfa *.\n", - " f_two a i j k Spin.Alfa Spin.Alfa \n", - " )\n", - " else\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Alfa *.\n", - " f_two a l k l Spin.Alfa Spin.Alfa +.\n", - " h_two j l a l Spin.Alfa Spin.Alfa *.\n", - " f_two a i j k Spin.Alfa Spin.Alfa )\n", - " )\n", - "\n", - "\n", - "\n", - "let m_1111_2Hb_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " if l=i then\n", - " sum mos_cabs (fun a ->\n", - " h_two j l a l Spin.Alfa Spin.Beta *.\n", - " f_two a i j k Spin.Alfa Spin.Beta \n", - " )\n", - " else\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Beta *.\n", - " f_two a l k l Spin.Alfa Spin.Alfa +.\n", - " h_two j l a l Spin.Alfa Spin.Beta *.\n", - " f_two a i j k Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1111_2Ha_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Alfa *.\n", - " f_two a l k l Spin.Alfa Spin.Beta +.\n", - " h_two j l a l Spin.Alfa Spin.Beta *.\n", - " f_two a i j k Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "\n", - "\n", - "let m_1111_2Hb_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Beta *.\n", - " f_two a l k l Spin.Alfa Spin.Beta +.\n", - " h_two j l a l Spin.Alfa Spin.Alfa *.\n", - " f_two a i j k Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "\n", - "\n", - " \n", - "\n", - "\n", - "let m_1121_2Ha_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j k a Spin.Alfa Spin.Alfa *.\n", - " f_two l a l j Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1121_2Hb_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j k a Spin.Alfa Spin.Beta *.\n", - " f_two l a l j Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "let m_1121_2Ha_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j k a Spin.Alfa Spin.Alfa *.\n", - " f_two l a l j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1121_2Hb_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j k a Spin.Alfa Spin.Beta *.\n", - " f_two l a l j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "let m_1122_va =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two j i a l Spin.Alfa Spin.Alfa *.\n", - " f_two l a k j Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - " \n", - "let m_1111_1H_2Fa = \n", - " array_3_init mo_num mo_num mo_num (fun j i k ->\n", - " sum mos_in (fun l -> m_1122_va.{l,j,i,k}) +.\n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Alfa +.\n", - " h_two i j a j Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.\n", - " h_one j a Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa +.\n", - " h_two i j k a Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa +.\n", - " sum mos_cabs (fun b -> if b > a then 0. else\n", - " h_two i j a b Spin.Alfa Spin.Alfa *.\n", - " f_two a b k j Spin.Alfa Spin.Alfa )\n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1122_v2 =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j l a Spin.Alfa Spin.Beta *.\n", - " f_two l a k j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1122_v3 =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a l Spin.Alfa Spin.Beta *.\n", - " f_two a l k j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - " \n", - "let m_1111_1H_2Fb = \n", - " array_3_init mo_num mo_num mo_num (fun j i k ->\n", - " sum mos_in (fun l -> m_1122_v2.{l,j,i,k} +. m_1122_v3.{l,j,i,k}) +.\n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Beta +.\n", - " h_two i j a j Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.\n", - " h_one j a Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta +.\n", - " h_two i j k a Spin.Alfa Spin.Beta *. f_one a j Spin.Beta +.\n", - " sum mos_cabs (fun b ->\n", - " h_two i j a b Spin.Alfa Spin.Beta *.\n", - " f_two a b k j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - " )\n", - " \n", - "let m_1122_oa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " if l > j then\n", - " sum mos_cabs (fun a ->\n", - " h_two j l a k Spin.Alfa Spin.Alfa *.\n", - " f_two i a l j Spin.Alfa Spin.Alfa \n", - " )\n", - " else 0.\n", - " )\n", - "\n", - "let m_1122_o =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun l j i k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two l j k a Spin.Alfa Spin.Beta *.\n", - " f_two i a l j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - " \n", - "\n", - "\n", - "(*----*)\n", - "\n", - "let integral_value ki kj = \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " let mos_novirt, mos_novirt' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logor i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logor i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - " \n", - " let mos_ij, mos_ij' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - " \n", - " let mos_i, mos_i' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in\n", - " \n", - " let mos_j, mos_j' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a kj, mos_b kj\n", - " | Spin.Beta -> mos_b kj, mos_a kj\n", - " in\n", - " \n", - " let result = \n", - " m_1111_1H_1F.{i,k} +. \n", - " sum mos_ij (fun j -> \n", - " m_1111_1H_2Fa.{j,i,k} \n", - " +. sum mos_i (fun l -> m_1111_2Ha_2Fa.{l,j,i,k})\n", - " +. sum mos_i' (fun l -> m_1111_2Ha_2Fb.{l,j,i,k})\n", - " +. sum mos_j (fun l -> m_1121_2Ha_2Fa.{l,j,i,k})\n", - " +. sum mos_j' (fun l -> m_1121_2Ha_2Fb.{l,j,i,k})\n", - " -. sum mos_novirt (fun l -> m_1122_va.{l,j,i,k})\n", - " -. sum mos_ij (fun l -> m_1122_oa.{l,j,i,k} )\n", - " ) +.\n", - " sum mos_ij' (fun j ->\n", - " m_1111_1H_2Fb.{j,i,k} \n", - " +. sum mos_i (fun l -> m_1111_2Hb_2Fa.{l,j,i,k})\n", - " +. sum mos_i' (fun l -> m_1111_2Hb_2Fb.{l,j,i,k})\n", - " +. sum mos_j (fun l -> m_1121_2Hb_2Fb.{l,j,i,k})\n", - " +. sum mos_j' (fun l -> m_1121_2Hb_2Fa.{l,j,i,k})\n", - " -. sum mos_novirt (fun l -> m_1122_v2.{l,j,i,k}) \n", - " -. sum mos_novirt' (fun l -> m_1122_v3.{l,j,i,k})\n", - " -. sum mos_ij (fun l -> m_1122_o.{l,j,i,k})\n", - " ) \n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "(*\n", - "let ki = det_I.(77)\n", - "let kj = det_I.(83)\n", - "\n", - "let _ = integral_value ki kj\n", - "let _ = \n", - " let alphas = generate_alphas ki kj 1 1\n", - " in compute_HaaF ki alphas kj\n", - "*)\n", - "\n", - "let _ = check 100 integral_value 1 \n", - "\n" - ] - }, - { - "cell_type": "raw", - "metadata": { - "hidden": true - }, - "source": [ - "Timing : 40.020974 0.019294" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "heading_collapsed": true - }, - "source": [ - "# 3. 2" - ] - }, - { - "cell_type": "code", - "execution_count": 129, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val m_2112_1H_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2112_1H_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2112_2Ha_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2112_2Hb_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2112_2Ha_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2121_2Ha_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2121_2Hb_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2121_2Ha_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2122_2Ha_2Fa_ij :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2122_2Hb_2Fb_ij :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2122_2Hb_2Fb_ij2 :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2122_2Ha_2Fa_ij2 :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2122_2Ha_2Fa_nv :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2122_2Hb_2Fb_nv :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_2122_2Hb_2Fb_nv2 :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val integral_value : Determinant.t -> Determinant.t -> float = \n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "OK: (2, 45) | 2.332967e-02 2.332967e-02 | 2.428613e-17 | cpu : 109.679883 0.039116\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val ki : Determinant.t =\n", - " phase:+1\n", - " a:+1 +--++-----------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - "\n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val kj : Determinant.t =\n", - " phase:+1\n", - " a:+1 +-+-+-----------------------------------------------------------\n", - " b:+1 ++-+------------------------------------------------------------\n", - "\n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : float = 0.000896378780435275082\n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : float = 0.000896378780435274107\n" - ] - }, - "execution_count": 129, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let m_2112_1H_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +.\n", - " h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Alfa +. \n", - " h_two i j a l Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.\n", - " h_two i j k a Spin.Alfa Spin.Alfa *. f_one a l Spin.Alfa +.\n", - " sum mos_in (fun m -> -. h_two i j a m Spin.Alfa Spin.Alfa *.\n", - " f_two m a k l Spin.Alfa Spin.Alfa) +.\n", - " sum mos_cabs (fun b -> if b >= a then 0. else\n", - " h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b k l Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - " )\n", - "\n", - "let m_2112_1H_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.\n", - " h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Beta +.\n", - " h_two i j a l Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.\n", - " h_two i j k a Spin.Alfa Spin.Beta *. f_one a l Spin.Alfa +.\n", - " sum mos_in (fun m ->\n", - " h_two i j a m Spin.Alfa Spin.Beta *. f_two a m k l Spin.Alfa Spin.Beta +.\n", - " h_two i j m a Spin.Alfa Spin.Beta *. f_two m a k l Spin.Alfa Spin.Beta ) +.\n", - " sum mos_cabs (fun b -> \n", - " h_two i j a b Spin.Alfa Spin.Beta *. f_two a b k l Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - " )\n", - "\n", - "let m_2112_2Ha_2Fa =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i n a n Spin.Alfa Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +. \n", - " h_two j n a n Spin.Alfa Spin.Alfa *. f_two a i l k Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - " \n", - "let m_2112_2Hb_2Fa =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i n a n Spin.Alfa Spin.Beta *. f_two a j k l Spin.Alfa Spin.Alfa +.\n", - " h_two j n a n Spin.Alfa Spin.Beta *. f_two a i l k Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - " \n", - "let m_2112_2Ha_2Fb =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i n a n Spin.Alfa Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.\n", - " h_two j n a n Spin.Alfa Spin.Beta *. f_two a i l k Spin.Alfa Spin.Beta )\n", - " )\n", - " \n", - " \n", - "let m_2121_2Ha_2Fa =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a l Spin.Alfa Spin.Alfa *. f_two a n k n Spin.Alfa Spin.Alfa +.\n", - " h_two j i a k Spin.Alfa Spin.Alfa *. f_two a n l n Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - " \n", - "\n", - "let m_2121_2Hb_2Fa =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a l Spin.Alfa Spin.Beta *. f_two a n k n Spin.Alfa Spin.Alfa +.\n", - " h_two j i a k Spin.Alfa Spin.Beta *. f_two a n l n Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - " \n", - "let m_2121_2Ha_2Fb =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a l Spin.Alfa Spin.Alfa *. f_two a n k n Spin.Alfa Spin.Beta +.\n", - " h_two j i a k Spin.Alfa Spin.Alfa *. f_two a n l n Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - " \n", - "\n", - "let m_2122_2Ha_2Fa_ij =\n", - " let s = Spin.Alfa in\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i n a k s s *. f_two j a n l s s \n", - " +. h_two i n a l s s *. f_two j a k n s s \n", - " -. h_two j n a k s s *. f_two i a n l s s \n", - " -. h_two j n a l s s *. f_two i a k n s s\n", - " )\n", - " )\n", - " \n", - "let m_2122_2Hb_2Fb_ij =\n", - " let s, s' = Spin.(Alfa, Beta) in\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two n i a k s s *. f_two a j n l s s'\n", - " +. h_two n j a l s s' *. f_two i a k n s s \n", - " -. h_two n j k a s s' *. f_two i a n l s s'\n", - " )\n", - " )\n", - " \n", - "let m_2122_2Hb_2Fb_ij2 =\n", - " let s, s' = Spin.(Alfa, Beta) in\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " -. h_two i n a l s s' *. f_two a j k n s s' +.\n", - " (if n < j then\n", - " h_two i n k a s s' *. f_two j a l n s' s'\n", - " +. h_two n j a l s' s' *. f_two i a k n s s'\n", - " else \n", - " -. h_two i n k a s s' *. f_two j a n l s' s' \n", - " -. h_two j n a l s' s' *. f_two i a k n s s'\n", - " )\n", - " )\n", - " )\n", - " \n", - "let m_2122_2Ha_2Fa_ij2 =\n", - " let s, s' = Spin.(Alfa, Beta) in\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i n k a s s' *. f_two j a l n s s'\n", - " +. h_two j n l a s s' *. f_two i a k n s s'\n", - " -. h_two i n l a s s' *. f_two j a k n s s'\n", - " -. h_two j n k a s s' *. f_two i a l n s s'\n", - " )\n", - " ) \n", - " \n", - "let m_2122_2Ha_2Fa_nv =\n", - " let s = Spin.Alfa in\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a -> h_two i j a n s s *. f_two n a k l s s ) ) \n", - " \n", - " \n", - " \n", - "let m_2122_2Hb_2Fb_nv =\n", - " let s, s' = Spin.(Alfa, Beta) in\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a -> -. h_two i j a n s s' *. f_two a n k l s s' ) ) \n", - " \n", - "let m_2122_2Hb_2Fb_nv2 =\n", - " let s, s' = Spin.(Alfa, Beta) in\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun n i j k l ->\n", - " sum mos_cabs (fun a -> -. h_two i j n a s s' *. f_two n a k l s s' ) ) \n", - " \n", - " \n", - " \n", - "let integral_value ki kj = \n", - " let i, j, k, l, s, s', phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " let mos_i, mos_i' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in\n", - " \n", - " let mos_j, mos_j' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a kj, mos_b kj\n", - " | Spin.Beta -> mos_b kj, mos_a kj\n", - " in\n", - " \n", - " let mos_ij, mos_ij' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - " \n", - " let mos_novirt, mos_novirt' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logor i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logor i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - " \n", - " let result = \n", - " if s = s' then\n", - " m_2112_1H_2Fa.{i,j,k,l} +. \n", - " sum mos_i (fun n -> m_2112_2Ha_2Fa.{n,i,j,k,l} ) +.\n", - " sum mos_i' (fun n -> m_2112_2Hb_2Fa.{n,i,j,k,l} ) +.\n", - " sum mos_j (fun n -> m_2121_2Ha_2Fa.{n,i,j,k,l} ) +.\n", - " sum mos_j' (fun n -> m_2121_2Ha_2Fb.{n,i,j,k,l} ) +.\n", - " sum mos_ij (fun n -> m_2122_2Ha_2Fa_ij.{n,i,j,k,l} ) +. \n", - " sum mos_ij' (fun n -> m_2122_2Ha_2Fa_ij2.{n,i,j,k,l} ) +. \n", - " sum mos_novirt (fun n -> m_2122_2Ha_2Fa_nv.{n,i,j,k,l} ) \n", - " else\n", - " m_2112_1H_2Fb.{i,j,k,l} +. \n", - " sum mos_i (fun n -> m_2112_2Ha_2Fb.{n,i,j,k,l} ) +.\n", - " sum mos_i' (fun n -> m_2112_2Ha_2Fb.{n,j,i,l,k} ) +.\n", - " sum mos_j (fun n -> m_2121_2Hb_2Fa.{n,i,j,k,l} ) +.\n", - " sum mos_j' (fun n -> m_2121_2Hb_2Fa.{n,j,i,l,k} ) +.\n", - " sum mos_novirt'(fun n -> m_2122_2Hb_2Fb_nv.{n,i,j,k,l} ) +.\n", - " sum mos_novirt (fun n -> m_2122_2Hb_2Fb_nv2.{n,i,j,k,l} )+.\n", - " sum mos_ij (fun n -> m_2122_2Hb_2Fb_ij.{n,i,j,k,l} ) +. \n", - " sum mos_ij' (fun n -> m_2122_2Hb_2Fb_ij2.{n,i,j,k,l} ) \n", - " in\n", - "\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "let _ = check 100 integral_value 2 \n", - "\n", - "let ki = det_I.(7)\n", - "let kj = det_I.(89)\n", - "\n", - "let _ = integral_value ki kj\n", - "let _ = \n", - " let alphas = generate_alphas ki kj 2 \n", - " in compute_HaaF ki alphas kj\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "heading_collapsed": true - }, - "source": [ - "# 4. 3" - ] - }, - { - "cell_type": "code", - "execution_count": 130, - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val integral_value : Determinant.t -> Determinant.t -> float = \n" - ] - }, - "execution_count": 130, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "OK: (13, 52) | 6.122906e-04 6.122906e-04 | 3.252607e-19 | cpu : 77.238524 0.119682\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 130, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let integral_value ki kj = \n", - " let i, j, m, k, l, n, s1, s2, s3, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Triple (phase,\n", - " { hole=h1 ; particle=p1 ; spin=s1 },\n", - " { hole=h2 ; particle=p2 ; spin=s2 },\n", - " { hole=h3 ; particle=p3 ; spin=s3 }) ) -> h1, h2, h3, p1, p2, p3, s1, s2, s3, phase\n", - " | _ -> assert false\n", - " in\n", - "\n", - " let result = \n", - " let open Spin in \n", - " match s1, s2, s3 with\n", - " | Alfa, Alfa, Alfa\n", - " | Beta, Beta, Beta -> \n", - " sum mos_cabs (fun a -> \n", - " h_two i j a k s1 s2 *. f_two m a l n s3 s3 \n", - " +. h_two i j a n s1 s2 *. f_two m a k l s3 s2 \n", - " +. h_two i m a l s1 s3 *. f_two j a k n s2 s3 \n", - " +. h_two j m a k s2 s3 *. f_two i a l n s1 s3 \n", - " +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n", - " -. h_two i j a l s1 s2 *. f_two m a k n s3 s3 \n", - " -. h_two i m a k s1 s3 *. f_two j a l n s2 s3 \n", - " -. h_two i m a n s1 s3 *. f_two j a k l s2 s2 \n", - " -. h_two j m a l s2 s3 *. f_two i a k n s1 s3 )\n", - " | Alfa, Alfa, Beta\n", - " | Beta, Beta, Alfa -> \n", - " sum mos_cabs (fun a -> \n", - " h_two i j a l s1 s2 *. f_two a m k n s1 s3\n", - " +. h_two i m k a s1 s3 *. f_two j a l n s2 s3\n", - " +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n", - " +. h_two j m l a s2 s3 *. f_two i a k n s1 s3\n", - " -. h_two i j a k s1 s2 *. f_two a m l n s1 s3\n", - " -. h_two i m a n s1 s3 *. f_two j a k l s2 s2 \n", - " -. h_two i m l a s1 s3 *. f_two j a k n s2 s3\n", - " -. h_two j m k a s2 s3 *. f_two i a l n s1 s3\n", - " ) \n", - " | Alfa, Beta, Beta\n", - " | Beta, Alfa, Alfa -> \n", - " sum mos_cabs (fun a -> \n", - " h_two i j a l s1 s2 *. f_two a m k n s1 s3 \n", - " +. h_two i m a n s1 s3 *. f_two a j k l s1 s2 \n", - " +. h_two i m k a s1 s3 *. f_two j a l n s2 s3 \n", - " +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n", - " -. h_two i j a n s1 s2 *. f_two a m k l s1 s2 \n", - " -. h_two i j k a s1 s2 *. f_two m a l n s2 s3 \n", - " -. h_two i m a l s1 s3 *. f_two a j k n s1 s3 \n", - " -. h_two j m a l s2 s3 *. f_two i a k n s1 s3 \n", - " ) \n", - " | Beta, Alfa, Beta\n", - " | Alfa, Beta, Alfa -> assert false (*TODO *)\n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "let _ = check 100 integral_value 3 " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "hidden": true - }, - "source": [ - "---------------------------" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "hidden": true, - "scrolled": false - }, - "outputs": [], - "source": [ - "let ki = det_I.(129)\n", - "let kj = det_I.(349)\n", - "\n", - "let alpha_to_string alpha = \n", - " \n", - " let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n", - " \n", - " let i, j, m, k, l, n, s, s', s'', phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Triple (phase,\n", - " { hole ; particle ; spin },\n", - " {hole=hole' ; particle=particle' ; spin=spin' }, \n", - " {hole=hole''; particle=particle''; spin=spin''} )) ->\n", - " hole, hole', hole'', particle, particle', particle'', spin, spin', spin'', phase\n", - " | _ -> assert false\n", - " in\n", - " let spin = function\n", - " | Spin.Alfa -> 0\n", - " | _ -> 1\n", - " in\n", - " exc0.(i).(spin s ) <- \"i\" \n", - " ; exc0.(j).(spin s' ) <- \"j\" \n", - " ; exc0.(k).(spin s ) <- \"k\" \n", - " ; exc0.(l).(spin s' ) <- \"l\" \n", - " ; exc0.(m).(spin s'') <- \"m\" \n", - " ; exc0.(n).(spin s'') <- \"n\" \n", - " ;\n", - " let s0, s0', s0'' = s, s', s'' in\n", - " \n", - " let i, j, k, l, s, s', p1 =\n", - " match Excitation.of_det ki alpha with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " if exc0.(i).(spin s ) = \"-\" then exc0.(i).(spin s ) <- \"p\";\n", - " if exc0.(j).(spin s') = \"-\" then exc0.(j).(spin s') <- \"p\";\n", - " if exc0.(k).(spin s ) = \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"q\";\n", - " if exc0.(l).(spin s') = \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"q\";\n", - " \n", - " let string_h = \n", - " Printf.sprintf \"h_two %s %s %s %s %s %s *. \" \n", - " exc0.(i).(spin s )\n", - " exc0.(j).(spin s')\n", - " exc0.(k).(spin s )\n", - " exc0.(l).(spin s')\n", - " (if s = s0 then \"s \" else if s = s0' then \"s'\" else \"s''\")\n", - " (if s' = s0' then \"s'\" else if s = s0'' then \"s''\" else \"s\" )\n", - " in \n", - " \n", - " let i, j, k, l, s, s', p2 =\n", - " match Excitation.of_det alpha kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " let string_f = \n", - " Printf.sprintf \"f_two %s %s %s %s %s %s\" \n", - " exc0.(i).(spin s )\n", - " exc0.(j).(spin s')\n", - " exc0.(k).(spin s )\n", - " exc0.(l).(spin s')\n", - " (if s = s0 then \"s \" else if s = s0' then \"s'\" else \"s''\")\n", - " (if s' = s0' then \"s'\" else if s = s0'' then \"s''\" else \"s\" )\n", - " in\n", - " (*\n", - " Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n", - " Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n", - " *)\n", - "\n", - " \n", - " let sign = \n", - " if Phase.add p1 p2 = phase then \"+.\" else \"-.\"\n", - " in\n", - " sign ^ string_h ^ string_f\n", - " \n", - "\n", - "let alpha_debug alpha = \n", - " \n", - " let i, j, k, l, s, s', p1 =\n", - " match Excitation.of_det ki alpha with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " Printf.printf \"%d %d %d %d \" i j k l;\n", - " \n", - " let i, j, k, l, s, s', p2 =\n", - " match Excitation.of_det alpha kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " (*\n", - " Format.printf \"|I> -> |a> : %a | \\n@.\" Excitation.pp (Excitation.of_det ki alpha) ;\n", - " Format.printf \"|a> -> |J> : %a | \\n@.\" Excitation.pp (Excitation.of_det alpha kj) ;\n", - " *)\n", - " Printf.printf \"%d %d %d %d \\n%!\" i j k l\n", - "\n", - " \n", - "let strings = \n", - " Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n", - " generate_alphas ki kj 3 1 2 2\n", - " |> Array.of_list\n", - " |> Array.mapi (fun kk alpha -> alpha_to_string alpha)\n", - " |> Array.to_list\n", - " |> List.sort_uniq compare\n", - " |> Array.of_list\n", - "\n", - "let _ = Array.iteri (fun i x -> Printf.printf \"%d %s \\n%!\" i x) strings\n", - "\n", - "let _ =\n", - " let v =\n", - " let alphas =\n", - " generate_alphas ki kj 3 1 2 2\n", - " (*\n", - " |> List.filter (fun alpha ->\n", - " let x = alpha_to_string alpha in\n", - " x = strings.(6)\n", - " )\n", - " *)\n", - " in\n", - " (*\n", - " List.iter alpha_debug alphas ;\n", - " Printf.printf \"\\n%!\";\n", - " *)\n", - " compute_HaaF ki alphas kj \n", - " in\n", - " let x = (integral_value ki kj) in\n", - " Printf.printf \"%20.8e %20.8e %20.8e\\n%!\" x v (v-. x)\n" - ] - } - ], - "metadata": { - "celltoolbar": "Initialization Cell", - "kernelspec": { - "display_name": "OCaml 4.10.0", - "language": "OCaml", - "name": "ocaml-jupyter" - }, - "language_info": { - "codemirror_mode": "text/x-ocaml", - "file_extension": ".ml", - "mimetype": "text/x-ocaml", - "name": "OCaml", - "nbconverter_exporter": null, - "pygments_lexer": "OCaml", - "version": "4.10.0" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/Notebooks/F12_matrix.ipynb b/Notebooks/F12_matrix.ipynb deleted file mode 100644 index 22d7b29..0000000 --- a/Notebooks/F12_matrix.ipynb +++ /dev/null @@ -1,9743 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Test of F12 matrix elements" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Initialization" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val png_image : string -> unit = \n" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "- : unit = ()\n", - "Findlib has been successfully loaded. Additional directives:\n", - " #require \"package\";; to load a package\n", - " #list;; to list the available packages\n", - " #camlp4o;; to load camlp4 (standard syntax)\n", - " #camlp4r;; to load camlp4 (revised syntax)\n", - " #predicates \"p,q,...\";; to set these predicates\n", - " Topfind.reset();; to force that packages will be reloaded\n", - " #thread;; to enable threads\n", - "\n", - "- : unit = ()\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/scemama/qp2/external/opam/4.07.1/lib/bytes: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/base64: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/base64/base64.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs/ocamlcommon.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/result: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/result/result.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving/runtime: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving/runtime/ppx_deriving_runtime.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving_yojson/runtime: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/ppx_deriving_yojson/runtime/ppx_deriving_yojson_runtime.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/unix.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/uuidm: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/uuidm/uuidm.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/easy-format: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/easy-format/easy_format.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/biniou: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/biniou/biniou.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/yojson: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/yojson/yojson.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/jupyter.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/notebook: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/jupyter/notebook/jupyter_notebook.cma: loaded\n" - ] - }, - { - "data": { - "text/plain": [ - "val png_image : string -> Jupyter_notebook.display_id = \n" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs/ocamlbytecomp.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/compiler-libs/ocamltoplevel.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/bigarray.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/lacaml: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/lacaml/lacaml.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/lacaml/top: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/lacaml/top/lacaml_top.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/astring: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/astring/astring.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/cmdliner: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/cmdliner/cmdliner.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/seq: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/stdlib-shims: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/stdlib-shims/stdlib_shims.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/fmt: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt_cli.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/fmt/fmt_tty.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/alcotest: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/alcotest/alcotest.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/ocaml/str.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/zarith: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/zarith/zarith.cma: loaded\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/getopt: added to search path\n", - "/home/scemama/qp2/external/opam/4.07.1/lib/getopt/getopt.cma: loaded\n" - ] - } - ], - "source": [ - "let png_image = print_endline ;;\n", - "\n", - "(* --------- *)\n", - "\n", - "#cd \"/home/scemama/QCaml\";;\n", - "#use \"topfind\";;\n", - "#require \"jupyter.notebook\";;\n", - "\n", - "let png_image name = \n", - " Jupyter_notebook.display_file ~base64:true \"image/png\" (\"Notebooks/images/\"^name)\n", - ";;\n", - "\n", - "#require \"lacaml.top\";;\n", - "#require \"alcotest\";;\n", - "#require \"str\";;\n", - "#require \"bigarray\";;\n", - "#require \"zarith\";;\n", - "#require \"getopt\";;\n", - "#directory \"_build\";;\n", - "#directory \"_build/Basis\";;\n", - "#directory \"_build/CI\";;\n", - "#directory \"_build/MOBasis\";;\n", - "#directory \"_build/Nuclei\";;\n", - "#directory \"_build/Parallel\";;\n", - "#directory \"_build/Perturbation\";;\n", - "#directory \"_build/SCF\";;\n", - "#directory \"_build/Utils\";;" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Modules" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "#load \"Constants.cmo\";;\n", - "#load_rec \"Util.cma\";;\n", - "#load_rec \"Matrix.cmo\";;\n", - "#load_rec \"Simulation.cmo\";;\n", - "#load_rec \"Spindeterminant.cmo\";;\n", - "#load_rec \"Determinant.cmo\";;\n", - "#load_rec \"HartreeFock.cmo\";;\n", - "#load_rec \"MOBasis.cmo\";;\n", - "#load_rec \"F12CI.cmo\";;" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Printers" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val pp_mo : Format.formatter -> MOBasis.t -> unit = \n" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "#install_printer AngularMomentum.pp_string ;;\n", - "#install_printer Basis.pp ;;\n", - "#install_printer Charge.pp ;;\n", - "#install_printer Coordinate.pp ;;\n", - "#install_printer Vector.pp;;\n", - "#install_printer Matrix.pp;;\n", - "#install_printer Util.pp_float_2darray;;\n", - "#install_printer Util.pp_float_array;;\n", - "#install_printer Util.pp_matrix;;\n", - "#install_printer HartreeFock.pp ;;\n", - "#install_printer Fock.pp ;;\n", - "#install_printer MOClass.pp ;;\n", - "let pp_mo ppf t = MOBasis.pp ~start:1 ~finish:0 ppf t ;;\n", - "#install_printer pp_mo;;\n", - "(*\n", - "#install_printer DeterminantSpace.pp;;\n", - "*)\n", - "#install_printer SpindeterminantSpace.pp;;\n", - "#install_printer Bitstring.pp;;\n", - "\n", - "(* --------- *)\n", - "\n", - "open Lacaml.D\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Run" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Simulation\n" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val basis_filename : string = \"/home/scemama/qp2/data/basis/6-31g\"\n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val aux_basis_filename : string = \"/home/scemama/qp2/data/basis/cc-pvdz\"\n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val nuclei : Nuclei.t = [|(Element.N, 0.0000 0.0000 0.0000)|]\n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val frozen_core : bool = true\n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val multiplicity : int = 2\n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val state : int = 1\n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val basis : Basis.t =\n", - " \n", - " Atomic Basis set\n", - " ----------------\n", - "\n", - "-----------------------------------------------------------------------\n", - " # Angular Coordinates (Bohr) Exponents Coefficients\n", - " Momentum X Y Z\n", - "-----------------------------------------------------------------------\n", - " 1-3 S 0.0000 0.0000 0.0000 4.17351100e+03 1.83480000e-03\n", - " 6.27457900e+02 1.39950000e-02\n", - " 1.42902100e+02 6.85870000e-02\n", - " 4.02343300e+01 2.32241000e-01\n", - " 1.28202100e+01 4.69070000e-01\n", - " 4.39043700e+00 3.60455000e-01\n", - " \n", - " 1.16263580e+01 -1.14961000e-01\n", - " 2.71628000e+00 -1.69118000e-01\n", - " 7.72218000e-01 1.14585200e+00\n", - " \n", - " 2.12031300e-01 1.00000000e+00\n", - " \n", - " \n", - "-----------------------------------------------------------------------\n", - " 3-8 P 0.0000 0.0000 0.0000 1.16263580e+01 6.75800000e-02\n", - " 2.71628000e+00 3.23907000e-01\n", - " 7.72218000e-01 7.40895000e-01\n", - " \n", - " 2.12031300e-01 1.00000000e+00\n", - " \n", - " \n", - "-----------------------------------------------------------------------\n", - "\n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val aux_basis : Basis.t =\n", - " \n", - " Atomic Basis set\n", - " ----------------\n", - "\n", - "-----------------------------------------------------------------------\n", - " # Angular Coordinates (Bohr) Exponents Coefficients\n", - " Momentum X Y Z\n", - "-----------------------------------------------------------------------\n", - " 1-6 S 0.0000 0.0000 0.0000 4.17351100e+03 1.83480000e-03\n", - " 6.27457900e+02 1.39950000e-02\n", - " 1.42902100e+02 6.85870000e-02\n", - " 4.02343300e+01 2.32241000e-01\n", - " 1.28202100e+01 4.69070000e-01\n", - " 4.39043700e+00 3.60455000e-01\n", - " \n", - " 1.16263580e+01 -1.14961000e-01\n", - " 2.71628000e+00 -1.69118000e-01\n", - " 7.72218000e-01 1.14585200e+00\n", - " \n", - " 2.12031300e-01 1.00000000e+00\n", - " \n", - " 9.04600000e+03 7.00000000e-04\n", - " 1.35700000e+03 5.38900000e-03\n", - " 3.09300000e+02 2.74060000e-02\n", - " 8.77300000e+01 1.03207000e-01\n", - " 2.85600000e+01 2.78723000e-01\n", - " 1.02100000e+01 4.48540000e-01\n", - " 3.83800000e+00 2.78238000e-01\n", - " 7.46600000e-01 1.54400000e-02\n", - " \n", - " 9.04600000e+03 -1.53000000e-04\n", - " 1.35700000e+03 -1.20800000e-03\n", - " 3.09300000e+02 -5.99200000e-03\n", - " 8.77300000e+01 -2.45440000e-02\n", - " 2.85600000e+01 -6.74590000e-02\n", - " 1.02100000e+01 -1.58078000e-01\n", - " 3.83800000e+00 -1.21831000e-01\n", - " 7.46600000e-01 5.49003000e-01\n", - " \n", - " 2.24800000e-01 1.00000000e+00\n", - " \n", - " \n", - "-----------------------------------------------------------------------\n", - " 3-14 P 0.0000 0.0000 0.0000 1.16263580e+01 6.75800000e-02\n", - " 2.71628000e+00 3.23907000e-01\n", - " 7.72218000e-01 7.40895000e-01\n", - " \n", - " 2.12031300e-01 1.00000000e+00\n", - " \n", - " 1.35500000e+01 3.99190000e-02\n", - " 2.91700000e+00 2.17169000e-01\n", - " 7.97300000e-01 5.10319000e-01\n", - " \n", - " 2.18500000e-01 1.00000000e+00\n", - " \n", - " \n", - "-----------------------------------------------------------------------\n", - " 19-24 D 0.0000 0.0000 0.0000 8.17000000e-01 1.00000000e+00\n", - " \n", - " \n", - "-----------------------------------------------------------------------\n", - "\n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val f12 : F12factor.t =\n", - " {F12factor.expo_s = 1.;\n", - " gaussian =\n", - " {GaussianOperator.coef_g =\n", - " [ -0.314400 -0.303700 -0.168100 -0.098110 -0.060240 -0.037260 ];\n", - " expo_sg =\n", - " [ 0.220900 1.004000 3.622000 12.160000 45.870000 254.400000 ];\n", - " expo_sg_inv =\n", - " [ 4.526935 0.996016 0.276091 0.082237 0.021801 0.003931 ]}}\n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val charge : int = 0\n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val simulation : Simulation.t = \n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let basis_filename = \"/home/scemama/qp2/data/basis/6-31g\" \n", - "let aux_basis_filename = \"/home/scemama/qp2/data/basis/cc-pvdz\" \n", - "let nuclei = Nuclei.of_zmt_string \"n\" \n", - "let frozen_core = true \n", - "let multiplicity = 2\n", - "let state = 1\n", - "\n", - "let basis = Basis.of_nuclei_and_basis_filenames ~nuclei [basis_filename] \n", - "let aux_basis = Basis.of_nuclei_and_basis_filenames ~nuclei (basis_filename :: aux_basis_filename :: []) \n", - "let f12 = F12factor.gaussian_geminal 1.0 \n", - "let charge = 0 \n", - "\n", - "\n", - "let simulation =\n", - " Simulation.make \n", - " ~f12 ~charge ~multiplicity ~nuclei\n", - " ~cartesian:true\n", - " basis\n" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val n_elec_alfa : int = 4\n", - "val n_elec_beta : int = 3\n", - "val n_elec : int = 7\n" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let n_elec_alfa, n_elec_beta, n_elec = \n", - " let e = Simulation.electrons simulation in\n", - " Electrons.(n_alfa e, n_beta e, n_elec e)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Hartree-Fock" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "15 significant shell pairs computed in 0.005208 seconds\n", - "1\n", - "2\n", - "5\n", - "6\n", - "Computed ERIs in 0.026325 seconds\n", - "MOs =\n", - "\n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0.995805 -0.228629 -0 0 -0\n", - " 2 0.0207488 0.523688 2.54045E-16 1.78891E-15 -0\n", - " 3 0 -3.45043E-16 0.516899 5.11587E-15 0.306901\n", - " ... ... ... ... ...\n", - " 7 0 -0 0.381023 3.3482E-15 0.401251\n", - " 8 0 -6.37589E-16 -0.238604 0.273454 0.404641\n", - " 9 0 -6.8E-16 0.182264 0.357982 -0.309095\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 -0 0 0.0896964 4.08276E-15\n", - " 2 1.33506E-15 -3.60646E-15 -1.51213 -6.87142E-14\n", - " 3 -0.759946 0.656011 -2.25085E-15 -1.25628E-14\n", - " ... ... ... ...\n", - " 7 0.836375 -0.602939 2.17188E-15 1.39379E-14\n", - " 8 -0.523755 -0.608033 -2.87741E-14 0.655571\n", - " 9 0.400083 0.464461 -3.95033E-14 0.858218\n", - " \n" - ] - }, - { - "data": { - "text/plain": [ - "val hf : HartreeFock.t = \n", - "======================================================================\n", - " Restricted Open-shell Hartree-Fock \n", - "======================================================================\n", - "\n", - " ------------------------------------------------------------\n", - " # HF energy Convergence HOMO-LUMO\n", - " ------------------------------------------------------------\n", - " 1 -52.57862719 9.9817e-01 0.0835\n", - " 2 -54.20380931 2.2021e-01 0.2639\n", - " 3 -54.23392256 5.7771e-02 0.2682\n", - " 4 -54.24023663 2.1083e-02 0.2680\n", - " 5 -54.24159726 8.9827e-03 0.2673\n", - " 6 -54.24188853 4.2281e-03 0.2669\n", - " 7 -54.24195106 1.9862e-03 0.2667\n", - " 8 -54.24196836 1.6000e-05 0.2665\n", - " 9 -54.24196836 1.6302e-06 0.2665\n", - " 10 -54.24196843 3.8429e-08 0.2665\n", - " ------------------------------------------------------------\n", - "\n", - "\n", - " ============================================================\n", - " One-electron energy -73.7477460896\n", - " Kinetic 54.1465371332\n", - " Potential -127.8942832228\n", - " -------------------------------------------------------- \n", - " Two-electron energy 19.5057776578\n", - " Coulomb 26.0005985081\n", - " Exchange -6.4948208503\n", - " -------------------------------------------------------- \n", - " HF HOMO -5.3102635644\n", - " HF LUMO 1.9421331121\n", - " HF LUMO-LUMO 7.2523966765\n", - " -------------------------------------------------------- \n", - " Electronic energy -54.2419684318\n", - " Nuclear repulsion 0.0000000000\n", - " Hartree-Fock energy -54.2419684318\n", - " ============================================================\n", - " \n", - "\n" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mo_basis : MOBasis.t =\n", - " Eigenvalues: -15.681404 -0.961606 -0.451178 -0.195149 0.040479 \n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0.995805 -0.228629 -0 0 -0\n", - " 2 0.0207488 0.523688 2.54045E-16 1.78891E-15 -0\n", - " 3 0 -3.45043E-16 0.516899 5.11587E-15 0.306901\n", - " ... ... ... ... ...\n", - " 7 0 -0 0.381023 3.3482E-15 0.401251\n", - " 8 0 -6.37589E-16 -0.238604 0.273454 0.404641\n", - " 9 0 -6.8E-16 0.182264 0.357982 -0.309095\n", - " \n", - " Eigenvalues: 0.908849 0.950925 0.975309 0.912008 \n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 -0 0 0.0896964 4.08276E-15\n", - " 2 1.33506E-15 -3.60646E-15 -1.51213 -6.87142E-14\n", - " 3 -0.759946 0.656011 -2.25085E-15 -1.25628E-14\n", - " ... ... ... ...\n", - " 7 0.836375 -0.602939 2.17188E-15 1.39379E-14\n", - " 8 -0.523755 -0.608033 -2.87741E-14 0.655571\n", - " 9 0.400083 0.464461 -3.95033E-14 0.858218\n", - " \n", - " \n" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let hf = HartreeFock.make ~guess:`Hcore ~max_scf:10 simulation ;;\n", - "\n", - "let mo_basis = MOBasis.of_hartree_fock hf" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " FCI-F12" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notations:\n", - "\n", - "* $\\langle ij || kl \\rangle = \\int \\phi_i(r_1) \\phi_j(r_2) \\frac{1}{r_{12}} \\phi_k(r1) \\phi_l(r2) $ \n", - "* $\\left[ ij || kl \\right] = \\int \\phi_i(r_1) \\phi_j(r_2) f_{12} \\phi_k(r1) \\phi_l(r2) $ \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Common functions" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val f12 : F12factor.t =\n", - " {F12factor.expo_s = 1.;\n", - " gaussian =\n", - " {GaussianOperator.coef_g =\n", - " [ -0.314400 -0.303700 -0.168100 -0.098110 -0.060240 -0.037260 ];\n", - " expo_sg =\n", - " [ 0.220900 1.004000 3.622000 12.160000 45.870000 254.400000 ];\n", - " expo_sg_inv =\n", - " [ 4.526935 0.996016 0.276091 0.082237 0.021801 0.003931 ]}}\n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mo_num : int = 9\n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val pp_spindet : Format.formatter -> Spindeterminant.t -> unit = \n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val pp_det : Format.formatter -> Determinant.t -> unit = \n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let f12 = Util.of_some @@ Simulation.f12 simulation \n", - "\n", - "let mo_num = MOBasis.size mo_basis \n", - "\n", - "let pp_spindet = Spindeterminant.pp mo_num\n", - "\n", - "let pp_det = Determinant.pp mo_num\n", - "\n", - ";;\n", - "\n", - "#install_printer pp_spindet ;;\n", - "#install_printer pp_det ;;\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val simulation_aux : Simulation.t = \n" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "66 significant shell pairs computed in 0.050789 seconds\n", - "1\n", - "2\n", - "5\n", - "6\n", - "9\n", - "10\n", - "11\n", - "12\n", - "15\n", - "18\n", - "Computed ERIs in 0.889029 seconds\n" - ] - }, - { - "data": { - "text/plain": [ - "val aux_basis : MOBasis.t =\n", - " Eigenvalues: -15.681404 -0.961606 -0.451178 -0.195149 0.040479 \n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0.995805 -0.228629 -1.04121E-12 -1.20393E-11 -7.74166E-12\n", - " 2 0.0207488 0.523688 -3.08871E-13 -4.88506E-13 -3.2349E-13\n", - " 3 2.26649E-12 -2.08563E-12 0.516899 3.82452E-12 0.306901\n", - " ... ... ... ... ...\n", - " 22 0 0 0 0 -0\n", - " 23 0 0 0 0 -0\n", - " 24 0 0 0 0 -0\n", - " \n", - " Eigenvalues: 0.908849 0.950925 0.975309 0.912008 2.032635 \n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 -- -- 10 --\n", - " 1 -1.59863E-11 1.67271E-11 0.0896964 8.01274E-12 0\n", - " 2 7.28187E-13 -1.60327E-12 -1.51213 -2.11029E-13 0\n", - " 3 -0.759946 0.656011 -6.79771E-13 -6.65308E-12 0\n", - " ... ... ... ... ...\n", - " 22 -0 -0 0 0 0\n", - " 23 -0 -0 0 0 1\n", - " 24 -0 -0 0 0 0\n", - " \n", - " Eigenvalues: 2.209274 2.205946 2.198723 2.627905 18.044176 \n", - " -- 11 -- -- 12 -- -- 13 -- -- 14 -- -- 15 --\n", - " 1 4.4959E-10 -2.92245E-09 -6.60522E-10 7.27202 39.53\n", - " 2 -2.27871E-11 1.81557E-11 8.06971E-11 -19.3218 -84.1067\n", - " 3 -8.99756 -28.2245 -4.1365 -1.31641E-12 -1.85784E-10\n", - " ... ... ... ... ...\n", - " 22 -0 -0 2.75019E-14 0 0\n", - " 23 -0 -0 0 0 0\n", - " 24 -3.45546E-14 -7.00504E-14 0 0 0\n", - " \n", - " Eigenvalues: 31.400935 31.392955 31.387019 476.102993 2.036553 \n", - " -- 16 -- -- 17 -- -- 18 -- -- 19 -- -- 20 --\n", - " 1 -2.50732E-08 -1.36441E-09 1.64713E-08 416.882 -2.63792E-11\n", - " 2 5.37419E-10 -1.14011E-10 5.52992E-10 -1.46938 4.55954E-13\n", - " 3 -190.497 18.1424 30.0485 -1.1041E-08 -1.61968E-10\n", - " ... ... ... ... ...\n", - " 22 1.51034E-13 2.01121E-13 1.28118E-13 0 -0.128674\n", - " 23 -0 -0 -0 0 -0\n", - " 24 -7.82065E-13 -0 -0 0 0.923094\n", - " \n", - " Eigenvalues: 2.033307 2.036684 2.036990 \n", - " -- 21 -- -- 22 -- -- 23 --\n", - " 1 -5.67082E-11 1.56263E-12 3.6287E-10\n", - " 2 9.80094E-13 -2.68735E-14 -6.29775E-12\n", - " 3 -4.74932E-12 1.67489E-13 -0\n", - " ... ... ...\n", - " 22 0.986223 -0.103886 -0.00379526\n", - " 23 0 0 -0\n", - " 24 -0.383449 0.0293605 0.00152471\n", - " \n", - " \n" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val aux_num : int = 23\n" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let simulation_aux = \n", - " let charge = Charge.to_int @@ Simulation.charge simulation \n", - " and multiplicity = Electrons.multiplicity @@ Simulation.electrons simulation\n", - " and nuclei = Simulation.nuclei simulation\n", - " in\n", - " let general_basis = \n", - " Basis.general_basis @@ Simulation.basis simulation\n", - " in\n", - " GeneralBasis.combine [\n", - " general_basis ; GeneralBasis.read aux_basis_filename\n", - " ]\n", - " |> Basis.of_nuclei_and_general_basis nuclei\n", - " |> Simulation.make ~f12 ~charge ~multiplicity ~nuclei \n", - "\n", - "\n", - "let aux_basis = \n", - " MOBasis.of_mo_basis simulation_aux mo_basis\n", - "\n", - "let aux_num = \n", - " MOBasis.size aux_basis\n" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "66 significant shell pairs computed in 0.842000 seconds\n", - "1\n", - "2\n", - "5\n", - "6\n", - "9\n", - "10\n", - "11\n", - "12\n", - "15\n", - "18\n", - "Computed ERIs in 17.257765 seconds\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "4-idx transformation \n", - "23 / 23\n", - "4-idx transformation \n", - "23 / 23\n" - ] - } - ], - "source": [ - "let () = ignore @@ MOBasis.f12_ints aux_basis\n", - "let () = ignore @@ MOBasis.two_e_ints aux_basis" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Integral-based functions" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\\begin{equation}\n", - "\\langle I | \\hat{H} | J \\rangle = \\begin{cases}\n", - "\\sum_i h_{ii} + \\frac{1}{2} \\sum_{ij} \\langle ij || ij \\rangle \\text{ when } |J\\rangle = |I\\rangle \\\\\n", - "h_{ik} + \\sum_{j} \\langle ij || kj \\rangle \\text{ when } |J\\rangle = \\hat{T}_i^k |I\\rangle \\\\\n", - "\\langle ij || kl \\rangle \\text{ when } |J\\rangle = \\hat{T}_{ij}^{kl} |I\\rangle \\\\\n", - "\\end{cases}\n", - "\\end{equation}\n", - "\n", - "\n", - "\\begin{equation}\n", - "\\langle I | \\hat{F} | J \\rangle = \\begin{cases}\n", - "\\sum_i f_{ii} + \\frac{1}{2} \\sum_{ij} \\langle ij || ij \\rangle \\text{ when } |J\\rangle = |I\\rangle \\\\\n", - "f_{ik} + \\sum_{j} \\langle ij || kj \\rangle \\text{ when } |J\\rangle = \\hat{T}_i^k |I\\rangle \\\\\n", - "\\langle ij || kl \\rangle \\text{ when } |J\\rangle = \\hat{T}_{ij}^{kl} |I\\rangle \\\\\n", - "\\end{cases}\n", - "\\end{equation}" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val cancel_singles : bool = false\n" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mos_cabs : int list =\n", - " [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]\n" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mos_abs : int list =\n", - " [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21;\n", - " 22; 23]\n" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mos_in : int list = [1; 2; 3; 4; 5; 6; 7; 8; 9]\n" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mos_a : Determinant.t -> int list = \n" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val mos_b : Determinant.t -> int list = \n" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let cancel_singles = false \n", - "\n", - "let mos_cabs = \n", - " Util.list_range (mo_num+1) aux_num\n", - " \n", - "let mos_abs = \n", - " Util.list_range 1 aux_num\n", - " \n", - "let mos_in = \n", - " Util.list_range 1 mo_num\n", - "\n", - "let mos_a k =\n", - " Determinant.alfa k\n", - " |> Spindeterminant.to_list\n", - " \n", - "let mos_b k =\n", - " Determinant.beta k\n", - " |> Spindeterminant.to_list\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### H integrals" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val h_one : int -> int -> '_weak2 -> float = \n" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val h_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = \n" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let h_one =\n", - " let h = \n", - " MOBasis.one_e_ints aux_basis\n", - " in fun i j _ -> h.{i,j}\n", - " \n", - "let h_two = \n", - " let two_e_ints = MOBasis.two_e_ints aux_basis in\n", - " let h2 i j k l (s:Spin.t) (s':Spin.t) =\n", - " if s' <> s then\n", - " ERI.get_phys two_e_ints i j k l\n", - " else\n", - " (ERI.get_phys two_e_ints i j k l) -. \n", - " (ERI.get_phys two_e_ints i j l k)\n", - " in\n", - " h2\n", - "\n", - " \n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### F12 integrals" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val f_two : int -> int -> int -> int -> Spin.t -> Spin.t -> float = \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val f_one : 'a -> 'b -> 'c -> float = \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val f_one : int -> int -> '_weak2 -> float = \n" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let f_two = \n", - " let two_e_ints = MOBasis.f12_ints aux_basis in\n", - " let f2 i j k l (s:Spin.t) (s':Spin.t) =\n", - " if s' <> s then\n", - " 0.5 *. F12.get_phys two_e_ints i j k l\n", - " else\n", - " 0.5 *. (\n", - " (F12.get_phys two_e_ints i j k l) -. \n", - " (F12.get_phys two_e_ints i j l k) )\n", - " in\n", - " let f3 i j k l (s:Spin.t) (s':Spin.t) = \n", - " if (i=k && j<>l) || (j=l && i<>k) then\n", - " 0.\n", - " else\n", - " f2 i j k l s s'\n", - " in\n", - " if cancel_singles then f3 else f2\n", - "\n", - "let f_one = fun _ _ _ -> 0.\n", - "\n", - "(*\n", - "let f_two = h_two\n", - "*)\n", - "\n", - "let f_one = h_one" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Determinant-based functions" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Integrals" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val f12_integrals :\n", - " 'a ->\n", - " (int -> int -> '_weak2 -> float) *\n", - " (int -> int -> int -> int -> Spin.t -> Spin.t -> float) * 'b option = \n" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val h_ij : MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n", - " \n" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val f_ij : 'a -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float =\n", - " \n" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val hf_ij :\n", - " MOBasis.t -> CIMatrixElement.De.t -> CIMatrixElement.De.t -> float list =\n", - " \n" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let f12_integrals mo_basis =\n", - " ( f_one, f_two, None )\n", - "\n", - "let h_ij mo_basis ki kj =\n", - " let integrals =\n", - " List.map (fun f -> f mo_basis)\n", - " [ CI.h_integrals ]\n", - " in\n", - " CIMatrixElement.make integrals ki kj \n", - " |> List.hd\n", - "\n", - "\n", - "let f_ij mo_basis ki kj =\n", - " let integrals =\n", - " List.map (fun f -> f mo_basis)\n", - " [ f12_integrals ]\n", - " in\n", - " CIMatrixElement.make integrals ki kj \n", - " |> List.hd \n", - "\n", - "\n", - "let hf_ij mo_basis ki kj =\n", - " let integrals =\n", - " List.map (fun f -> f mo_basis)\n", - " [ CI.h_integrals ; f12_integrals ]\n", - " in\n", - " CIMatrixElement.make integrals ki kj\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Determinant space" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val is_a_double : DeterminantSpace.t -> Determinant.t -> bool = \n" - ] - }, - "execution_count": 33, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let is_a_double det_space =\n", - " let mo_class = DeterminantSpace.mo_class det_space in\n", - " let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n", - " let m l =\n", - " List.fold_left (fun accu i ->\n", - " let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n", - " ) (Bitstring.zero mo_num) l\n", - " in\n", - " let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n", - " fun k -> \n", - " let alfa =\n", - " Determinant.alfa k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let beta =\n", - " Determinant.beta k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let a = Bitstring.logand aux_mask alfa\n", - " and b = Bitstring.logand aux_mask beta\n", - " in\n", - " match Bitstring.popcount a + Bitstring.popcount b with\n", - " | 2 | 1 -> true\n", - " | 0 | _ -> false\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of determinants : 56 28 1568\n" - ] - }, - { - "data": { - "text/plain": [ - "val in_space : DeterminantSpace.t = \n" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of determinants : 1540 231 355740\n" - ] - }, - { - "data": { - "text/plain": [ - "val aux_space : DeterminantSpace.t = \n" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val det_space_in : unit -> Determinant.t Stream.t = \n" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val det_space_out : unit -> (Determinant.t * Determinant.t) Stream.t = \n" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let in_space = \n", - " DeterminantSpace.fci_f12_of_mo_basis aux_basis ~frozen_core mo_num\n", - " \n", - "let aux_space = \n", - " DeterminantSpace.fci_of_mo_basis aux_basis ~frozen_core \n", - "\n", - "let det_space_in () =\n", - " DeterminantSpace.determinant_stream in_space\n", - "\n", - "let det_space_out () =\n", - " let s = \n", - " DeterminantSpace.determinant_stream aux_space\n", - " in\n", - " Stream.from (fun _ ->\n", - " try\n", - " let is_a_double = is_a_double in_space in\n", - " let rec result () =\n", - " let ki = Stream.next s in\n", - " if is_a_double ki then\n", - " Some (ki,ki)\n", - " else\n", - " result ()\n", - " in\n", - " result ()\n", - " with Stream.Failure -> None\n", - " )\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val ci : CI.t =\n", - " {CI.e_shift = -54.2419683633284677; det_space = ; m_H = ;\n", - " m_S2 = ; eigensystem = ; n_states = 1}\n" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " 1 0.0000000000 5.38465905e-01\n", - " 2 -0.0538262193 1.87217169e-01\n", - " 3 -0.0657011468 6.52524404e-02\n", - " 4 -0.0682884307 4.47790537e-02\n", - " 5 -0.0722202576 2.28670803e-02\n", - " 6 -0.0732730385 5.26351716e-03\n", - " 7 -0.0733234182 9.38250052e-04\n", - " 8 -0.0733249420 2.14671657e-04\n", - " 0 -0.0733250301 7.26676403e-05\n", - " 1 -0.0733250395 2.46738965e-05\n", - " 2 -0.0733250400 1.50948498e-05\n", - " 3 -0.0733250400 4.00236940e-06\n", - " 4 -0.0733250400 1.38596264e-06\n" - ] - }, - { - "data": { - "text/plain": [ - "val ci_coef : Lacaml.D.Mat.t =\n", - " \n", - "\n", - " -- 1 --\n", - " 1 0.701258\n", - " 2 0\n", - " 3 0\n", - " ...\n", - " 1566 0\n", - " 1567 0\n", - " 1568 0\n", - " \n", - "val ci_energy : Lacaml.D.Vec.t =\n", - " R1 R2 R3 R5 R6 R7\n", - " -54.3153 -54.1549 -53.2726 ... -51.7367 -51.4918 -50.3061\n" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " 5 -0.0733250400 7.40047633e-07\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let ci = CI.make ~n_states:state in_space\n", - "\n", - "let ci_coef, ci_energy = Lazy.force ci.eigensystem \n", - "\n", - "let _ = print_newline () \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Permutation operator $p_{12}$ that generates a new determinant with electrons 1 and 2 swapped." - ] - }, - { - "cell_type": "raw", - "metadata": {}, - "source": [ - "let p12 det_space =\n", - " let mo_class = DeterminantSpace.mo_class det_space in\n", - " let mo_num = Array.length @@ MOClass.mo_class_array mo_class in\n", - " let m l =\n", - " List.fold_left (fun accu i ->\n", - " let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n", - " ) (Bitstring.zero mo_num) l\n", - " in\n", - " let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n", - " let not_aux_mask =\n", - " Bitstring.(shift_left_one mo_num (mo_num-1) |> minus_one |> logxor aux_mask)\n", - " in\n", - " fun k ->\n", - " let alfa =\n", - " Determinant.alfa k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let beta =\n", - " Determinant.beta k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let a = Bitstring.logand aux_mask alfa\n", - " and b = Bitstring.logand aux_mask beta\n", - " in\n", - " match Bitstring.popcount a, Bitstring.popcount b with\n", - " | 2, 0 \n", - " | 0, 2 -> Some (Determinant.negate_phase k)\n", - " | 1, 1 -> Some (Determinant.of_spindeterminants\n", - " (Spindeterminant.of_bitstring @@\n", - " Bitstring.(logor b (logand not_aux_mask alfa)) )\n", - " (Spindeterminant.of_bitstring @@\n", - " Bitstring.(logor a (logand not_aux_mask beta))\n", - " ) )\n", - " | 1, 0 \n", - " | 0, 1 -> Some k\n", - " | _ -> None\n", - " \n", - " \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Matrices $\\langle I | H | \\alpha \\rangle$ and $\\langle I | F | \\alpha \\rangle$ " - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val randomize : bool = false\n" - ] - }, - "execution_count": 36, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val out_list : (Determinant.t * Determinant.t) list =\n", - " [(phase:+1\n", - " a:+1 +++------+------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 +++------+------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - " a:+1 ++-+-----+------------------------------------------------------\n", - " b:+1 +++-------------------------------------------------------------\n", - ",\n", - "phase:+1\n", - "a:+1 ++-+-----+------------------------------------------------------\n", - "b:+1 +++-------------------------------------------------------------\n", - ");\n", - "(phase:+1\n", - " a:+1 +-++-----+------------------------------------------------------\n", - 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";\n", - "phase:+1\n", - "a:+1 +-+-++----------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+++----------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +++---+---------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-+--+---------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-++--+---------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++--+-+---------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+-+-+---------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--++-+---------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++---++---------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+--++---------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+-++---------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +---+++---------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - 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";\n", - "phase:+1\n", - "a:+1 ++---+-+--------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+--+-+--------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+-+-+--------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +---++-+--------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++----++--------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+---++--------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+--++--------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +---+-++--------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +----+++--------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +++-----+-------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-+----+-------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-++----+-------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++--+---+-------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+-+---+-------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--++---+-------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++---+--+-------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+--+--+-------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+-+--+-------------------------------------------------------\n", - "b:+1 ++--+-----------------------------------------------------------\n", - 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";\n", - "phase:+1\n", - "a:+1 ++++------------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +++-+-----------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-++-----------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+++-----------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +++--+----------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-+-+----------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-++-+----------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++--++----------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+-++----------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+++----------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +++---+---------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-+--+---------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - 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";\n", - "phase:+1\n", - "a:+1 ++----++--------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+---++--------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+--++--------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +---+-++--------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +----+++--------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +++-----+-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-+----+-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-++----+-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++--+---+-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+-+---+-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--++---+-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++---+--+-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - 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";\n", - "phase:+1\n", - "a:+1 +---+-+-+-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +----++-+-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-----++-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+----++-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+---++-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +---+--++-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +----+-++-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-----+++-------------------------------------------------------\n", - "b:+1 +-+-+-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++++------------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +++-+-----------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-++-----------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+++-----------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +++--+----------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-+-+----------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-++-+----------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++--++----------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+-++----------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+++----------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +++---+---------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++-+--+---------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-++--+---------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++--+-+---------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+-+-+---------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--++-+---------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 ++---++---------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +-+--++---------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "phase:+1\n", - "a:+1 +--+-++---------------------------------------------------------\n", - "b:+1 +--++-----------------------------------------------------------\n", - ";\n", - "...|]\n" - ] - }, - "execution_count": 36, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let randomize = false\n", - "\n", - "let out_list =\n", - " Util.stream_to_list (det_space_out ())\n", - " \n", - "let in_list =\n", - " Util.stream_to_list (det_space_in ())\n", - " \n", - "let det_a = Array.of_list out_list\n", - " |> Array.map (fun (i,_) -> i)\n", - "\n", - "let det_I =\n", - " if randomize then\n", - " let n = 123456789 in\n", - " in_list\n", - " |> List.map (fun k -> (Random.int n, k))\n", - " |> List.sort compare\n", - " |> List.map (fun (_,k) -> k)\n", - " |> Array.of_list\n", - " else\n", - " Array.of_list in_list\n" - ] - }, - { - "cell_type": "raw", - "metadata": { - "raw_mimetype": "text/markdown" - }, - "source": [ - "let m_H_aux, m_F_aux = \n", - " \n", - " let rec col_vecs_list accu_H accu_F = function\n", - " | [] -> \n", - " List.rev accu_H, \n", - " List.rev accu_F \n", - " | (ki, ki') :: rest when ki = ki' ->\n", - " begin\n", - " let h, f = \n", - " List.map (fun kj ->\n", - " match hf_ij aux_basis kj ki with\n", - " | [ a ; b ] -> a, b\n", - " | _ -> assert false ) in_list\n", - " |> List.split\n", - " in\n", - " let h = Vec.of_list h in\n", - " let f = Vec.of_list f in\n", - " scal 0.5 f; (* Specific to He singlet *)\n", - " col_vecs_list (h::accu_H) (f::accu_F) rest\n", - " end\n", - " | (ki, ki') :: rest ->\n", - " begin\n", - " assert false;\n", - " end\n", - " in\n", - " let h, f = \n", - " col_vecs_list [] [] out_list\n", - " in\n", - " Mat.of_col_vecs_list h,\n", - " Mat.of_col_vecs_list f" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Function to generate all intermediate external determinants $|\\alpha \\rangle$ between $|I\\rangle$ and $|J\\rangle$, with a positive phase factor.\n", - "\n", - "* `exc` is the degree of excitation between $|I\\rangle$ and $|J\\rangle$\n", - "* `cabs` is the number of electrons in the CABS\n", - "* `l` is the degree of excitation between $|I\\rangle$ and $|\\alpha \\rangle$\n", - "* `r` is the degree of excitation between $|\\alpha \\rangle$ and $|J\\rangle$" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val generate_alphas :\n", - " Determinant.t ->\n", - " Determinant.t -> int -> int -> int -> int -> Determinant.t list = \n" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val compute_HaaF :\n", - " CIMatrixElement.De.t ->\n", - " CIMatrixElement.De.t list -> CIMatrixElement.De.t -> float = \n" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let generate_alphas ki kj exc cabs l r =\n", - " (* Check input excitation degree *)\n", - " let d = Determinant.degree ki kj in\n", - " if d <> exc then\n", - " Printf.sprintf \"Invalid excitation degree. Expected %d and found %d.\" exc d\n", - " |> failwith;\n", - " \n", - " (* Generate single excitations *)\n", - " let all_singles ki =\n", - " let mos_a, mos_b = Determinant.to_lists ki in\n", - " [ List.map (fun hole -> \n", - " List.map (fun particle ->\n", - " if hole = particle then None else\n", - " Some (Determinant.single_excitation Spin.Alfa hole particle ki)\n", - " ) mos_abs\n", - " ) mos_a\n", - " ;\n", - " List.map (fun hole -> \n", - " List.map (fun particle ->\n", - " if hole = particle then None else\n", - " Some (Determinant.single_excitation Spin.Beta hole particle ki)\n", - " ) mos_abs\n", - " ) mos_b \n", - " ]\n", - " |> List.concat\n", - " |> List.concat\n", - " |> Util.list_some\n", - " |> List.filter (fun x -> Determinant.is_none x = false)\n", - " |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n", - " in\n", - " \n", - " (* Generate double excitations *)\n", - " let all_doubles ki =\n", - " let mos_a, mos_b = Determinant.to_lists ki in\n", - " [ List.map (fun hole -> (* Alpha-Alpha *)\n", - " List.map (fun particle ->\n", - " List.map (fun hole' -> \n", - " List.map (fun particle' ->\n", - " if hole = particle || hole' = particle' then None else\n", - " if hole' > hole && particle' < particle then\n", - " Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki)\n", - " else None\n", - " ) mos_abs\n", - " ) mos_a \n", - " ) mos_abs\n", - " ) mos_a\n", - " ; \n", - " List.map (fun hole -> (* Beta-Beta *)\n", - " List.map (fun particle ->\n", - " List.map (fun hole' -> \n", - " List.map (fun particle' ->\n", - " if hole' > hole && particle' < particle && hole <> particle && hole' <> particle' then\n", - " Some (Determinant.double_excitation Spin.Beta hole particle Spin.Beta hole' particle' ki)\n", - " else None\n", - " ) mos_abs\n", - " ) mos_b \n", - " ) mos_abs\n", - " ) mos_b\n", - " ;\n", - " List.map (fun hole -> (* Alpha-Beta *)\n", - " List.map (fun particle ->\n", - " List.map (fun hole' -> \n", - " List.map (fun particle' ->\n", - " if hole = particle || hole' = particle' then None else\n", - " Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Beta hole' particle' ki)\n", - " ) mos_abs\n", - " ) mos_b \n", - " ) mos_abs\n", - " ) mos_a\n", - " ]\n", - " |> List.concat\n", - " |> List.concat\n", - " |> List.concat\n", - " |> List.concat\n", - " |> Util.list_some\n", - " |> List.filter (fun x -> Determinant.is_none x = false)\n", - " |> List.map (fun x -> Determinant.set_phase Phase.Pos x)\n", - " in\n", - "\n", - " (* Generate left and right excitations *)\n", - " let al = \n", - " match l with\n", - " | 1 -> all_singles ki\n", - " | 2 -> all_doubles ki\n", - " | _ -> assert false\n", - " in\n", - " let ar = \n", - " match r with\n", - " | 1 -> all_singles kj\n", - " | 2 -> all_doubles kj\n", - " | _ -> assert false\n", - " in\n", - " \n", - " let mo_class = DeterminantSpace.mo_class in_space in\n", - " let m l =\n", - " List.fold_left (fun accu i ->\n", - " let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j)\n", - " ) (Bitstring.zero mo_num) l\n", - " in\n", - " let aux_mask = m (MOClass.auxiliary_mos mo_class) in\n", - " let good_cabs k = \n", - " let alfa =\n", - " Determinant.alfa k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let beta =\n", - " Determinant.beta k\n", - " |> Spindeterminant.bitstring\n", - " in\n", - " let a = Bitstring.logand aux_mask alfa\n", - " and b = Bitstring.logand aux_mask beta\n", - " in\n", - " Bitstring.popcount a + Bitstring.popcount b = cabs\n", - " in\n", - " let good_lr k =\n", - " Determinant.degree ki k = l &&\n", - " Determinant.degree k kj = r \n", - " in\n", - "\n", - "\n", - " \n", - " (* Merge lists in a set of unique determinants *)\n", - " List.concat [ al; ar ]\n", - " |> List.sort_uniq compare\n", - " \n", - " (* Filter out all determinants with incorrect numbers of electrons in the CABS *)\n", - " |> List.filter good_cabs \n", - " \n", - " (* Filter out all determinants with incorrect excitation numbers *)\n", - " |> List.filter good_lr \n", - " \n", - " \n", - "let compute_HaaF ki alphas kj =\n", - " List.fold_left (fun accu alpha -> accu\n", - " +. h_ij aux_basis ki alpha\n", - " *. f_ij aux_basis alpha kj\n", - " ) 0. alphas\n" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val check :\n", - " int ->\n", - " (CIMatrixElement.De.t -> CIMatrixElement.De.t -> float) ->\n", - " int -> int -> int -> int -> unit = \n" - ] - }, - "execution_count": 38, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val sum : 'a list -> ('a -> float) -> float = \n" - ] - }, - "execution_count": 38, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let check n integral_value exc cabs lexc rexc =\n", - " let cpudet, cpuint = ref 0., ref 0. in\n", - " let det_list =\n", - " match n with\n", - " | 0 -> det_I\n", - " | n -> Array.sub det_I 0 n\n", - " in\n", - " let result =\n", - " Printf.printf \"Checking ... \\n%!\";\n", - " let percent = ref 0 in\n", - " let task (i,ki) =\n", - " (let p = (10 * (i+1))/(Array.length det_list) in\n", - " if p <> !percent then\n", - " ( percent := p ; Printf.printf \" - %3d %%\\n%!\" (p*10) ));\n", - " Array.mapi (fun j kj -> \n", - " if i > j || Determinant.degree ki kj <> exc then\n", - " (0,0,0.,0.)\n", - " else\n", - " begin\n", - " let alphas = generate_alphas ki kj exc cabs lexc rexc in\n", - " let det_value =\n", - " let t0 = Unix.gettimeofday () in\n", - " let result = compute_HaaF ki alphas kj in\n", - " cpudet := !cpudet +. Unix.gettimeofday () -. t0;\n", - " result\n", - " in\n", - " let int_value = \n", - " let t0 = Unix.gettimeofday () in\n", - " let result = integral_value ki kj in\n", - " cpuint := !cpuint +. Unix.gettimeofday () -. t0;\n", - " result\n", - " in\n", - "(* Printf.printf \"%d %d %e %e\\n%!\" i j det_value int_value; *)\n", - " (i,j,det_value,int_value)\n", - " end\n", - " ) det_list\n", - " in\n", - " det_list\n", - " |> Array.mapi (fun i ki -> (i,ki))\n", - " |> Array.to_list\n", - " |> Stream.of_list\n", - " |> Farm.run ~f:task\n", - " |> Util.stream_to_list\n", - " |> Array.concat\n", - " in\n", - " let i,j,d,v = \n", - " let rec aux k imax jmax emax dmax vmax = \n", - " if k = -1 then\n", - " imax, jmax, dmax, vmax\n", - " else\n", - " let i, j, d, v = result.(k) in\n", - " let e = abs_float (d -. v) in\n", - " if e >= emax then\n", - " aux (k-1) i j e d v\n", - " else\n", - " aux (k-1) imax jmax emax dmax vmax\n", - " in\n", - " aux (Array.length result - 1) 0 0 0. 0. 0.\n", - " in\n", - " let error = abs_float (d -. v) in\n", - " if error < epsilon_float then\n", - " (*\n", - " Printf.printf \"OK: %e\\n%!\" error\n", - " *)\n", - " Printf.printf \"OK: (%d, %d) | %e %e | %e | cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n", - " else\n", - " Printf.printf \"Failed: (%d, %d) | %e %e | %e | cpu : %f %f\\n%!\" i j d v error !cpudet !cpuint\n", - "\n", - " \n", - "let sum l f = List.fold_left (fun accu i -> accu +. f i) 0. l" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val array_3_init :\n", - " int ->\n", - " int ->\n", - " int ->\n", - " (int -> int -> int -> float) ->\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 39, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val array_4_init :\n", - " int ->\n", - " int ->\n", - " int ->\n", - " int ->\n", - " (int -> int -> int -> int -> float) ->\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 39, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val array_5_init :\n", - " int ->\n", - " int ->\n", - " int ->\n", - " int ->\n", - " int ->\n", - " (int -> int -> int -> int -> int -> float) ->\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t =\n", - " \n" - ] - }, - "execution_count": 39, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let array_3_init d1 d2 d3 f =\n", - " let result = \n", - " Bigarray.(Array3.create Float64 fortran_layout) d1 d2 d3\n", - " in\n", - " for k=1 to d3 do\n", - " for j=1 to d2 do\n", - " for i=1 to d1 do\n", - " result.{i,j,k} <- f i j k\n", - " done\n", - " done\n", - " done;\n", - " result\n", - "\n", - "\n", - "let array_4_init d1 d2 d3 d4 f =\n", - " let result = \n", - " Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4 |]\n", - " in\n", - " for l=1 to d4 do\n", - " for k=1 to d3 do\n", - " for j=1 to d2 do\n", - " for i=1 to d1 do\n", - " result.{i,j,k,l} <- f i j k l\n", - " done\n", - " done\n", - " done\n", - " done;\n", - " result\n", - "\n", - "\n", - "let array_5_init d1 d2 d3 d4 d5 f =\n", - " let result = \n", - " Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4;d5 |]\n", - " in\n", - " for m=1 to d5 do\n", - " for l=1 to d4 do\n", - " for k=1 to d3 do\n", - " for j=1 to d2 do\n", - " for i=1 to d1 do\n", - " result.{i,j,k,l,m} <- f i j k l m\n", - " done\n", - " done\n", - " done\n", - " done\n", - " done;\n", - " result\n", - "\n", - "(* ----- *)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "******" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 1. 0 1 11" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/plain": [ - "- : Jupyter_notebook.display_id = \n" - ] - }, - "execution_count": 40, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let _ = png_image \"0_1_11.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n", - "\n", - "$\\sum_i \\sum_a \\hat{T}_{i}^{a} \\hat{T}_{a}^{i}$\n", - "\n", - "\\begin{align}\n", - "\\sum_{a} \\sum_{i}\n", - " \\left( h_{ia} +\n", - " \\sum_{j} \\langle i j || a j \\rangle +\n", - " \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle \\right) \n", - " \\left( f_{ai} +\n", - " \\sum_{j} \\left[ a j || i j \\right] + \n", - " \\sum_{\\bar{j}} \\left[ a \\bar{j} | i \\bar{j} \\right] \\right) + \\\\\n", - "\\sum_{\\bar{a}} \\sum_{\\bar{i}}\n", - " \\left( h_{ia} +\n", - " \\sum_{j} \\langle \\bar{i} j | \\bar{a} j \\rangle +\n", - " \\sum_{\\bar{j}} \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{j} \\rangle \\right) \n", - " \\left( f_{ai} +\n", - " \\sum_{j} \\left[ \\bar{a} j | \\bar{i} j \\right] + \n", - " \\sum_{\\bar{j}} \\left[ \\bar{a} \\bar{j} || \\bar{i} \\bar{j} \\right] \\right) \n", - "\\end{align}" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val integral_value : Determinant.t -> 'a -> float = \n" - ] - }, - "execution_count": 41, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "Failed: (135, 135) | 2.284769e+00 2.284769e+00 | 1.776357e-15 | cpu : 2.160390 0.491860\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 41, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let integral_value ki kj = \n", - " (* Alpha-Beta *)\n", - " let s, s' = Spin.(Alfa, Beta) in \n", - " let mos_a, mos_b = mos_a ki, mos_b ki in\n", - " \n", - " sum mos_cabs (fun a ->\n", - " sum mos_a (fun i -> \n", - " (h_one i a s +.\n", - " sum mos_a (fun j -> h_two i j a j s s ) +.\n", - " sum mos_b (fun j -> h_two i j a j s s')\n", - " ) *. \n", - " (f_one a i s +.\n", - " sum mos_a (fun j -> f_two a j i j s s ) +.\n", - " sum mos_b (fun j -> f_two a j i j s s')\n", - " )\n", - " )\n", - " +.\n", - " sum mos_b (fun i -> \n", - " (h_one i a s' +.\n", - " sum mos_b (fun j -> h_two i j a j s' s') +.\n", - " sum mos_a (fun j -> h_two i j a j s' s )\n", - " ) *. \n", - " (f_one a i s' +.\n", - " sum mos_b (fun j -> f_two a j i j s' s') +.\n", - " sum mos_a (fun j -> f_two a j i j s' s )\n", - " )\n", - " ) \n", - " ) \n", - " \n", - "let _ =\n", - " check 0 integral_value 0 1 1 1\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": { - "scrolled": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "val m_0111_1H_1F : Lacaml.D.vec =\n", - " R1 R2 R3 R7 R8 R9\n", - " 1.23163 0.512679 0.379158 ... 1.15717 0.783246 0.94134\n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_1H_2Fa : Lacaml.D.mat =\n", - " \n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0 9.54805E-05 0.000949414 0.00102124 0.000612123\n", - " 2 0.0157601 0 0.00387182 0.0040609 0.00288411\n", - " 3 0.0123451 0.00482411 0 0.00262065 0.00153994\n", - " ... ... ... ... ...\n", - " 7 0.0638665 0.0309407 0.0280828 0.0291155 0.0201909\n", - " 8 0.035099 0.00993291 0.0123105 0.0128627 0.0095454\n", - " 9 0.0546496 0.0268732 0.0249878 0.0209954 0.02047\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 0.00135039 0.00168769 -2.50132E-05 0.00127857\n", - " 2 0.00164244 0.00263016 -0.0049468 0.00145336\n", - " 3 -0.00786828 0.00262225 0.000307787 0.00154154\n", - " ... ... ... ...\n", - " 7 0.0210255 0 0.0169901 0.0199928\n", - " 8 0.0097481 0.0125132 0 0.00919583\n", - " 9 0.0187406 0.0232584 0.0154703 0\n", - " \n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_1H_2Fb : Lacaml.D.mat =\n", - " \n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0.00838947 0.000802512 0.000774268 0.000824527 0.000531664\n", - " 2 0.0167558 0.00284141 0.00289398 0.00311638 0.00181881\n", - " 3 0.0138217 0.00142914 0.000717031 0.00205097 0.00097096\n", - " ... ... ... ... ...\n", - " 7 0.0672127 0.0297099 0.0280681 0.029107 0.022267\n", - " 8 0.0361343 0.0135355 0.0127802 0.0133849 0.00974314\n", - " 9 0.0572555 0.0267995 0.0251558 0.0264006 0.020602\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 0.000838226 0.00108083 0.000590322 0.000787968\n", - " 2 0.00312393 0.0041991 0.00210452 0.00290152\n", - " 3 0.00156923 0.00296985 0.000876672 0.00188984\n", - " ... ... ... ...\n", - " 7 0.0206994 0.0254055 0.0187116 0.0196605\n", - " 8 0.00965382 0.0126909 0.00818378 0.00904916\n", - " 9 0.0183365 0.0228903 0.0168998 0.0166274\n", - " \n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_2Ha_1F : Lacaml.D.mat =\n", - " \n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0 0.00346355 -0.00957818 -0.0103791 -0.00586334\n", - " 2 -0.121634 0 -0.019873 -0.0209946 -0.0141534\n", - " 3 -0.115395 -0.0247239 0 -0.017339 -0.0100747\n", - " ... ... ... ... ...\n", - " 7 -0.405587 -0.140299 -0.129164 -0.134263 -0.0844326\n", - " 8 -0.207751 -0.0414479 -0.0574012 -0.0601297 -0.0438726\n", - " 9 -0.335499 -0.120993 -0.113422 -0.0875797 -0.091945\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 -0.0155848 -0.0192997 0.00228062 -0.0147839\n", - " 2 -0.0112498 -0.0169694 0.0224836 -0.0101282\n", - " 3 0.0322167 -0.0204013 -0.00423111 -0.013137\n", - " ... ... ... ...\n", - " 7 -0.106147 0 -0.0844097 -0.101048\n", - " 8 -0.0490936 -0.0626221 0 -0.0463651\n", - " 9 -0.0928575 -0.114335 -0.0760592 0\n", - " \n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_2Hb_1F : Lacaml.D.mat =\n", - " \n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 -0.267262 -0.0092275 -0.00385375 -0.00417671 -0.00235846\n", - " 2 -0.165952 -0.0180838 -0.0197588 -0.0214917 -0.0115557\n", - " 3 -0.149576 -0.0113644 -0.010116 -0.0155245 -0.00736965\n", - " ... ... ... ... ...\n", - " 7 -0.487134 -0.140774 -0.13287 -0.138318 -0.111128\n", - " 8 -0.253633 -0.0687529 -0.0664679 -0.0700869 -0.0486229\n", - " 9 -0.399565 -0.125537 -0.117439 -0.133629 -0.0946778\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 -0.00636217 -0.00785747 -0.00673128 -0.00603921\n", - " 2 -0.0272961 -0.0354992 -0.0184917 -0.0255632\n", - " 3 -0.0207391 -0.0252065 -0.0100414 -0.0170516\n", - " ... ... ... ...\n", - " 7 -0.111178 -0.151723 -0.0978176 -0.10573\n", - " 8 -0.0587109 -0.0765558 -0.0468344 -0.0550919\n", - " 9 -0.0962035 -0.118965 -0.0866369 -0.0978307\n", - " \n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_2Ha_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_2Hb_2Fa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_2Ha_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0111_2Hb_2Fb :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val integral_value : Determinant.t -> 'a -> float = \n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "Failed: (225, 225) | 2.333780e+00 2.333780e+00 | 1.776357e-15 | cpu : 2.156856 0.039502\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let m_0111_1H_1F = \n", - " Vec.init mo_num (fun i -> \n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_one a i Spin.Alfa ))\n", - "\n", - " \n", - "let m_0111_1H_2Fa = \n", - " Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Alfa ))\n", - "\n", - " \n", - "let m_0111_1H_2Fb = \n", - " Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Beta ))\n", - "\n", - "\n", - "let m_0111_2Ha_1F = \n", - " Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Alfa *. f_one a i Spin.Alfa ))\n", - "\n", - " \n", - "let m_0111_2Hb_1F = \n", - " Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Beta *. f_one a i Spin.Alfa ))\n", - "\n", - "\n", - "let m_0111_2Ha_2Fa =\n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Alfa *.\n", - " f_two a k i k Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_0111_2Hb_2Fa =\n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Beta *.\n", - " f_two a k i k Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_0111_2Ha_2Fb =\n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Alfa *.\n", - " f_two a k i k Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_0111_2Hb_2Fb =\n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Beta *.\n", - " f_two a k i k Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "\n", - "let integral_value ki kj = \n", - "\n", - " let mos_a, mos_b = mos_a ki, mos_b ki in\n", - " \n", - " sum mos_a (fun i ->\n", - " m_0111_1H_1F.{i} +. \n", - " sum mos_a (fun j ->\n", - " m_0111_2Ha_1F.{i,j} +.\n", - " m_0111_1H_2Fa.{i,j} +.\n", - " sum mos_a (fun k -> m_0111_2Ha_2Fa.{i,j,k}) +.\n", - " sum mos_b (fun k -> m_0111_2Ha_2Fb.{i,j,k})\n", - " ) +.\n", - " sum mos_b (fun j ->\n", - " m_0111_2Hb_1F.{i,j} +.\n", - " m_0111_1H_2Fb.{i,j} +.\n", - " sum mos_a (fun k -> m_0111_2Hb_2Fa.{i,j,k}) +.\n", - " sum mos_b (fun k -> m_0111_2Hb_2Fb.{i,j,k})\n", - " )\n", - " )\n", - " +.\n", - " sum mos_b (fun i ->\n", - " m_0111_1H_1F.{i} +. \n", - " sum mos_b (fun j ->\n", - " m_0111_2Ha_1F.{i,j} +.\n", - " m_0111_1H_2Fa.{i,j} +.\n", - " sum mos_b (fun k -> m_0111_2Ha_2Fa.{i,j,k}) +.\n", - " sum mos_a (fun k -> m_0111_2Ha_2Fb.{i,j,k})\n", - " ) +.\n", - " sum mos_a (fun j ->\n", - " m_0111_2Hb_1F.{i,j} +.\n", - " m_0111_1H_2Fb.{i,j} +.\n", - " sum mos_b (fun k -> m_0111_2Hb_2Fa.{i,j,k}) +.\n", - " sum mos_a (fun k -> m_0111_2Hb_2Fb.{i,j,k})\n", - " )\n", - " )\n", - " \n", - "let _ =\n", - " check 0 integral_value 0 1 1 1\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 2. 0 1 22" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/plain": [ - "- : Jupyter_notebook.display_id = \n" - ] - }, - "execution_count": 43, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let _ = png_image \"0_1_22.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n", - "\n", - "$k$ : orbital indices of MOs unoccupied in $|I\\rangle$.\n", - "\n", - "$\\sum_i \\sum_a \\sum_j \\sum_k \\hat{T}_{ij}^{ak} \\hat{T}_{ak}^{ij}$\n", - "\n", - "\n", - "\\begin{align}\n", - "\\sum_{a} \\sum_{k} \\sum_{i} \\sum_{j Determinant.t -> float = \n" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "OK: (22, 22) | -3.896807e-02 -3.896807e-02 | 6.245005e-17 | cpu : 2.708850 0.154509\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let integral_value ki kj = \n", - " (* mos unoccupied in both I and J *)\n", - " let mos_virt_a, mos_virt_b = \n", - " Array.init mo_num (fun i -> Some (i+1)) , \n", - " Array.init mo_num (fun i -> Some (i+1)) \n", - " in\n", - " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n", - " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n", - " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n", - " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n", - " \n", - " let mos_virt_a, mos_virt_b = \n", - " Array.to_list mos_virt_a |> Util.list_some,\n", - " Array.to_list mos_virt_b |> Util.list_some\n", - " in\n", - " \n", - " (* Alpha-Beta *)\n", - " let s, s' = Spin.(Alfa, Beta) in\n", - " sum mos_cabs (fun a ->\n", - " sum (mos_b ki) (fun j -> \n", - " sum (mos_a ki) (fun i -> \n", - " sum mos_virt_b (fun k -> \n", - " h_two i j a k s s' *. f_two a k i j s s'\n", - " )))\n", - " +.\n", - " sum (mos_a ki) (fun j -> \n", - " sum (mos_b ki) (fun i -> \n", - " sum mos_virt_a (fun k -> \n", - " h_two i j a k s s' *. f_two a k i j s s'\n", - " )))) \n", - " +.\n", - " (* Alpha-Alpha / Beta-Beta *)\n", - " List.fold_left (fun accu (mos_virt,mos,s) -> \n", - " let s' = s in accu +.\n", - " sum mos (fun j -> \n", - " sum mos (fun i -> if i < j then 0. else\n", - " sum mos_virt (fun k -> \n", - " sum mos_cabs (fun a -> \n", - " h_two i j a k s s' *. f_two a k i j s s'\n", - " )))) \n", - " ) 0. [ (mos_virt_a,mos_a ki,Spin.Alfa) ; (mos_virt_b,mos_b ki,Spin.Beta)]\n", - " \n", - "let _ =\n", - " check 100 integral_value 0 1 2 2\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val m_0122_Haa :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 46, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0122_Hab :\n", - " (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array3.t =\n", - " \n" - ] - }, - "execution_count": 46, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val integral_value : Determinant.t -> Determinant.t -> float = \n" - ] - }, - "execution_count": 46, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "OK: (22, 22) | -3.896807e-02 -3.896807e-02 | 6.938894e-17 | cpu : 2.688957 0.003098\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 46, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let m_0122_Haa = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a k Spin.Alfa Spin.Alfa *. f_two a k i j Spin.Alfa Spin.Alfa\n", - " ) )\n", - " \n", - "let m_0122_Hab = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a k Spin.Alfa Spin.Beta *. f_two a k i j Spin.Alfa Spin.Beta\n", - " ) )\n", - "\n", - "\n", - "let integral_value ki kj = \n", - " (* mos unoccupied in both I and J *)\n", - " let mos_virt_a, mos_virt_b = \n", - " Array.init mo_num (fun i -> Some (i+1)) , \n", - " Array.init mo_num (fun i -> Some (i+1)) \n", - " in\n", - " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n", - " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n", - " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n", - " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n", - " \n", - " let mos_virt_a, mos_virt_b = \n", - " Array.to_list mos_virt_a |> Util.list_some,\n", - " Array.to_list mos_virt_b |> Util.list_some\n", - " in\n", - " \n", - " let result = \n", - " sum (mos_a ki) (fun i -> \n", - " sum (mos_b ki) (fun j -> \n", - " sum mos_virt_b (fun k -> m_0122_Hab.{i,j,k} )))\n", - " +.\n", - " sum (mos_b ki) (fun i -> \n", - " sum (mos_a ki) (fun j -> \n", - " sum mos_virt_a (fun k -> m_0122_Hab.{i,j,k} )))\n", - " +.\n", - " (* Alpha-Alpha / Beta-Beta *)\n", - " List.fold_left (fun accu (mos_virt,mos) -> \n", - " accu +.\n", - " sum mos (fun j -> \n", - " sum mos (fun i -> if i <= j then 0. else\n", - " sum mos_virt (fun k -> m_0122_Haa.{i,j,k} )))\n", - " ) 0. [ (mos_virt_a,mos_a ki) ; (mos_virt_b,mos_b ki)]\n", - " in \n", - " result\n", - " \n", - "let _ =\n", - " check 100 integral_value 0 1 2 2\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 3. 0 2 22" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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- }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/plain": [ - "- : Jupyter_notebook.display_id = \n" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let _ = png_image \"0_2_22.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$i,j$ : orbital indices of MOs occupied in $|I\\rangle$.\n", - "\n", - "$\\sum_i \\sum_a \\sum_j \\sum_b \\hat{T}_{ij}^{ab} \\hat{T}_{ab}^{ij}$\n", - "\n", - "\\begin{align}\n", - "\\sum_{a} \\sum_{b>a} \\sum_{i} \\sum_{j\\bar{a}} \\sum_{\\bar{i}} \\sum_{\\bar{j}<\\bar{i}}\n", - " \\langle \\bar{i} \\bar{j} || \\bar{a} \\bar{b} \\rangle \n", - " \\left[ \\bar{a} \\bar{b} || \\bar{i} \\bar{j} \\right] \n", - "\\end{align}" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val integral_value : Determinant.t -> 'a -> float = \n" - ] - }, - "execution_count": 48, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "OK: (95, 95) | -1.697991e-02 -1.697991e-02 | 2.775558e-17 | cpu : 3.329183 0.257722\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 48, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let integral_value ki kj = \n", - " (* Alpha-Beta *)\n", - " let s, s' = Spin.(Alfa, Beta) in\n", - " sum mos_cabs (fun a -> \n", - " sum mos_cabs (fun b -> \n", - " sum (mos_a ki) (fun i -> \n", - " sum (mos_b ki) (fun j -> \n", - " h_two i j a b s s' *. f_two a b i j s s'\n", - " ))))\n", - " +.\n", - " (* Alpha-Alpha / Beta-Beta *)\n", - " List.fold_left (fun accu (mos,s) -> \n", - " let s' = s in accu +.\n", - " sum mos_cabs (fun b -> \n", - " sum mos_cabs (fun a -> if b > a then 0. else\n", - " sum mos (fun j -> \n", - " sum mos (fun i -> if i < j then 0. else\n", - " h_two i j a b s s' *. f_two a b i j s s'\n", - " ))))\n", - " ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)]\n", - " \n", - "let _ =\n", - " check 100 integral_value 0 2 2 2\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val m_0222_Haa : Lacaml.D.mat =\n", - " \n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 0 -1.0063E-05 -0.000334496 -0.000347188 -0.000267608\n", - " 2 -1.0063E-05 0 -0.00016695 -0.000173345 -0.000134367\n", - " 3 -0.000334496 -0.00016695 0 -0.00370788 -0.00334839\n", - " ... ... ... ... ...\n", - " 7 -0.000232416 -0.000151236 -0.000542986 -0.000572891 -2.9266E-05\n", - " 8 -4.11752E-05 -3.98219E-05 -0.000454591 -0.00047264 -0.000369248\n", - " 9 -0.000152836 -0.000112257 -0.000183496 -2.9266E-05 -0.000103812\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 -0.000165528 -0.000232416 -4.11752E-05 -0.000152836\n", - " 2 -0.000118652 -0.000151236 -3.98219E-05 -0.000112257\n", - " 3 -2.9266E-05 -0.000542986 -0.000454591 -0.000183496\n", - " ... ... ... ...\n", - " 7 -0.00083789 0 -0.000621663 -0.000807984\n", - " 8 -0.00053632 -0.000621663 0 -0.000518271\n", - " 9 -0.000728301 -0.000807984 -0.000518271 0\n", - " \n" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_0222_Hab : Lacaml.D.mat =\n", - " \n", - "\n", - " -- 1 -- -- 2 -- -- 3 -- -- 4 -- -- 5 --\n", - " 1 -0.0026356 -8.37274E-05 -0.000318312 -0.000329372 -0.000258412\n", - " 2 -8.37274E-05 -0.00329888 -0.00055028 -0.00055898 -0.000498185\n", - " 3 -0.000318312 -0.00055028 -0.00651939 -0.00351919 -0.00318906\n", - " ... ... ... ... ...\n", - " 7 -0.000177876 -0.000280993 -0.000526737 -0.000561143 -0.000637823\n", - " 8 -7.32564E-05 -0.000232089 -0.00062993 -0.000653508 -0.000521154\n", - " 9 -0.000106915 -0.000220198 -0.000196607 -0.000319215 -0.000105067\n", - " \n", - "\n", - " -- 6 -- -- 7 -- -- 8 -- -- 9 --\n", - " 1 -0.000117975 -0.000177876 -7.32564E-05 -0.000106915\n", - " 2 -0.000228899 -0.000280993 -0.000232089 -0.000220198\n", - " 3 -0.000355709 -0.000526737 -0.00062993 -0.000196607\n", - " ... ... ... ...\n", - " 7 -0.00104342 -0.00180231 -0.000934604 -0.00100902\n", - " 8 -0.000825828 -0.000934604 -0.000964699 -0.00080225\n", - " 9 -0.000917478 -0.00100902 -0.00080225 -0.00135053\n", - " \n" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val integral_value : Determinant.t -> 'a -> float = \n" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "OK: (58, 58) | -2.336186e-02 -2.336186e-02 | 3.122502e-17 | cpu : 3.329266 0.000941\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let m_0222_Haa = \n", - " Mat.init_cols mo_num mo_num (fun i j ->\n", - " sum mos_cabs (fun a ->\n", - " sum mos_cabs (fun b -> if b >= a then 0. else\n", - " h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b i j Spin.Alfa Spin.Alfa\n", - " ) )\n", - " )\n", - " \n", - "let m_0222_Hab = \n", - " Mat.init_cols mo_num mo_num (fun i j ->\n", - " sum mos_cabs (fun a ->\n", - " sum mos_cabs (fun b ->\n", - " h_two i j a b Spin.Alfa Spin.Beta *. f_two a b i j Spin.Alfa Spin.Beta\n", - " ) )\n", - " )\n", - " \n", - "let integral_value ki kj = \n", - " (* Alpha-Beta *)\n", - " sum (mos_a ki) (fun i -> \n", - " sum (mos_b ki) (fun j -> \n", - " m_0222_Hab.{i,j} \n", - " ))\n", - " +.\n", - " (* Alpha-Alpha / Beta-Beta *)\n", - " List.fold_left (fun accu (mos) -> \n", - " accu +.\n", - " sum mos (fun j -> \n", - " sum mos (fun i -> if i < j then 0. else\n", - " m_0222_Haa.{i,j} \n", - " ))\n", - " ) 0. [ (mos_a ki) ; (mos_b ki)]\n", - " \n", - "let _ =\n", - " check 100 integral_value 0 2 2 2\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 4. 1 1 11" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/plain": [ - "- : Jupyter_notebook.display_id = \n" - ] - }, - "execution_count": 50, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let _ = png_image \"1_1_11.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n", - "\n", - "$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n", - "\n", - "$\\sum_a \\hat{T}_{i}^{a} \\hat{T}_{a}^{k}$\n", - "\n", - "\\begin{align}\n", - " \\sum_{a} \n", - " \\left( h_{ia} +\\sum_{j} \\langle i j || a j \\rangle +\n", - " \\sum_{\\bar{j}} \\langle i \\bar{j} | a \\bar{j} \\rangle \\right)\n", - " \\left( f_{ak} +\\sum_{j} \\left[ a j || k j \\right] + \n", - " \\sum_{\\bar{j}} \\left[ a \\bar{j} | k \\bar{j} \\right]\\right) \\\\\n", - "\\end{align}" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val integral_value : Determinant.t -> Determinant.t -> float = \n" - ] - }, - "execution_count": 51, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Checking ... \n", - " - 10 %\n", - " - 20 %\n", - " - 30 %\n", - " - 40 %\n", - " - 50 %\n", - " - 60 %\n", - " - 70 %\n", - " - 80 %\n", - " - 90 %\n", - " - 100 %\n", - "OK: (0, 0) | 0.000000e+00 0.000000e+00 | 0.000000e+00 | cpu : 4.151429 1.045428\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 51, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let integral_value ki kj = \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - "\n", - " let mos_i, mos_i' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in\n", - " let mos_j, mos_j' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a kj, mos_b kj\n", - " | Spin.Beta -> mos_b kj, mos_a kj\n", - " in\n", - "\n", - " let result = \n", - " let s' = Spin.other s in\n", - " \n", - " sum mos_cabs (fun a -> \n", - " (h_one i a s +. \n", - " sum mos_i (fun j -> h_two i j a j s s ) +.\n", - " sum mos_i' (fun j -> h_two i j a j s s') ) *.\n", - " (f_one a k s +. \n", - " sum mos_j (fun j -> f_two a j k j s s ) +.\n", - " sum mos_j' (fun j -> f_two a j k j s s') ) \n", - " )\n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "let _ = check 0 integral_value 1 1 1 1" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let ki = det_I.(77)\n", - "let kj = det_I.(83)\n", - "\n", - "let _ = integral_value ki kj" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": false - }, - "outputs": [], - "source": [ - "let m_1111_1H_1F = \n", - " Mat.init_cols mo_num mo_num (fun i k -> \n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_one a k Spin.Alfa ))\n", - "\n", - "\n", - "let m_1111_1H_2Fa = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Alfa ))\n", - "\n", - " \n", - "let m_1111_1H_2Fb = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Beta ))\n", - "\n", - "\n", - "let m_1111_2Ha_1F = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa ))\n", - "\n", - " \n", - "let m_1111_2Hb_1F = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa ))\n", - "\n", - "\n", - "let m_1111_2Ha_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Alfa *.\n", - " f_two a l k l Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1111_2Hb_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Beta *.\n", - " f_two a l k l Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1111_2Ha_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Alfa *.\n", - " f_two a l k l Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1111_2Hb_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a j Spin.Alfa Spin.Beta *.\n", - " f_two a l k l Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let integral_value_11 ki kj = \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " let mos_a, mos_b =\n", - " match s with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in \n", - " \n", - " let result = \n", - " m_1111_1H_1F.{i,k} +. \n", - " sum mos_a (fun j -> if j = i then 0. else\n", - " m_1111_1H_2Fa.{i,j,k} +. m_1111_2Ha_1F.{i,j,k} +.\n", - " sum mos_a (fun l -> if l = i then 0. else m_1111_2Ha_2Fa.{i,j,k,l}) +.\n", - " sum mos_b (fun l -> m_1111_2Ha_2Fb.{i,j,k,l})) +.\n", - " sum mos_b (fun j ->\n", - " m_1111_1H_2Fb.{i,j,k} +. m_1111_2Hb_1F.{i,j,k} +.\n", - " sum mos_a (fun l -> if l = i then 0. else m_1111_2Hb_2Fa.{i,j,k,l}) +.\n", - " sum mos_b (fun l -> m_1111_2Hb_2Fb.{i,j,k,l}))\n", - " in\n", - " \n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "let _ =\n", - " check 0 integral_value_11 1 1 1 1\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 5. 1 1 12" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let _ = png_image \"1_1_12.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n", - "\n", - "$\\sum_{j} \\sum_a \\hat{T}_{j}^{a} \\hat{T}_{ai}^{jk}$\n", - "\n", - "$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n", - "\n", - "\\begin{align}\n", - " \\sum_{a} \\sum_{j} \n", - " \\left( h_{ja} +\\sum_{m} \\langle j m || a m \\rangle +\n", - " \\sum_{\\bar{m}} \\langle j \\bar{m} | a \\bar{m} \\rangle \\right)\n", - " \\left[ a i || j k \\right] + \\\\\n", - " \\sum_{\\bar{a}} \\sum_{\\bar{j}} \n", - " \\left( h_{\\bar{j}\\bar{a}} +\\sum_{m} \\langle \\bar{j} m | \\bar{a} m \\rangle +\n", - " \\sum_{\\bar{m}} \\langle \\bar{j} \\bar{m} || \\bar{a} \\bar{m} \\rangle \\right)\n", - " \\left[ \\bar{a} i | \\bar{j} k \\right] \n", - "\\end{align}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let integral_value ki kj = \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - "\n", - " let mos_j, mos_j' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - " \n", - " let mos_i, mos_i' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in\n", - "\n", - " let result = \n", - " let s' = Spin.other s in\n", - " sum mos_cabs (fun a -> \n", - " sum mos_j (fun j -> \n", - " (h_one j a s +. \n", - " sum mos_i (fun m -> h_two j m a m s s ) +.\n", - " sum mos_i' (fun m -> h_two j m a m s s') ) *.\n", - " (f_two a i j k s s )\n", - " ) \n", - " +.\n", - " sum mos_j' (fun j -> \n", - " (h_one j a s +. \n", - " sum mos_i (fun m -> h_two j m a m s' s ) +.\n", - " sum mos_i' (fun m -> h_two j m a m s' s') ) *.\n", - " (f_two a i j k s' s )\n", - " ) \n", - " ) \n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "let _ = check 100 integral_value 1 1 1 2" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let m_1112_1H_2Fa = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_one j a Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa ))\n", - "\n", - " \n", - "let m_1112_1H_2Fb = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_one j a Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta ))\n", - "\n", - "\n", - "let m_1112_2Ha_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two j m a m Spin.Alfa Spin.Alfa *.\n", - " f_two a i j k Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1112_2Hb_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two j m a m Spin.Alfa Spin.Beta *.\n", - " f_two a i j k Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "let m_1112_2Ha_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two j m a m Spin.Alfa Spin.Alfa *.\n", - " f_two a i j k Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1112_2Hb_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two j m a m Spin.Alfa Spin.Beta *.\n", - " f_two a i j k Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let integral_value_12 ki kj = \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " let mos_j, mos_j' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - " \n", - " let mos_i, mos_i' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in\n", - " \n", - " let result = \n", - " sum mos_j (fun j -> \n", - " m_1112_1H_2Fa.{i,j,k} +. \n", - " sum mos_i (fun m -> m_1112_2Ha_2Fa.{i,j,k,m}) +.\n", - " sum mos_i' (fun m -> m_1112_2Hb_2Fa.{i,j,k,m})) +.\n", - " sum mos_j' (fun j ->\n", - " m_1112_1H_2Fb.{i,j,k} +. \n", - " sum mos_i (fun m -> m_1112_2Hb_2Fb.{i,j,k,m}) +.\n", - " sum mos_i' (fun m -> m_1112_2Ha_2Fb.{i,j,k,m}))\n", - " in\n", - " \n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - " \n", - "\n", - "let _ = check 100 integral_value_12 1 1 1 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 6. 1 1 21" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": false - }, - "outputs": [], - "source": [ - "let _ = png_image \"1_1_21.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n", - "\n", - "$\\sum_{j} \\sum_a \\hat{T}_{ij}^{ka} \\hat{T}_{a}^{j}$\n", - "\n", - "$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n", - "\n", - "\\begin{align}\n", - " \\sum_{a} \\sum_{j} \n", - " \\langle i j || k a \\rangle \n", - " \\left( f_{aj} +\\sum_{m} \\left[ m a || m j \\right] +\n", - " \\sum_{\\bar{m}} \\left[ \\bar{m} a | \\bar{m} j \\right] \\right) + \\\\\n", - " \\sum_{\\bar{a}} \\sum_{\\bar{j}} \n", - " \\langle i \\bar{j} | k \\bar{a} \\rangle\n", - " \\left( f_{\\bar{a}\\bar{j}} +\\sum_{m} \\left[ m \\bar{a} | m \\bar{j} \\right] +\n", - " \\sum_{\\bar{m}} \\left[ \\bar{m} \\bar{a} || \\bar{m} \\bar{j} \\right] \\right)\n", - "\\end{align}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let integral_value ki kj = \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - "\n", - " let mos_j, mos_j' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - " \n", - " let mos_i, mos_i' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a kj, mos_b kj\n", - " | Spin.Beta -> mos_b kj, mos_a kj\n", - " in\n", - "\n", - " let result = \n", - " let s' = Spin.other s in\n", - " sum mos_cabs (fun a -> \n", - " sum mos_j (fun j -> \n", - " (h_two i j k a s s ) *.\n", - " (f_one a j s +. \n", - " sum mos_i (fun m -> f_two m a m j s s) +.\n", - " sum mos_i' (fun m -> f_two m a m j s' s) ) \n", - " ) \n", - " +.\n", - " sum mos_j' (fun j -> \n", - " (h_two i j k a s s') *.\n", - " (f_one a j s' +. \n", - " sum mos_i (fun m -> f_two m a m j s s') +.\n", - " sum mos_i' (fun m -> f_two m a m j s' s') ) \n", - " )) \n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "let _ = check 100 integral_value 1 1 2 1" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let m_1121_2Ha_1F = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j k a Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa))\n", - "\n", - " \n", - "let m_1121_2Hb_1F = \n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j k a Spin.Alfa Spin.Beta *. f_one a j Spin.Beta))\n", - "\n", - "\n", - "let m_1121_2Ha_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j k a Spin.Alfa Spin.Alfa *.\n", - " f_two m a m j Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1121_2Hb_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j k a Spin.Alfa Spin.Beta *.\n", - " f_two m a m j Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "let m_1121_2Ha_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j k a Spin.Alfa Spin.Alfa *.\n", - " f_two m a m j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let m_1121_2Hb_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j k a Spin.Alfa Spin.Beta *.\n", - " f_two m a m j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let integral_value_21 ki kj = \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " let mos_j, mos_j' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - " \n", - " let mos_i, mos_i' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a kj, mos_b kj\n", - " | Spin.Beta -> mos_b kj, mos_a kj\n", - " in\n", - " \n", - " let result = \n", - " sum mos_j (fun j -> \n", - " m_1121_2Ha_1F.{i,j,k} +. \n", - " sum mos_i (fun m -> m_1121_2Ha_2Fa.{i,j,k,m}) +.\n", - " sum mos_i' (fun m -> m_1121_2Ha_2Fb.{i,j,k,m})) +.\n", - " sum mos_j' (fun j ->\n", - " m_1121_2Hb_1F.{i,j,k} +. \n", - " sum mos_i (fun m -> m_1121_2Hb_2Fb.{i,j,k,m}) +.\n", - " sum mos_i' (fun m -> m_1121_2Hb_2Fa.{i,j,k,m}))\n", - " in\n", - " \n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - " \n", - "\n", - "let _ = check 100 integral_value_21 1 1 2 1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 7. 1 1 22" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let _ = png_image \"1_1_22.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n", - "\n", - "$\\sum_{j} \\sum_{a} \\sum_{m}\n", - " \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kj} - \n", - " \\hat{T}_{lj}^{ka} \\hat{T}_{ia}^{lj} + \\\\\n", - "\\sum_{\\bar{j}} \\sum_{\\bar{a}} \\sum_{m}\n", - " \\hat{T}_{i\\bar{j}}^{m\\bar{a}} \\hat{T}_{m\\bar{a}}^{k\\bar{j}} - \n", - " \\hat{T}_{l\\bar{j}}^{k\\bar{a}} \\hat{T}_{i\\bar{a}}^{l\\bar{j}} +\n", - "\\sum_{\\bar{j}} \\sum_{a} \\sum_{\\bar{m}}\n", - " \\hat{T}_{i\\bar{j}}^{a\\bar{m}} \\hat{T}_{a\\bar{m}}^{k\\bar{j}} \n", - "$\n", - "\n", - "$j,l$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n", - "\n", - "$m$ : orbital indices of virtual MOs, unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n", - "\n", - "$a$ : orbital indices of CABS MOs\n", - "\n", - "\\begin{align}\n", - " \\sum_{a} \\sum_{j} \\sum_{m}\n", - " \\langle i j || m a \\rangle \\left[ m a || k j \\right] - \\\\\n", - " \\sum_{a} \\sum_{j} \\sum_{l}\n", - " \\langle l j || k a \\rangle \\left[ i a || l j \\right] + \\\\\n", - " \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{m}\n", - " \\langle i \\bar{j} | m \\bar{a} \\rangle \\left[ m \\bar{a} | k \\bar{j} \\right] + \\\\\n", - " \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{l}\n", - " \\langle l \\bar{j} | k \\bar{a} \\rangle \\left[ i \\bar{a} | l \\bar{j} \\right] - \\\\\n", - " \\sum_{\\bar{a}} \\sum_{\\bar{j}} \\sum_{\\bar{m}}\n", - " \\langle i \\bar{j} | a \\bar{m} \\rangle \\left[ a \\bar{m} | k \\bar{j} \\right] \n", - "\\end{align}" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "(*\n", - "let ki = det_I.(6)\n", - "let kj = det_I.(58)\n", - "\n", - "let _ = \n", - " Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n", - "generate_alphas ki kj 1 1 2 2\n", - "|> Array.of_list\n", - "|> Array.mapi (fun kk alpha -> \n", - "\n", - "(*\n", - "let _ = Determinant.to_lists ki\n", - "let _ = Determinant.to_lists alpha\n", - "let _ = Determinant.to_lists kj\n", - "\n", - " \n", - "let _ = \n", - " Format.printf \"|I> -> |J> : %a\\n@.\" Excitation.pp (Excitation.of_det ki kj);\n", - " Format.printf \"|I> -> |a> : %a\\n@.\" Excitation.pp (Excitation.of_det ki alpha);\n", - " Format.printf \"|a> -> |J> : %a\\n@.\" Excitation.pp (Excitation.of_det alpha kj)\n", - "*)\n", - "\n", - " let integral_value ki kj = \n", - " \n", - " let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n", - " let exc1 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in \n", - " let exc2 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in \n", - " \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin } )) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - " let spin = function\n", - " | Spin.Alfa -> 0\n", - " | _ -> 1\n", - " in\n", - " exc0.(i).(spin s ) <- \"i\" \n", - " ; exc0.(k).(spin s ) <- \"k\" \n", - " ;\n", - " let s0 = s in\n", - " \n", - " let i, j, k, l, s, s', p1 =\n", - " match Excitation.of_det ki alpha with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " if exc0.(i).(spin s ) = \"-\" then exc0.(i).(spin s ) <- \"n\";\n", - " if exc0.(j).(spin s') = \"-\" then exc0.(j).(spin s') <- \"n\";\n", - " if exc0.(k).(spin s ) = \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"m\";\n", - " if exc0.(l).(spin s') = \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"m\";\n", - " \n", - " let string_h = \n", - " Printf.sprintf \"h_two %s %s %s %s %s %s *. \" \n", - " exc0.(i).(spin s )\n", - " exc0.(j).(spin s')\n", - " exc0.(k).(spin s )\n", - " exc0.(l).(spin s')\n", - " (if s = s0 then \"s \" else \"s'\")\n", - " (if s' = s0 then \"s \" else \"s'\")\n", - " (*\n", - " (if exc0.(i).(spin s ) = \"i\" || exc0.(k).(spin s ) = \"k\" then \"s \" else \n", - " if exc0.(i).(spin s ) = \"j\" || exc0.(k).(spin s ) = \"l\" then \"s' \" else \"s''\")\n", - " (if exc0.(j).(spin s') = \"i\" || exc0.(l).(spin s') = \"k\" then \"s \" else \n", - " if exc0.(j).(spin s') = \"j\" || exc0.(l).(spin s') = \"l\" then \"s' \" else \"s''\")\n", - " *)\n", - " in \n", - " \n", - " let i, j, k, l, s, s', p2 =\n", - " match Excitation.of_det alpha kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " let string_f = \n", - " Printf.sprintf \"f_two %s %s %s %s %s %s\" \n", - " exc0.(i).(spin s )\n", - " exc0.(j).(spin s')\n", - " exc0.(k).(spin s )\n", - " exc0.(l).(spin s')\n", - " (*\n", - " (if exc0.(i).(spin s ) = \"i\" || exc0.(k).(spin s ) = \"k\" then \"s \" else \n", - " if exc0.(i).(spin s ) = \"j\" || exc0.(k).(spin s ) = \"l\" then \"s' \" else \n", - " if exc0.(i).(spin s ) = \"n\" || exc0.(k).(spin s ) = \"n\" then \"s''\" else\n", - " if s = s0 then \"s\" else \"s'\")\n", - " (if exc0.(j).(spin s') = \"i\" || exc0.(l).(spin s') = \"k\" then \"s \" else \n", - " if exc0.(j).(spin s') = \"j\" || exc0.(l).(spin s') = \"l\" then \"s' \" else \n", - " if exc0.(j).(spin s') = \"n\" || exc0.(l).(spin s') = \"n\" then \"s''\" else\n", - " if s' = s0 then \"s\" else \"s'\")\n", - " *)\n", - " (if s = s0 then \"s \" else \"s'\")\n", - " (if s' = s0 then \"s \" else \"s'\")\n", - " in\n", - " \n", - " Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n", - " Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n", - " \n", - " let sign = \n", - " if Phase.add p1 p2 = phase then \"+. \" else \"-. \"\n", - " in\n", - "sign ^ string_h ^ string_f\n", - "(*\n", - " \n", - " let mos, mos' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in\n", - "\n", - " let result = \n", - " let k=4 and l=5 in\n", - " let i=1 and j=2 in\n", - " let n=2 and a=7 in\n", - " let s = Spin.Alfa\n", - " and s' = Spin.Alfa\n", - " and s'' = Spin.Beta\n", - " in\n", - " (* \n", - " h_two j n l a s' s'' *. f_two a i n k s s''\n", - " *)\n", - " h_two i n k a s s'' *. f_two j a l n s s''\n", - " in\n", - "\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " *)\n", - "\n", - "in\n", - "integral_value ki kj\n", - "(*\n", - "let a = (compute_HaaF ki [alpha] kj)\n", - "and b = (integral_value ki kj)\n", - "in\n", - "if kk = 31 then\n", - " Format.printf \"%6d %e %e@.@.\" (kk) a b\n", - " *)\n", - ")\n", - "|> Array.to_list\n", - "|> List.sort_uniq compare\n", - "\n", - "let _ = compute_HaaF ki (generate_alphas ki kj 1 1 2 2) kj\n", - "\n", - "let _ = integral_value ki kj\n", - "\n", - "*)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": false - }, - "outputs": [], - "source": [ - "let integral_value ki kj = \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " (* MOs unoccupied in both I and J *)\n", - " let mos_virt_a, mos_virt_b = \n", - " Array.init mo_num (fun i -> Some (i+1)) , \n", - " Array.init mo_num (fun i -> Some (i+1)) \n", - " in\n", - " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n", - " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n", - " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n", - " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n", - " \n", - " let mos_virt_a, mos_virt_b = \n", - " Array.to_list mos_virt_a |> Util.list_some,\n", - " Array.to_list mos_virt_b |> Util.list_some\n", - " in\n", - "\n", - " let mos_virt, mos_virt' =\n", - " match s with\n", - " | Spin.Alfa -> mos_virt_a, mos_virt_b\n", - " | Spin.Beta -> mos_virt_b, mos_virt_a\n", - " in\n", - " \n", - " let mos_j, mos_j' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - " let result = \n", - " let s' = Spin.other s in\n", - " sum mos_cabs (fun a -> \n", - " sum mos_j (fun n -> \n", - " sum mos_virt (fun m -> \n", - " h_two n i a m s s *. f_two m a k n s s \n", - " ))) +.\n", - " sum mos_cabs (fun a' -> \n", - " sum mos_j' (fun n' -> \n", - " sum mos_virt (fun m -> \n", - " h_two i n' m a' s s' *. f_two m a' k n' s s'\n", - " ))) +.\n", - " sum mos_cabs (fun a -> \n", - " sum mos_j' (fun n' -> \n", - " sum mos_virt' (fun m' -> \n", - " h_two i n' a m' s s' *. f_two a m' k n' s s'\n", - " ))) -. \n", - " sum mos_cabs (fun a -> \n", - " sum mos_j (fun n -> \n", - " sum mos_j (fun l -> if l <=n then 0. else\n", - " h_two n l a k s s *. f_two i a l n s s \n", - " ))) -. \n", - " sum mos_cabs (fun a' -> \n", - " sum mos_j' (fun n' -> \n", - " sum mos_j (fun l -> \n", - " h_two l n' k a' s s' *. f_two i a' l n' s s'\n", - " ))) \n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "let _ = check 100 integral_value 1 1 2 2\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": false - }, - "outputs": [], - "source": [ - "let m_1122_va =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two j i a m Spin.Alfa Spin.Alfa *.\n", - " f_two m a k j Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "let m_1122_v2 =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j m a Spin.Alfa Spin.Beta *.\n", - " f_two m a k j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "let m_1122_v3 =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k m ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a m Spin.Alfa Spin.Beta *.\n", - " f_two a m k j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "let m_1122_oa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two j l a k Spin.Alfa Spin.Alfa *.\n", - " f_two i a l j Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - "\n", - "let m_1122_o =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two l j k a Spin.Alfa Spin.Beta *.\n", - " f_two i a l j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - "\n", - "\n", - "let integral_value_22 ki kj = \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " (* MOs unoccupied in both I and J *)\n", - " let mos_virt_a, mos_virt_b = \n", - " Array.init mo_num (fun i -> Some (i+1)) , \n", - " Array.init mo_num (fun i -> Some (i+1)) \n", - " in\n", - " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n", - " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n", - " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n", - " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n", - " \n", - " let mos_virt_a, mos_virt_b = \n", - " Array.to_list mos_virt_a |> Util.list_some,\n", - " Array.to_list mos_virt_b |> Util.list_some\n", - " in\n", - "\n", - " let mos_virt, mos_virt' =\n", - " match s with\n", - " | Spin.Alfa -> mos_virt_a, mos_virt_b\n", - " | Spin.Beta -> mos_virt_b, mos_virt_a\n", - " in\n", - " \n", - " let mos_j, mos_j' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - " \n", - " let result = \n", - " sum mos_j (fun j -> \n", - " sum mos_virt (fun m -> \n", - " m_1122_va.{i,j,k,m}\n", - " )) +.\n", - " sum mos_j' (fun j -> \n", - " sum mos_virt (fun m -> \n", - " m_1122_v2.{i,j,k,m}\n", - " )) +.\n", - " \n", - " sum mos_j' (fun j -> \n", - " sum mos_virt' (fun m -> \n", - " m_1122_v3.{i,j,k,m}\n", - " )) -.\n", - " sum mos_j (fun j -> \n", - " sum mos_j (fun l -> if l <= j then 0. else\n", - " m_1122_oa.{i,j,k,l}\n", - " )) -. \n", - " sum mos_j' (fun j -> \n", - " sum mos_j (fun l -> \n", - " m_1122_o.{i,j,k,l}\n", - " )) \n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "let _ = check 100 integral_value_22 1 1 2 2\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let ki = det_I.(77) and kj = det_I.(83)\n", - "\n", - "let _ =\n", - "integral_value_11 ki kj\n", - "+. integral_value_12 ki kj\n", - "+. integral_value_21 ki kj\n", - "+. integral_value_22 ki kj " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 8. 1 2 22" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let _ = png_image \"1_2_22.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{i}^{k}|I\\rangle$\n", - "\n", - "$j$ : orbital indices of MOs occupied both in $|I\\rangle$ and $|J\\rangle$.\n", - "\n", - "$\\sum_{j} \\sum_{a} \\sum_{b}\n", - " \\hat{T}_{ij}^{ab} \\hat{T}_{ab}^{kj} +\n", - "\\sum_{\\bar{j}} \\sum_{a} \\sum_{\\bar{b}}\n", - " \\hat{T}_{i\\bar{j}}^{a\\bar{b}} \\hat{T}_{a\\bar{b}}^{k\\bar{j}} \n", - "$\n", - "\n", - "\n", - "$$\n", - "\\sum_{j} \\sum_{b}\\sum_{a\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - "\n", - " let mos, mos' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in\n", - " \n", - " \n", - "\n", - " let result = \n", - " (* Alpha-Beta *)\n", - " let s' = Spin.other s in\n", - " sum mos_cabs (fun b -> \n", - " sum mos_cabs (fun a -> \n", - " sum mos' (fun j -> h_two h j a b s s' *. f_two a b p j s s')\n", - " ))\n", - " +.\n", - " (* Alpha-Alpha / Beta-Beta *)\n", - " sum mos_cabs (fun b -> \n", - " sum mos_cabs (fun a -> if b >= a then 0. else\n", - " sum mos (fun j -> h_two h j a b s s *. f_two a b p j s s)\n", - " )) \n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "let _ = check 100 integral_value 1 2 2 2" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": false - }, - "outputs": [], - "source": [ - "let m_1222a =\n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " sum mos_cabs (fun b -> if b > a then 0. else\n", - " h_two i j a b Spin.Alfa Spin.Alfa *.\n", - " f_two a b k j Spin.Alfa Spin.Alfa \n", - " )\n", - " )\n", - " )\n", - "\n", - "let m_1222 =\n", - " array_3_init mo_num mo_num mo_num (fun i j k ->\n", - " sum mos_cabs (fun a ->\n", - " sum mos_cabs (fun b ->\n", - " h_two i j a b Spin.Alfa Spin.Beta *.\n", - " f_two a b k j Spin.Alfa Spin.Beta \n", - " )\n", - " )\n", - " )\n", - " \n", - "\n", - "let integral_value ki kj = \n", - " let i, k, s, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Single (phase, { hole ; particle ; spin })) ->\n", - " hole, particle, spin, phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " (* MOs unoccupied in both I and J *)\n", - " let mos_j, mos_j' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - "\n", - " let result = \n", - " sum mos_j (fun j -> m_1222a.{i,j,k} ) +.\n", - " sum mos_j' (fun j -> m_1222.{i,j,k} )\n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "let _ = check 100 integral_value 1 2 2 2\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 9. 2 1 12" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let _ = png_image \"2_1_12.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n", - "\n", - "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n", - "\n", - "$n$ : orbital indices of MOs occupied in $|I\\rangle$\n", - "\n", - "$\\sum_{a} \n", - " \\hat{T}_{i}^{a} \\hat{T}_{aj}^{kl} +\n", - " \\hat{T}_{j}^{a} \\hat{T}_{ia}^{kl} \n", - "$\n", - "\n", - "\n", - "$$\n", - "\\sum_{a}\n", - " \\left( h_{ia} + \\sum_{n} \\langle i n || a n \\rangle + \\sum_{\\bar{n}} \\langle i \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a j || k l \\right] + \\\\\n", - "\\sum_{a}\n", - " \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ i a || k l \\right] \n", - "$$" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "let integral_value ki kj = \n", - " let i, j, k, l, s, s', phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - "\n", - " let mos, mos' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in\n", - " \n", - " let mos2, mos2' =\n", - " match s' with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in\n", - "\n", - " let result = \n", - " sum mos_cabs (fun a -> \n", - " let s'' = Spin.other s in\n", - " ( h_one i a s +.\n", - " sum mos (fun n -> h_two i n a n s s ) +.\n", - " sum mos' (fun n -> h_two i n a n s s'') \n", - " ) *. f_two a j k l s s'\n", - " ) +.\n", - " sum mos_cabs (fun a -> \n", - " let s'' = Spin.other s' in\n", - " ( h_one j a s' +.\n", - " sum mos2 (fun n -> h_two j n a n s' s' ) +.\n", - " sum mos2' (fun n -> h_two j n a n s' s'') \n", - " ) *. f_two i a k l s s'\n", - " ) \n", - " in\n", - "\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - "\n", - "\n", - "let _ = check 100 integral_value 2 1 1 2\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n", - "\n", - "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n", - "\n", - "$n$ : orbital indices of MOs occupied in $|I\\rangle$\n", - "\n", - "$\\sum_{a} \n", - " \\hat{T}_{i}^{a} \\hat{T}_{aj}^{kl} +\n", - " \\hat{T}_{j}^{a} \\hat{T}_{ia}^{kl} \n", - "$\n", - "\n", - "\n", - "$$\n", - "\\sum_{a}\n", - " \\left( h_{ia} + \\sum_{n} \\langle i n || a n \\rangle + \\sum_{\\bar{n}} \\langle i \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ a j || k l \\right] + \\\\\n", - "\\sum_{a}\n", - " \\left( h_{ja} + \\sum_{n} \\langle j n || a n \\rangle + \\sum_{\\bar{n}} \\langle j \\bar{n} | a \\bar{n} \\rangle \\right) \\left[ i a || k l \\right] \n", - "$$" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": false - }, - "outputs": [], - "source": [ - "let m_2112_1H_2Fa =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +.\n", - " h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Alfa )\n", - " )\n", - "\n", - "let m_2112_1H_2Fb =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +.\n", - " h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Beta)\n", - " )\n", - "\n", - "let m_2112_2Ha_2Fa =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i n a n Spin.Alfa Spin.Alfa *.\n", - " f_two a j k l Spin.Alfa Spin.Alfa )\n", - " )\n", - " \n", - "let m_2112_2Hb_2Fa =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i n a n Spin.Alfa Spin.Beta *.\n", - " f_two a j k l Spin.Alfa Spin.Alfa )\n", - " )\n", - " \n", - "let m_2112_2Ha_2Fb =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i n a n Spin.Alfa Spin.Alfa *.\n", - " f_two a j k l Spin.Alfa Spin.Beta )\n", - " )\n", - " \n", - "let m_2112_2Hb_2Fb =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i n a n Spin.Alfa Spin.Beta *.\n", - " f_two a j k l Spin.Alfa Spin.Beta )\n", - " )\n", - " \n", - "let integral_value ki kj = \n", - " let i, j, k, l, s, s', phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " let mos, mos' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a ki, mos_b ki\n", - " | Spin.Beta -> mos_b ki, mos_a ki\n", - " in\n", - " \n", - " let result = \n", - " if s = s' then\n", - " m_2112_1H_2Fa.{i,j,k,l} +. \n", - " sum mos (fun n ->\n", - " m_2112_2Ha_2Fa.{i,j,k,l,n} +. m_2112_2Ha_2Fa.{j,i,l,k,n}\n", - " ) +.\n", - " sum mos' (fun n ->\n", - " m_2112_2Hb_2Fa.{i,j,k,l,n} +. m_2112_2Hb_2Fa.{j,i,l,k,n}\n", - " ) \n", - " else\n", - " m_2112_1H_2Fb.{i,j,k,l} +.\n", - " sum mos (fun n ->\n", - " m_2112_2Ha_2Fb.{i,j,k,l,n} +. m_2112_2Hb_2Fb.{j,i,l,k,n}\n", - " ) +.\n", - " sum mos' (fun n ->\n", - " m_2112_2Hb_2Fb.{i,j,k,l,n} +. m_2112_2Ha_2Fb.{j,i,l,k,n}\n", - " ) \n", - " in\n", - "\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "let _ = check 100 integral_value 2 1 1 2\n", - "\n", - "let ki = det_I.(2)\n", - "let kj = det_I.(33)\n", - "\n", - "let _ = integral_value ki kj\n", - "let _ = \n", - " let alphas = generate_alphas ki kj 2 1 1 2\n", - " in compute_HaaF ki alphas kj\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 10. 2 1 21" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let _ = png_image \"2_1_21.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n", - "\n", - "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n", - "\n", - "$n$ : orbital indices of MOs occupied in $|J\\rangle$\n", - "\n", - "$\\sum_{a} \n", - " \\hat{T}_{ij}^{al} \\hat{T}_{a}^{k} +\n", - " \\hat{T}_{ij}^{ka} \\hat{T}_{a}^{l} +\n", - " \\hat{T}_{i\\bar{j}}^{a\\bar{l}} \\hat{T}_{a}^{k} +\n", - " \\hat{T}_{i\\bar{j}}^{k\\bar{a}} \\hat{T}_{\\bar{a}}^{\\bar{l}}\n", - "$\n", - "\n", - "\n", - "$$\n", - "\\sum_{a}\n", - " \\langle i j || a l \\rangle \\left( f_{ak} + \\sum_{n} \\left[ a n || k n \\right] + \\sum_{\\bar{n}} \\left[ a \\bar{n} | k \\bar{n} \\right] \\right) + \\\\\n", - "\\sum_{a}\n", - " \\langle i j || k a \\rangle \\left( f_{al} + \\sum_{n} \\left[ n a || n l \\right] + \\sum_{\\bar{n}} \\left[ \\bar{n} a | \\bar{n} l \\right] \\right) \n", - "$$" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let integral_value ki kj = \n", - " let i, j, k, l, s, s', phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - "\n", - " let result = \n", - " \n", - " let mos, mos', s'' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a kj, mos_b kj, Spin.Beta\n", - " | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa\n", - " in\n", - " sum mos_cabs (fun a -> \n", - " h_two i j a l s s' *.\n", - " ( f_one a k s +.\n", - " sum mos (fun n -> f_two a n k n s s) +.\n", - " sum mos' (fun n -> f_two a n k n s s'') \n", - " ) ) +.\n", - "\n", - " let mos, mos', s'' =\n", - " match s' with\n", - " | Spin.Alfa -> mos_a kj, mos_b kj, Spin.Beta\n", - " | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa\n", - " in\n", - " sum mos_cabs (fun a -> \n", - " h_two j i a k s' s *.\n", - " ( f_one a l s' +.\n", - " sum mos (fun n -> f_two a n l n s' s') +.\n", - " sum mos' (fun n -> f_two a n l n s' s'') \n", - " ) \n", - " ) \n", - " in\n", - "\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - "\n", - "\n", - "let _ = check 100 integral_value 2 1 2 1" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": false - }, - "outputs": [], - "source": [ - "let m_2121_2Ha_1F =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a l Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +.\n", - " h_two i j k a Spin.Alfa Spin.Alfa *. f_one a l Spin.Alfa)\n", - " )\n", - "\n", - "let m_2121_2Hb_1F =\n", - " array_4_init mo_num mo_num mo_num mo_num (fun i j k l ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a l Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +.\n", - " h_two i j k a Spin.Alfa Spin.Beta *. f_one a l Spin.Alfa)\n", - " )\n", - "\n", - "let m_2121_2Ha_2Fa =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a l Spin.Alfa Spin.Alfa *.\n", - " f_two a n k n Spin.Alfa Spin.Alfa )\n", - " )\n", - " \n", - "let m_2121_2Hb_2Fa =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a l Spin.Alfa Spin.Beta *.\n", - " f_two a n k n Spin.Alfa Spin.Alfa )\n", - " )\n", - " \n", - "let m_2121_2Ha_2Fb =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a l Spin.Alfa Spin.Alfa *.\n", - " f_two a n k n Spin.Alfa Spin.Beta )\n", - " )\n", - " \n", - "let m_2121_2Hb_2Fb =\n", - " array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n ->\n", - " sum mos_cabs (fun a ->\n", - " h_two i j a l Spin.Alfa Spin.Beta *.\n", - " f_two a n k n Spin.Alfa Spin.Beta )\n", - " )\n", - " \n", - "let integral_value ki kj = \n", - " let i, j, k, l, s, s', phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " let mos, mos' =\n", - " match s with\n", - " | Spin.Alfa -> mos_a kj, mos_b kj\n", - " | Spin.Beta -> mos_b kj, mos_a kj\n", - " in\n", - " \n", - " let result = \n", - " if s = s' then\n", - " m_2121_2Ha_1F.{i,j,k,l} +. \n", - " sum mos (fun n ->\n", - " m_2121_2Ha_2Fa.{i,j,k,l,n} +. m_2121_2Ha_2Fa.{j,i,l,k,n}\n", - " ) +.\n", - " sum mos' (fun n ->\n", - " m_2121_2Ha_2Fb.{i,j,k,l,n} +. m_2121_2Ha_2Fb.{j,i,l,k,n}\n", - " ) \n", - " else\n", - " m_2121_2Hb_1F.{i,j,k,l} +.\n", - " sum mos (fun n ->\n", - " m_2121_2Hb_2Fa.{i,j,k,l,n} +. m_2121_2Hb_2Fb.{j,i,l,k,n}\n", - " ) +.\n", - " sum mos' (fun n ->\n", - " m_2121_2Hb_2Fb.{i,j,k,l,n} +. m_2121_2Hb_2Fa.{j,i,l,k,n}\n", - " ) \n", - " in\n", - "\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "let _ = check 100 integral_value 2 1 2 1\n", - "\n", - "(*\n", - "let ki = det_I.(2)\n", - "let kj = det_I.(33)\n", - "\n", - "let _ = integral_value ki kj\n", - "let _ = \n", - " let alphas = generate_alphas ki kj 2 1 2 1\n", - " in compute_HaaF ki alphas kj\n", - "*)\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 11. 2 1 22" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let _ = png_image \"2_1_22.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n", - "\n", - "$m$ : orbital indices of MOs unoccupied both in $|I\\rangle$ and $|J\\rangle$.\n", - "\n", - "$n$ : orbital indices of MOs occupied in both $|I\\rangle$ and $|J\\rangle$ .\n", - "\n", - "$\\sum_{a} \n", - " \\hat{T}_{ij}^{am} \\hat{T}_{am}^{kl} +\n", - " \\hat{T}_{ij}^{ma} \\hat{T}_{ma}^{kl} -\n", - " \\hat{T}_{in}^{al} \\hat{T}_{aj}^{kn} -\n", - " \\hat{T}_{nj}^{ka} \\hat{T}_{ia}^{nl} +\n", - " \\sum_{n}\n", - " \\hat{T}_{i\\bar{n}}^{k\\bar{a}} \\hat{T}_{\\bar{a}j}^{\\bar{n}l}\n", - "$\n", - "\n", - "\n", - "$$\n", - "\\sum_{a}\n", - "\\sum_{m} \\langle i j || a m \\rangle \\left[ a m || k l \\right] + \\langle i j || m a \\rangle \\left[ m a || k l \\right] - \\\\\n", - "\\sum_{n} \\langle i n || a l \\rangle \\left[ a j || k n \\right] + \\langle n j || k a \\rangle \\left[ i a || n l \\right] \n", - "$$" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let integral_value ki kj = \n", - " let i, j, k, l, s, s', phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - "\n", - " let mos_virt_a, mos_virt_b = \n", - " Array.init mo_num (fun i -> Some (i+1)) , \n", - " Array.init mo_num (fun i -> Some (i+1)) \n", - " in\n", - " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki);\n", - " List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj);\n", - " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki);\n", - " List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj);\n", - "\n", - " let mos_virt_a, mos_virt_b = \n", - " Array.to_list mos_virt_a |> Util.list_some,\n", - " Array.to_list mos_virt_b |> Util.list_some\n", - " in\n", - " \n", - " let result = \n", - " \n", - " let mos_virt, mos_virt' =\n", - " match s with\n", - " | Spin.Alfa -> mos_virt_a, mos_virt_b\n", - " | Spin.Beta -> mos_virt_b, mos_virt_a\n", - " in\n", - " \n", - " let mos, mos' =\n", - " let alfa = \n", - " let i = Spindeterminant.bitstring @@ Determinant.alfa ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.alfa kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " let beta = \n", - " let i = Spindeterminant.bitstring @@ Determinant.beta ki in\n", - " let j = Spindeterminant.bitstring @@ Determinant.beta kj in\n", - " Bitstring.to_list (Bitstring.logand i j)\n", - " in\n", - " match s with\n", - " | Spin.Alfa -> alfa, beta\n", - " | Spin.Beta -> beta, alfa\n", - " in\n", - "\n", - " if s = s' then \n", - " let s'' = Spin.other s' in\n", - " sum mos_cabs (fun a -> \n", - " sum mos (fun n ->\n", - " h_two i n a k s s *. f_two j a n l s s \n", - " +. h_two i n a l s s *. f_two j a k n s s \n", - " -. h_two j n a k s s *. f_two i a n l s s \n", - " -. h_two j n a l s s *. f_two i a k n s s\n", - " )\n", - " +. sum mos_virt (fun m ->\n", - " -. h_two i j a m s s *. f_two m a k l s s )\n", - " +. sum mos' (fun n ->\n", - " h_two i n k a s s'' *. f_two j a l n s s''\n", - " +. h_two j n l a s s'' *. f_two i a k n s s''\n", - " -. h_two i n l a s s'' *. f_two j a k n s s''\n", - " -. h_two j n k a s s'' *. f_two i a l n s s''\n", - " )\n", - " )\n", - " else\n", - " sum mos_cabs (fun a ->\n", - " sum mos_virt' (fun m ->\n", - " h_two i j a m s s' *. f_two a m k l s s' ) +.\n", - " sum mos_virt (fun m ->\n", - " h_two i j m a s s' *. f_two m a k l s s' ) +.\n", - " sum mos (fun n ->\n", - " h_two n i a k s s *. f_two a j n l s s'\n", - " +. h_two n j a l s s' *. f_two i a k n s s \n", - " -. h_two n j k a s s' *. f_two i a n l s s'\n", - " ) +.\n", - " sum mos' (fun n -> if n >= j then 0. else \n", - " h_two i n k a s s' *. f_two j a l n s' s'\n", - " +. h_two n j a l s' s' *. f_two i a k n s s' ) +. \n", - " sum mos' (fun n -> if n <= j then 0. else \n", - " -. h_two i n k a s s' *. f_two j a n l s' s' \n", - " -. h_two j n a l s' s' *. f_two i a k n s s' ) +.\n", - " sum mos' (fun n -> \n", - " -. h_two i n a l s s' *. f_two a j k n s s'\n", - " )\n", - " )\n", - " in\n", - "\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - "\n", - "\n", - "let _ = check 300 integral_value 2 1 2 2" - ] - }, - { - "cell_type": "raw", - "metadata": { - "raw_mimetype": "text/markdown", - "scrolled": false - }, - "source": [ - "let ki = det_I.(99)\n", - "let kj = det_I.(193)\n", - "\n", - "let alpha_to_string alpha = \n", - " \n", - " let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n", - " \n", - " let i, j, k, l, s, s', phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " let spin = function\n", - " | Spin.Alfa -> 0\n", - " | _ -> 1\n", - " in\n", - " exc0.(i).(spin s ) <- \"i\" \n", - " ; exc0.(j).(spin s') <- \"j\" \n", - " ; exc0.(k).(spin s ) <- \"k\" \n", - " ; exc0.(l).(spin s') <- \"l\" \n", - " ;\n", - " let s0, s0' = s, s' in\n", - " \n", - " let i, j, k, l, s, s', p1 =\n", - " match Excitation.of_det ki alpha with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " if exc0.(i).(spin s ) = \"-\" then exc0.(i).(spin s ) <- \"n\";\n", - " if exc0.(j).(spin s') = \"-\" then exc0.(j).(spin s') <- \"n\";\n", - " if exc0.(k).(spin s ) = \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"m\";\n", - " if exc0.(l).(spin s') = \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"m\";\n", - " \n", - " let string_h = \n", - " Printf.sprintf \"h_two %s %s %s %s %s %s *. \" \n", - " exc0.(i).(spin s )\n", - " exc0.(j).(spin s')\n", - " exc0.(k).(spin s )\n", - " exc0.(l).(spin s')\n", - " (if s = s0 then \"s \" else \"s'\")\n", - " (if s' = s0 then \"s \" else \"s'\")\n", - " in \n", - " \n", - " let i, j, k, l, s, s', p2 =\n", - " match Excitation.of_det alpha kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " let string_f = \n", - " Printf.sprintf \"f_two %s %s %s %s %s %s\" \n", - " exc0.(i).(spin s )\n", - " exc0.(j).(spin s')\n", - " exc0.(k).(spin s )\n", - " exc0.(l).(spin s')\n", - " (if s = s0 then \"s \" else \"s'\")\n", - " (if s' = s0 then \"s \" else \"s'\")\n", - " in\n", - "(*\n", - " Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n", - " Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n", - " *)\n", - "\n", - " \n", - " let sign = \n", - " if Phase.add p1 p2 = phase then \"+.\" else \"-.\"\n", - " in\n", - " sign ^ string_h ^ string_f\n", - " \n", - "\n", - "let alpha_debug alpha = \n", - " \n", - " let i, j, k, l, s, s', p1 =\n", - " match Excitation.of_det ki alpha with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " Printf.printf \"%d %d %d %d \" i j k l;\n", - " \n", - " let i, j, k, l, s, s', p2 =\n", - " match Excitation.of_det alpha kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " (*\n", - " Format.printf \"|I> -> |a> : %a | \\n@.\" Excitation.pp (Excitation.of_det ki alpha) ;\n", - " Format.printf \"|a> -> |J> : %a | \\n@.\" Excitation.pp (Excitation.of_det alpha kj) ;\n", - " *)\n", - " Printf.printf \"%d %d %d %d \\n%!\" i j k l\n", - "\n", - " \n", - "let strings = \n", - " Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n", - " generate_alphas ki kj 2 1 2 2\n", - " |> Array.of_list\n", - " |> Array.mapi (fun kk alpha -> alpha_to_string alpha)\n", - " |> Array.to_list\n", - " |> List.sort_uniq compare\n", - " |> Array.of_list\n", - "\n", - "let _ = Array.iteri (fun i x -> Printf.printf \"%d %s \\n%!\" i x) strings\n", - "\n", - "let _ =\n", - " let v =\n", - " let alphas =\n", - " generate_alphas ki kj 2 1 2 2\n", - " (*\n", - " |> List.filter (fun alpha ->\n", - " let x = alpha_to_string alpha in\n", - " x = strings.(6)\n", - " )\n", - " *)\n", - " in\n", - " (*\n", - " List.iter alpha_debug alphas ;\n", - " Printf.printf \"\\n%!\";\n", - " *)\n", - " compute_HaaF ki alphas kj \n", - " in\n", - " let x = (integral_value ki kj) in\n", - " Printf.printf \"%20.8e %20.8e %20.8e\\n%!\" x v (v-. x)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 12. 2 2 22" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let _ = png_image \"2_2_22.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{ij}^{kl}|I\\rangle$\n", - "\n", - "$$\n", - "\\sum_{b}\\sum_{a h, h', p, p', s, s', phase\n", - " | _ -> assert false\n", - " in\n", - "\n", - " let result = \n", - " if s <> s' then (* Alpha-Beta *)\n", - " sum mos_cabs (fun b -> \n", - " sum mos_cabs (fun a -> \n", - " h_two h h' a b s s' *. f_two a b p p' s s'\n", - " )) \n", - " else (* Alpha-Alpha / Beta-Beta *)\n", - " sum mos_cabs (fun b -> \n", - " sum mos_cabs (fun a -> if b >= a then 0. else\n", - " h_two h h' a b s s' *. f_two a b p p' s s'\n", - " )) \n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "let _ = check 100 integral_value 2 2 2 2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 13. 3 1 2 2" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let _ = png_image \"3_1_22.png\"" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$|J\\rangle = \\hat{T}_{ijm}^{kln}|I\\rangle$\n", - "\n", - "$\\sum_{a}\n", - " \\hat{T}_{ij}^{al} \\hat{T}_{am}^{kn} \n", - " + \\hat{T}_{ij}^{ka} \\hat{T}_{am}^{ln} \n", - " + \\hat{T}_{im}^{ka} \\hat{T}_{ja}^{ln} \n", - " + \\hat{T}_{im}^{an} \\hat{T}_{aj}^{kl} \n", - " + \\hat{T}_{jm}^{an} \\hat{T}_{ia}^{kl} \n", - " + \\hat{T}_{jm}^{la} \\hat{T}_{ia}^{kn} \n", - "$\n", - "\n", - "$$\n", - "\\sum_{a} \\langle i j || a l \\rangle \\left[ a m || k n \\right] +\n", - " \\langle i j || k a \\rangle \\left[ a m || l n \\right] +\n", - " \\langle i m || k a \\rangle \\left[ j a || l n \\right] +\n", - " \\langle i m || a n \\rangle \\left[ a j || k l \\right] +\n", - " \\langle j m || a n \\rangle \\left[ i a || k l \\right] +\n", - " \\langle j m || l a \\rangle \\left[ i a || k n \\right] \n", - "$$" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "let integral_value ki kj = \n", - " let i, j, m, k, l, n, s1, s2, s3, phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Triple (phase,\n", - " { hole=h1 ; particle=p1 ; spin=s1 },\n", - " { hole=h2 ; particle=p2 ; spin=s2 },\n", - " { hole=h3 ; particle=p3 ; spin=s3 }) ) -> h1, h2, h3, p1, p2, p3, s1, s2, s3, phase\n", - " | _ -> assert false\n", - " in\n", - "\n", - " let result = \n", - " let open Spin in \n", - " match s1, s2, s3 with\n", - " | Alfa, Alfa, Alfa\n", - " | Beta, Beta, Beta -> \n", - " sum mos_cabs (fun a -> \n", - " h_two i j a k s1 s2 *. f_two m a l n s3 s3 \n", - " +. h_two i j a n s1 s2 *. f_two m a k l s3 s2 \n", - " +. h_two i m a l s1 s3 *. f_two j a k n s2 s3 \n", - " +. h_two j m a k s2 s3 *. f_two i a l n s1 s3 \n", - " +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n", - " -. h_two i j a l s1 s2 *. f_two m a k n s3 s3 \n", - " -. h_two i m a k s1 s3 *. f_two j a l n s2 s3 \n", - " -. h_two i m a n s1 s3 *. f_two j a k l s2 s2 \n", - " -. h_two j m a l s2 s3 *. f_two i a k n s1 s3 )\n", - " | Alfa, Alfa, Beta\n", - " | Beta, Beta, Alfa -> \n", - " sum mos_cabs (fun a -> \n", - " h_two i j a l s1 s2 *. f_two a m k n s1 s3\n", - " +. h_two i m k a s1 s3 *. f_two j a l n s2 s3\n", - " +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n", - " +. h_two j m l a s2 s3 *. f_two i a k n s1 s3\n", - " -. h_two i j a k s1 s2 *. f_two a m l n s1 s3\n", - " -. h_two i m a n s1 s3 *. f_two j a k l s2 s2 \n", - " -. h_two i m l a s1 s3 *. f_two j a k n s2 s3\n", - " -. h_two j m k a s2 s3 *. f_two i a l n s1 s3\n", - " ) \n", - " | Alfa, Beta, Beta\n", - " | Beta, Alfa, Alfa -> \n", - " sum mos_cabs (fun a -> \n", - " h_two i j a l s1 s2 *. f_two a m k n s1 s3 \n", - " +. h_two i m a n s1 s3 *. f_two a j k l s1 s2 \n", - " +. h_two i m k a s1 s3 *. f_two j a l n s2 s3 \n", - " +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 \n", - " -. h_two i j a n s1 s2 *. f_two a m k l s1 s2 \n", - " -. h_two i j k a s1 s2 *. f_two m a l n s2 s3 \n", - " -. h_two i m a l s1 s3 *. f_two a j k n s1 s3 \n", - " -. h_two j m a l s2 s3 *. f_two i a k n s1 s3 \n", - " ) \n", - " | Beta, Alfa, Beta\n", - " | Alfa, Beta, Alfa -> assert false (*TODO *)\n", - " in\n", - " match phase with\n", - " | Phase.Pos -> result\n", - " | Phase.Neg -> -. result\n", - " \n", - "\n", - "let _ = check 200 integral_value 3 1 2 2" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": false - }, - "outputs": [], - "source": [ - "let ki = det_I.(129)\n", - "let kj = det_I.(349)\n", - "\n", - "let alpha_to_string alpha = \n", - " \n", - " let exc0 = Array.init (aux_num+1) (fun _ -> [|\"-\";\"-\"|]) in\n", - " \n", - " let i, j, m, k, l, n, s, s', s'', phase =\n", - " match Excitation.of_det ki kj with\n", - " | Excitation.(Triple (phase,\n", - " { hole ; particle ; spin },\n", - " {hole=hole' ; particle=particle' ; spin=spin' }, \n", - " {hole=hole''; particle=particle''; spin=spin''} )) ->\n", - " hole, hole', hole'', particle, particle', particle'', spin, spin', spin'', phase\n", - " | _ -> assert false\n", - " in\n", - " let spin = function\n", - " | Spin.Alfa -> 0\n", - " | _ -> 1\n", - " in\n", - " exc0.(i).(spin s ) <- \"i\" \n", - " ; exc0.(j).(spin s' ) <- \"j\" \n", - " ; exc0.(k).(spin s ) <- \"k\" \n", - " ; exc0.(l).(spin s' ) <- \"l\" \n", - " ; exc0.(m).(spin s'') <- \"m\" \n", - " ; exc0.(n).(spin s'') <- \"n\" \n", - " ;\n", - " let s0, s0', s0'' = s, s', s'' in\n", - " \n", - " let i, j, k, l, s, s', p1 =\n", - " match Excitation.of_det ki alpha with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " if exc0.(i).(spin s ) = \"-\" then exc0.(i).(spin s ) <- \"p\";\n", - " if exc0.(j).(spin s') = \"-\" then exc0.(j).(spin s') <- \"p\";\n", - " if exc0.(k).(spin s ) = \"-\" then exc0.(k).(spin s ) <- if k > mo_num then \"a\" else \"q\";\n", - " if exc0.(l).(spin s') = \"-\" then exc0.(l).(spin s') <- if l > mo_num then \"a\" else \"q\";\n", - " \n", - " let string_h = \n", - " Printf.sprintf \"h_two %s %s %s %s %s %s *. \" \n", - " exc0.(i).(spin s )\n", - " exc0.(j).(spin s')\n", - " exc0.(k).(spin s )\n", - " exc0.(l).(spin s')\n", - " (if s = s0 then \"s \" else if s = s0' then \"s'\" else \"s''\")\n", - " (if s' = s0' then \"s'\" else if s = s0'' then \"s''\" else \"s\" )\n", - " in \n", - " \n", - " let i, j, k, l, s, s', p2 =\n", - " match Excitation.of_det alpha kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " \n", - " let string_f = \n", - " Printf.sprintf \"f_two %s %s %s %s %s %s\" \n", - " exc0.(i).(spin s )\n", - " exc0.(j).(spin s')\n", - " exc0.(k).(spin s )\n", - " exc0.(l).(spin s')\n", - " (if s = s0 then \"s \" else if s = s0' then \"s'\" else \"s''\")\n", - " (if s' = s0' then \"s'\" else if s = s0'' then \"s''\" else \"s\" )\n", - " in\n", - " (*\n", - " Format.printf \"|I> -> |a> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det ki alpha) string_h ;\n", - " Format.printf \"|a> -> |J> : %a | %s\\n@.\" Excitation.pp (Excitation.of_det alpha kj) string_f ;\n", - " *)\n", - "\n", - " \n", - " let sign = \n", - " if Phase.add p1 p2 = phase then \"+.\" else \"-.\"\n", - " in\n", - " sign ^ string_h ^ string_f\n", - " \n", - "\n", - "let alpha_debug alpha = \n", - " \n", - " let i, j, k, l, s, s', p1 =\n", - " match Excitation.of_det ki alpha with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " Printf.printf \"%d %d %d %d \" i j k l;\n", - " \n", - " let i, j, k, l, s, s', p2 =\n", - " match Excitation.of_det alpha kj with\n", - " | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) ->\n", - " hole, hole', particle, particle', spin, spin', phase\n", - " | _ -> assert false\n", - " in\n", - " (*\n", - " Format.printf \"|I> -> |a> : %a | \\n@.\" Excitation.pp (Excitation.of_det ki alpha) ;\n", - " Format.printf \"|a> -> |J> : %a | \\n@.\" Excitation.pp (Excitation.of_det alpha kj) ;\n", - " *)\n", - " Printf.printf \"%d %d %d %d \\n%!\" i j k l\n", - "\n", - " \n", - "let strings = \n", - " Format.printf \"|I> -> |J> : %a |\\n@.\" Excitation.pp (Excitation.of_det ki kj) ;\n", - " generate_alphas ki kj 3 1 2 2\n", - " |> Array.of_list\n", - " |> Array.mapi (fun kk alpha -> alpha_to_string alpha)\n", - " |> Array.to_list\n", - " |> List.sort_uniq compare\n", - " |> Array.of_list\n", - "\n", - "let _ = Array.iteri (fun i x -> Printf.printf \"%d %s \\n%!\" i x) strings\n", - "\n", - "let _ =\n", - " let v =\n", - " let alphas =\n", - " generate_alphas ki kj 3 1 2 2\n", - " (*\n", - " |> List.filter (fun alpha ->\n", - " let x = alpha_to_string alpha in\n", - " x = strings.(6)\n", - " )\n", - " *)\n", - " in\n", - " (*\n", - " List.iter alpha_debug alphas ;\n", - " Printf.printf \"\\n%!\";\n", - " *)\n", - " compute_HaaF ki alphas kj \n", - " in\n", - " let x = (integral_value ki kj) in\n", - " Printf.printf \"%20.8e %20.8e %20.8e\\n%!\" x v (v-. x)\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "celltoolbar": "Raw Cell Format", - "kernelspec": { - "display_name": "OCaml default", - "language": "OCaml", - "name": "ocaml-jupyter" - }, - "language_info": { - "codemirror_mode": "text/x-ocaml", - "file_extension": ".ml", - "mimetype": "text/x-ocaml", - "name": "OCaml", - "nbconverter_exporter": null, - "pygments_lexer": "OCaml", - "version": "4.07.1" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/Notebooks/SpVec.ipynb b/Notebooks/SpVec.ipynb deleted file mode 100644 index 4070396..0000000 --- a/Notebooks/SpVec.ipynb +++ /dev/null @@ -1,1765 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "- : unit = ()\n", - "Findlib has been successfully loaded. Additional directives:\n", - " #require \"package\";; to load a package\n", - " #list;; to list the available packages\n", - " #camlp4o;; to load camlp4 (standard syntax)\n", - " #camlp4r;; to load camlp4 (revised syntax)\n", - " #predicates \"p,q,...\";; to set these predicates\n", - " Topfind.reset();; to force that packages will be reloaded\n", - " #thread;; to enable threads\n", - "\n", - "- : unit = ()\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/scemama/qp2/external/opam/default/lib/bytes: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/base64: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/base64/base64.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/ocaml/compiler-libs: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/ocaml/compiler-libs/ocamlcommon.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/result: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/result/result.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/ppx_deriving/runtime: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/ppx_deriving/runtime/ppx_deriving_runtime.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/ppx_deriving_yojson/runtime: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/ppx_deriving_yojson/runtime/ppx_deriving_yojson_runtime.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/ocaml/unix.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/uuidm: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/uuidm/uuidm.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/easy-format: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/easy-format/easy_format.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/biniou: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/biniou/biniou.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/yojson: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/yojson/yojson.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/jupyter: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/jupyter/jupyter.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/jupyter/notebook: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/jupyter/notebook/jupyter_notebook.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/ocaml/compiler-libs/ocamlbytecomp.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/ocaml/compiler-libs/ocamltoplevel.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/ocaml/bigarray.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/lacaml: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/lacaml/lacaml.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/lacaml/top: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/lacaml/top/lacaml_top.cma: loaded\n" - ] - } - ], - "source": [ - "#use \"topfind\";;\n", - "#require \"jupyter.notebook\";;\n", - "#require \"lacaml.top\" ;;" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Sparse Vector module\n", - "----------------" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Types" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "module L = Lacaml.D\n" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "type t = {\n", - " dim : int;\n", - " nnz : int;\n", - " indices :\n", - " (int, Bigarray.int_elt, Bigarray.fortran_layout) Bigarray.Array1.t;\n", - " values : L.Vec.t;\n", - "}\n" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "module L = Lacaml.D\n", - "\n", - "type t =\n", - " {\n", - " dim: int ;\n", - " nnz: int ;\n", - " indices: (int, Bigarray.int_elt, Bigarray.fortran_layout) Bigarray.Array1.t ; (* Indices *)\n", - " values: L.Vec.t\n", - " }\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Printers" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val pp : Format.formatter -> t -> unit = \n" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let pp ppf t =\n", - " let pp_data ppf t =\n", - " for i=1 to t.nnz do\n", - " Format.fprintf ppf \"@[(%d,@ %g)@]@;\" t.indices.{i} t.values.{i}\n", - " done\n", - " in\n", - " Format.fprintf ppf \"@[{@[dim:@ %d@]@;@[%a@]}@]\" t.dim pp_data t" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [], - "source": [ - "#install_printer pp" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Creators" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val make0 : int -> t = \n" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let make0 dim =\n", - " { dim ;\n", - " nnz = 0;\n", - " indices = Bigarray.(Array1.create int fortran_layout) 32 ;\n", - " values = L.Vec.create 32;\n", - " }" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val of_vec : ?threshold:float -> Lacaml.D.vec -> t = \n" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let of_vec ?(threshold=0.) v =\n", - " let dim = L.Vec.dim v in\n", - " let buffer_idx = Bigarray.(Array1.create int fortran_layout) dim in\n", - " let buffer_val = Bigarray.(Array1.create float64 fortran_layout) dim in\n", - " let check = \n", - " if threshold = 0. then\n", - " fun x -> x <> 0.\n", - " else\n", - " fun x -> (abs_float x) > 0.\n", - " in\n", - " let rec aux k i =\n", - " if i > dim then\n", - " k-1\n", - " else if check v.{i} then\n", - " ( buffer_idx.{k} <- i ;\n", - " buffer_val.{k} <- v.{i} ;\n", - " aux (k+1) (i+1)\n", - " )\n", - " else\n", - " aux k (i+1)\n", - " in\n", - " let nnz = aux 1 1 in\n", - " let indices = Bigarray.(Array1.create int fortran_layout) nnz in\n", - " let values = L.Vec.create nnz in\n", - " for i=1 to nnz do\n", - " indices.{i} <- buffer_idx.{i};\n", - " values.{i} <- buffer_val.{i};\n", - " done ;\n", - " { dim ; nnz ; indices ; values }" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val of_array : ?threshold:float -> float array -> t = \n" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let of_array ?(threshold=0.) a =\n", - " L.Vec.of_array a\n", - " |> of_vec ~threshold " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val copy : t -> t = \n" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let copy t =\n", - " let indices = \n", - " Bigarray.(Array1.create int fortran_layout) t.nnz\n", - " in\n", - " Bigarray.Array1.blit t.indices indices ;\n", - " let values = L.copy t.values in\n", - " { dim = t.dim ;\n", - " nnz = t.nnz ;\n", - " indices ; values }" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val map : ?threshold:float -> (float -> float) -> t -> t = \n" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let map ?(threshold=0.) f t =\n", - " let indices = \n", - " Bigarray.(Array1.create int fortran_layout) t.nnz\n", - " in\n", - " let check =\n", - " if threshold = 0. then\n", - " fun x -> x <> 0.\n", - " else\n", - " fun x -> abs_float x > threshold\n", - " in\n", - " let values = L.Vec.create t.nnz in\n", - " let nnz = ref 0 in\n", - " for i=1 to t.nnz do\n", - " let w = f t.values.{i} in\n", - " if check w then (\n", - " incr nnz;\n", - " values.{!nnz} <- w ;\n", - " indices.{!nnz} <- t.indices.{i}\n", - " )\n", - " done;\n", - " { dim = t.dim ;\n", - " nnz = !nnz ;\n", - " indices ; values }" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Test" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val x : t =\n", - " {dim = 10; nnz = 0; indices = ;\n", - " values =\n", - " R1 R2 R3 R30 R31 R32\n", - " 6.91705E-310 6.91705E-310 0 ... 6.91705E-310 6.91705E-310 6.91705E-310}\n" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val dense_a : Lacaml.D.vec = R1 R2 R3 R7 R8 R9\n", - " 1 -2 0 ... 0 3 0\n" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val sparse_a : t =\n", - " {dim = 9; nnz = 5; indices = ;\n", - " values = R1 R2 R3 R4 R5\n", - " 1 -2 0.5 1E-08 3}\n" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : bool = true\n" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : bool = false\n" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let x = make0 10 \n", - "\n", - "let dense_a = \n", - " L.Vec.of_array [| 1. ; -2. ; 0. ; 0. ; 0.5 ; 1.e-8 ; 0. ; 3. ; 0. |]\n", - " \n", - "let sparse_a = of_vec dense_a \n", - "\n", - "let _ =\n", - " copy sparse_a = sparse_a\n", - " \n", - "let _ =\n", - " copy sparse_a == sparse_a\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Accessors" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val dim : t -> int = \n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val nnz : t -> int = \n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val indices :\n", - " t -> (int, Bigarray.int_elt, Bigarray.fortran_layout) Bigarray.Array1.t =\n", - " \n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val values : t -> L.Vec.t = \n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val density : t -> float = \n" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let dim t = t.dim\n", - "let nnz t = t.nnz\n", - "let indices t = t.indices\n", - "let values t = t.values\n", - "let density t = float_of_int t.nnz /. float_of_int t.dim" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val get : t -> int -> float = \n" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let get t i =\n", - " if i < 1 || i > dim t then invalid_arg \"index out of bounds\";\n", - " \n", - " let rec binary_search index value low high =\n", - " if high = low then\n", - " if index.{low} = value then\n", - " low\n", - " else\n", - " raise Not_found\n", - " else let mid = (low + high) / 2 in\n", - " if index.{mid} > value then\n", - " binary_search index value low (mid - 1)\n", - " else if index.{mid} < value then\n", - " binary_search index value (mid + 1) high\n", - " else\n", - " mid\n", - " in\n", - " try\n", - " let k = \n", - " let id = indices t in\n", - " binary_search id i id.{1} (nnz t)\n", - " in\n", - " t.values.{k}\n", - " with Not_found -> 0." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val iter : (int -> float -> 'a) -> t -> unit = \n" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let iter f t =\n", - " for k=1 to nnz t do\n", - " f t.indices.{k} t.values.{k}\n", - " done" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Test " - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "- : bool = true\n" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1 1.000000\n", - "2 -2.000000\n", - "5 0.500000\n", - "6 0.000000\n", - "8 3.000000\n" - ] - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dense_a = L.Vec.init (dim sparse_a) (get sparse_a);;\n", - "iter (fun i v -> Printf.printf \"%d %f\\n%!\" i v) sparse_a;;" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Converters" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val to_assoc_list : t -> (int * float) list = \n" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val to_vec : t -> Lacaml.D.vec = \n" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let to_assoc_list t = \n", - " let rec aux k accu =\n", - " if k = 0 then\n", - " accu\n", - " else\n", - " aux (k-1) ( (t.indices.{k}, t.values.{k})::accu )\n", - " in\n", - " aux (nnz t) []\n", - " \n", - " \n", - "let to_vec t =\n", - " let result = L.Vec.make0 (dim t) in\n", - " iter (fun k v -> result.{k} <- v) t;\n", - " result\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Test" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "- : (int * float) list = [(1, 1.); (2, -2.); (5, 0.5); (6, 1e-08); (8, 3.)]\n" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : bool = true\n" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "to_assoc_list sparse_a;;\n", - "to_vec sparse_a = dense_a;;" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Operations" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## One-vector operations" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val immutable : (t -> 'a) -> t -> t = \n" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val scale_mut : float -> t -> unit = \n" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val scale : float -> t -> t = \n" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val neg : t -> t = \n" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val norm : t -> float = \n" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let immutable f t =\n", - " let result = copy t in\n", - " f result;\n", - " result\n", - " \n", - "let scale_mut x t = \n", - " L.scal x t.values \n", - "\n", - "let scale x = immutable @@ scale_mut x\n", - " \n", - "let neg t =\n", - " { t with values = L.Vec.neg t.values }\n", - " \n", - "let norm t =\n", - " L.nrm2 t.values\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Test" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val sparse_b : t = {dim: 9 (1, 1) (2, -2) (5, 0.5) (6, 1e-08) (8, 3) }\n" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : bool = true\n" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val dense_b : L.vec = R1 R2 R3 R7 R8 R9\n", - " 1 -2 0 ... 0 3 0\n" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val sparse_c : t = {dim: 9 (1, 0.5) (2, -1) (5, 0.25) (6, 5e-09) (8, 1.5) }\n" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : bool = true\n" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : bool = true\n" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let sparse_b = copy sparse_a;;\n", - "scale_mut 0.5 sparse_b;;\n", - "\n", - "equal sparse_b @@ map (fun x -> x *. 0.5) sparse_a;;\n", - "\n", - "\n", - "let dense_b = L.copy dense_a;;\n", - "L.scal 0.5 dense_b;;\n", - "\n", - "let sparse_c = scale 0.5 sparse_a;;\n", - "\n", - "equal sparse_b sparse_c;;\n", - " \n", - "let _ =\n", - " let n1 = neg sparse_a in\n", - " neg n1 = sparse_a" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Two-vector operations" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val equal : t -> t -> bool = \n" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let equal x y =\n", - " (x.nnz + y.nnz = 0) || (\n", - " (x.dim = y.dim) &&\n", - " (x.nnz = y.nnz) &&\n", - " Bigarray.Array1.(sub x.indices 1 x.nnz = sub y.indices 1 y.nnz) &&\n", - " (Array.sub (L.Vec.to_array x.values) 0 (x.nnz-1) = Array.sub (L.Vec.to_array y.values) 0 (y.nnz-1) )\n", - " )" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## aX + Y\n", - "\n", - "Run along all the entries of `X` and `Y` simultaneously with indices `k` and `l`. `m` is the index of the new array.\n", - "\n", - "if `kl`, update using `y[l]`.\n", - "\n", - "if `k=l`, update using `a*x[k] + y[l]`." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val axpy : ?threshold:float -> ?alpha:float -> t -> t -> t = \n" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let axpy ?(threshold=0.) ?(alpha=1.) x y =\n", - "\n", - " if dim x <> dim y then \n", - " invalid_arg \"Inconsistent dimensions\";\n", - "\n", - " let check = (* Test if value should be added wrt threshold *)\n", - " if threshold = 0. then\n", - " fun x -> x <> 0.\n", - " else\n", - " fun x -> abs_float x > threshold\n", - " in\n", - " \n", - " let f = (* if a=1 in ax+y, then do x+y. If a=0 then do y *)\n", - " if alpha = 1. then\n", - " fun x y -> x +. y\n", - " else if alpha = 0. then\n", - " fun _ y -> y\n", - " else\n", - " fun x y -> alpha *. x +. y\n", - " in\n", - " \n", - " let dim = dim x in\n", - " let nnz = x.nnz + y.nnz in\n", - " let new_indices = Bigarray.(Array1.create int fortran_layout) nnz in\n", - " let new_values = L.Vec.create nnz in\n", - " \n", - " let rec aux k l m =\n", - " match k <= x.nnz, l <= y.nnz with\n", - " | true , true -> (* Both arrays are running *)\n", - " begin\n", - " if x.indices.{k} < y.indices.{l} then (\n", - " let w = f x.values.{k} 0. in\n", - " if check w then (\n", - " new_indices.{m} <- x.indices.{k};\n", - " new_values.{m} <- w ;\n", - " (aux [@tailcall]) (k+1) l (m+1)\n", - " ) else (aux [@tailcall]) (k+1) l m\n", - " )\n", - " else if x.indices.{k} > y.indices.{l} then (\n", - " let w = y.values.{l} in\n", - " if check w then (\n", - " new_indices.{m} <- y.indices.{l};\n", - " new_values.{m} <- w;\n", - " (aux [@tailcall]) k (l+1) (m+1)\n", - " ) else (aux [@tailcall]) k (l+1) m\n", - " )\n", - " else (\n", - " let w = f x.values.{k} y.values.{l} in\n", - " if check w then (\n", - " new_indices.{m} <- x.indices.{k};\n", - " new_values.{m} <- w;\n", - " (aux [@tailcall]) (k+1) (l+1) (m+1)\n", - " ) else (aux [@tailcall]) (k+1) (l+1) m\n", - " )\n", - " end\n", - " | false, true -> (* Array x is done running *)\n", - " begin\n", - " let m = ref m in\n", - " for i=l to y.nnz do\n", - " let w = y.values.{i} in\n", - " if check w then (\n", - " new_indices.{!m} <- y.indices.{i};\n", - " new_values.{!m} <- w;\n", - " incr m;\n", - " )\n", - " done; !m\n", - " end\n", - " | true, false -> (* Array y is done running *)\n", - " begin\n", - " let m = ref m in\n", - " for i=k to x.nnz do\n", - " let w = alpha *. x.values.{i} in\n", - " if check w then (\n", - " new_indices.{!m} <- x.indices.{i};\n", - " new_values.{!m} <- w;\n", - " incr m;\n", - " )\n", - " done; !m\n", - " end\n", - " | false, false -> (* Both arrays are done *)\n", - " m\n", - " in\n", - " let nnz = (aux 1 1 1) - 1 in\n", - " { dim ; nnz ;\n", - " indices = new_indices ; values = new_values }\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val add : ?threshold:float -> t -> t -> t = \n" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val sub : ?threshold:float -> t -> t -> t = \n" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let add ?(threshold=0.) x y = axpy ~threshold ~alpha:1. x y\n", - "\n", - "let sub ?(threshold=0.) x y = axpy ~threshold ~alpha:(-1.) y x\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Test" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val m_A : Lacaml.D.vec = R1 R2 R3 R8 R9 R10\n", - " 1 2 0 ... -0.001 0 0\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_B : Lacaml.D.vec = R1 R2 R3 R8 R9 R10\n", - " 0 1 2 ... 0 -0.001 2\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_As : t = {dim: 10 (1, 1 (2, 2 (5, 0.01 (6, -2 (8, -0.001 }\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_Bs : t = {dim: 10 (2, 1 (3, 2 (6, 0.01 (7, -2 (9, -0.001 (10, 2 }\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_C : L.vec = R1 R2 R3 R8 R9 R10\n", - " 0 1 2 ... 0 -0.001 2\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : L.vec = R1 R2 R3 R8 R9 R10\n", - " 2 5 2 ... -0.002 -0.001 2\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_D : L.vec = R1 R2 R3 R8 R9 R10\n", - " 1 2 0 ... -0.001 0 0\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : unit = ()\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : L.vec = R1 R2 R3 R8 R9 R10\n", - " 1 4 4 ... -0.001 -0.002 4\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_Cs : t =\n", - " {dim: 10\n", - " (1, 2 (2, 5 (3, 2 (5, 0.02 (6, -3.99 (7, -2 (8, -0.002 (9, -0.001 (10, 2 }\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : bool = true\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val m_Ds : t =\n", - " {dim: 10\n", - " (1, 1 (2, 4 (3, 4 (5, 0.01 (6, -1.98 (7, -4 (8, -0.001 (9, -0.002 (10, 4 }\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "- : bool = true\n" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let m_A = L.Vec.of_array [| 1. ; 2. ; 0. ; 0. ; 0.01 ; -2. ; 0. ; -1.e-3 ; 0. ; 0.|]\n", - "let m_B = L.Vec.of_array [| 0. ; 1. ; 2. ; 0. ; 0. ; 0.01 ; -2. ; 0. ; -1.e-3 ; 2. |]\n", - "\n", - "let m_As = of_vec m_A\n", - "let m_Bs = of_vec m_B\n", - "\n", - "let m_C = L.copy m_B ;;\n", - "L.axpy ~alpha:2. m_A m_C;;\n", - "m_C;;\n", - "\n", - "let m_D = L.copy m_A;;\n", - "L.axpy ~alpha:2. m_B m_D;;\n", - "m_D;;\n", - "\n", - "let m_Cs = axpy ~alpha:2. m_As m_Bs\n", - "\n", - "\n", - "let _ = equal (of_vec m_C) m_Cs;;\n", - "\n", - "let m_Ds = axpy ~alpha:2. m_Bs m_As\n", - "\n", - "let _ = equal (of_vec m_D) m_Ds;;\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Dot product" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val dot : t -> t -> float = \n" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let dot x y =\n", - "\n", - " let rec aux accu k l =\n", - " if k <= x.nnz && l <= y.nnz then\n", - " begin\n", - " if x.indices.{k} < y.indices.{l} then \n", - " (aux [@tailcall]) accu (k+1) l\n", - " else if x.indices.{k} > y.indices.{l} then (\n", - " (aux [@tailcall]) accu k (l+1)\n", - " )\n", - " else (\n", - " (aux [@tailcall]) (accu +. x.values.{k} *. y.values.{l}) (k+1) (l+1)\n", - " )\n", - " end\n", - " else\n", - " accu\n", - " in\n", - " aux 0. 1 1\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Test" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "- : bool = true\n" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dot sparse_a sparse_b = L.dot dense_a dense_b;;" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Tests" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/home/scemama/qp2/external/opam/default/lib/astring: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/astring/astring.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/cmdliner: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/cmdliner/cmdliner.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/seq: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/stdlib-shims: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/stdlib-shims/stdlib_shims.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/fmt: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/fmt/fmt.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/fmt/fmt_cli.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/fmt/fmt_tty.cma: loaded\n", - "/home/scemama/qp2/external/opam/default/lib/alcotest: added to search path\n", - "/home/scemama/qp2/external/opam/default/lib/alcotest/alcotest.cma: loaded\n" - ] - } - ], - "source": [ - "#require \"alcotest\";;" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val x1 : Lacaml.D.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " 0.852078 0 0 ... 0 0.656419 0\n", - "val x2 : Lacaml.D.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " -0.606197 0.411059 0 ... -0.368989 0 0.9001\n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val x3 : Lacaml.D.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " 1.70416 0 0 ... 0 1.31284 0\n", - "val x4 : Lacaml.D.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " 0.245881 0.411059 0 ... -0.368989 0.656419 0.9001\n", - "val x5 : Lacaml.D.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " 1.45827 -0.411059 0 ... 0.368989 0.656419 -0.9001\n", - "val x6 : L.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " 1.95004 0.411059 0 ... -0.368989 1.96926 0.9001\n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val v1 : Lacaml.D.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " 0.852078 0 0 ... 0 0.656419 0\n", - "val v2 : Lacaml.D.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " -0.606197 0.411059 0 ... -0.368989 0 0.9001\n", - "val v3 : Lacaml.D.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " 1.70416 0 0 ... 0 1.31284 0\n", - "val v4 : Lacaml.D.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " 0.245881 0.411059 0 ... -0.368989 0.656419 0.9001\n", - "val v5 : Lacaml.D.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " 1.45827 -0.411059 0 ... 0.368989 0.656419 -0.9001\n", - "val v6 : L.vec =\n", - " R1 R2 R3 R98 R99 R100\n", - " 1.95004 0.411059 0 ... -0.368989 1.96926 0.9001\n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val v1_s : t =\n", - " {dim: 100\n", - " (1, 0.852078 (4, 0.733763 (7, -0.818022 (10, -0.692304 (11, -0.980468\n", - " (15, 0.974355 (16, -0.665109 (24, 0.889086 (27, 0.736393 (30, -0.843748\n", - " (31, -0.750514 (34, 0.778919 (38, -0.790597 (40, 0.720996 (41, 0.978861\n", - " (42, -0.679388 (43, -0.853596 (46, 0.977185 (47, -0.811648 (49, -0.702925\n", - " (50, 0.89789 (54, -0.675687 (56, 0.752085 (57, -0.626277 (66, 0.664662\n", - " (67, 0.855765 (69, 0.673572 (71, -0.764248 (72, 0.61481 (73, -0.849851\n", - " (74, -0.983965 (84, -0.764701 (87, -0.834976 (92, -0.851806 (94, 0.696202\n", - " (95, 0.844479 (99, 0.656419 }\n", - "val v2_s : t =\n", - " {dim: 100\n", - " (1, -0.606197 (2, 0.411059 (4, 0.329122 (5, -0.740514 (7, 0.387312\n", - " (8, 0.977894 (9, -0.43281 (11, -0.971917 (15, -0.471397 (16, 0.863036\n", - " (17, -0.497091 (19, 0.8659 (20, 0.572763 (21, 0.963705 (23, -0.568959\n", - " (24, 0.643522 (25, 0.697603 (26, -0.706857 (29, -0.874151 (30, 0.559791\n", - " (32, -0.392582 (34, -0.488787 (36, -0.988593 (38, -0.817274 (39, -0.78555\n", - " (42, 0.505945 (43, 0.370838 (44, -0.734224 (45, -0.634506 (46, 0.304503\n", - " (47, -0.330526 (48, -0.800156 (49, -0.570671 (50, -0.514998 (51, -0.47082\n", - " (52, 0.731985 (53, -0.501758 (54, -0.856375 (55, 0.422431 (56, 0.819669\n", - " (57, 0.847078 (58, 0.301306 (59, -0.917181 (60, 0.391153 (61, -0.936169\n", - " (62, 0.855439 (63, 0.730839 (64, 0.763087 (65, 0.777606 (66, 0.945573\n", - " (67, -0.584689 (68, 0.312286 (69, 0.840451 (72, 0.980958 (73, 0.383844\n", - " (77, 0.509676 (79, 0.86618 (80, -0.767171 (82, -0.955884 (83, -0.326832\n", - " (88, 0.846553 (89, -0.578475 (90, -0.522823 (91, 0.802248 (92, 0.975437\n", - " (95, -0.816165 (96, -0.999559 (97, 0.738769 (98, -0.368989 (100, 0.9001 }\n", - "val v3_s : t =\n", - " {dim: 100\n", - " (1, 1.70416 (4, 1.46753 (7, -1.63604 (10, -1.38461 (11, -1.96094\n", - " (15, 1.94871 (16, -1.33022 (24, 1.77817 (27, 1.47279 (30, -1.6875\n", - " (31, -1.50103 (34, 1.55784 (38, -1.58119 (40, 1.44199 (41, 1.95772\n", - " (42, -1.35878 (43, -1.70719 (46, 1.95437 (47, -1.6233 (49, -1.40585\n", - " (50, 1.79578 (54, -1.35137 (56, 1.50417 (57, -1.25255 (66, 1.32932\n", - " (67, 1.71153 (69, 1.34714 (71, -1.5285 (72, 1.22962 (73, -1.6997\n", - " (74, -1.96793 (84, -1.5294 (87, -1.66995 (92, -1.70361 (94, 1.3924\n", - " (95, 1.68896 (99, 1.31284 }\n", - "val v4_s : t =\n", - " {dim: 100\n", - " (1, 0.245881 (2, 0.411059 (4, 1.06289 (5, -0.740514 (7, -0.43071\n", - " (8, 0.977894 (9, -0.43281 (10, -0.692304 (11, -1.95238 (15, 0.502957\n", - " (16, 0.197927 (17, -0.497091 (19, 0.8659 (20, 0.572763 (21, 0.963705\n", - " (23, -0.568959 (24, 1.53261 (25, 0.697603 (26, -0.706857 (27, 0.736393\n", - " (29, -0.874151 (30, -0.283957 (31, -0.750514 (32, -0.392582 (34, 0.290132\n", - " (36, -0.988593 (38, -1.60787 (39, -0.78555 (40, 0.720996 (41, 0.978861\n", - " (42, -0.173443 (43, -0.482758 (44, -0.734224 (45, -0.634506 (46, 1.28169\n", - " (47, -1.14217 (48, -0.800156 (49, -1.2736 (50, 0.382892 (51, -0.47082\n", - " (52, 0.731985 (53, -0.501758 (54, -1.53206 (55, 0.422431 (56, 1.57175\n", - " (57, 0.220801 (58, 0.301306 (59, -0.917181 (60, 0.391153 (61, -0.936169\n", - " (62, 0.855439 (63, 0.730839 (64, 0.763087 (65, 0.777606 (66, 1.61024\n", - " (67, 0.271076 (68, 0.312286 (69, 1.51402 (71, -0.764248 (72, 1.59577\n", - " (73, -0.466006 (74, -0.983965 (77, 0.509676 (79, 0.86618 (80, -0.767171\n", - " (82, -0.955884 (83, -0.326832 (84, -0.764701 (87, -0.834976 (88, 0.846553\n", - " (89, -0.578475 (90, -0.522823 (91, 0.802248 (92, 0.123631 (94, 0.696202\n", - " (95, 0.0283147 (96, -0.999559 (97, 0.738769 (98, -0.368989 (99, 0.656419\n", - " (100, 0.9001 }\n", - "val v5_s : t =\n", - " {dim: 100\n", - " (1, 1.45827 (2, -0.411059 (4, 0.404641 (5, 0.740514 (7, -1.20533\n", - " (8, -0.977894 (9, 0.43281 (10, -0.692304 (11, -0.00855015 (15, 1.44575\n", - " (16, -1.52814 (17, 0.497091 (19, -0.8659 (20, -0.572763 (21, -0.963705\n", - " (23, 0.568959 (24, 0.245564 (25, -0.697603 (26, 0.706857 (27, 0.736393\n", - " (29, 0.874151 (30, -1.40354 (31, -0.750514 (32, 0.392582 (34, 1.26771\n", - " (36, 0.988593 (38, 0.0266769 (39, 0.78555 (40, 0.720996 (41, 0.978861\n", - " (42, -1.18533 (43, -1.22443 (44, 0.734224 (45, 0.634506 (46, 0.672682\n", - " (47, -0.481123 (48, 0.800156 (49, -0.132254 (50, 1.41289 (51, 0.47082\n", - " (52, -0.731985 (53, 0.501758 (54, 0.180688 (55, -0.422431 (56, -0.067584\n", - " (57, -1.47335 (58, -0.301306 (59, 0.917181 (60, -0.391153 (61, 0.936169\n", - " (62, -0.855439 (63, -0.730839 (64, -0.763087 (65, -0.777606 (66, -0.280911\n", - " (67, 1.44045 (68, -0.312286 (69, -0.166879 (71, -0.764248 (72, -0.366148\n", - " (73, -1.2337 (74, -0.983965 (77, -0.509676 (79, -0.86618 (80, 0.767171\n", - " (82, 0.955884 (83, 0.326832 (84, -0.764701 (87, -0.834976 (88, -0.846553\n", - " (89, 0.578475 (90, 0.522823 (91, -0.802248 (92, -1.82724 (94, 0.696202\n", - " (95, 1.66064 (96, 0.999559 (97, -0.738769 (98, 0.368989 (99, 0.656419\n", - " (100, -0.9001 }\n", - "val v6_s : t =\n", - " {dim: 100\n", - " (1, 1.95004 (2, 0.411059 (4, 2.53041 (5, -0.740514 (7, -2.06675\n", - " (8, 0.977894 (9, -0.43281 (10, -2.07691 (11, -3.91332 (15, 2.45167\n", - " (16, -1.13229 (17, -0.497091 (19, 0.8659 (20, 0.572763 (21, 0.963705\n", - " (23, -0.568959 (24, 3.31078 (25, 0.697603 (26, -0.706857 (27, 2.20918\n", - " (29, -0.874151 (30, -1.97145 (31, -2.25154 (32, -0.392582 (34, 1.84797\n", - " (36, -0.988593 (38, -3.18907 (39, -0.78555 (40, 2.16299 (41, 2.93658\n", - " (42, -1.53222 (43, -2.18995 (44, -0.734224 (45, -0.634506 (46, 3.23606\n", - " (47, -2.76547 (48, -0.800156 (49, -2.67945 (50, 2.17867 (51, -0.47082\n", - " (52, 0.731985 (53, -0.501758 (54, -2.88344 (55, 0.422431 (56, 3.07592\n", - " (57, -1.03175 (58, 0.301306 (59, -0.917181 (60, 0.391153 (61, -0.936169\n", - " (62, 0.855439 (63, 0.730839 (64, 0.763087 (65, 0.777606 (66, 2.93956\n", - " (67, 1.98261 (68, 0.312286 (69, 2.86117 (71, -2.29274 (72, 2.82539\n", - " (73, -2.16571 (74, -2.9519 (77, 0.509676 (79, 0.86618 (80, -0.767171\n", - " (82, -0.955884 (83, -0.326832 (84, -2.2941 (87, -2.50493 (88, 0.846553\n", - " (89, -0.578475 (90, -0.522823 (91, 0.802248 (92, -1.57998 (94, 2.0886\n", - " (95, 1.71727 (96, -0.999559 (97, 0.738769 (98, -0.368989 (99, 1.96926\n", - " (100, 0.9001 }\n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val zero : Lacaml.D.vec = R1 R2 R3 R98 R99 R100\n", - " 0 0 0 ... 0 0 0\n", - "val zero_s : t = {dim: 100 }\n" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let x1 = L.Vec.map (fun x -> if abs_float x < 0.6 then 0. else x) (L.Vec.random 100)\n", - "and x2 = L.Vec.map (fun x -> if abs_float x < 0.3 then 0. else x) (L.Vec.random 100) \n", - "\n", - "let x3 = L.Vec.map (fun x -> 2. *. x) x1\n", - "and x4 = L.Vec.add x1 x2\n", - "and x5 = L.Vec.sub x1 x2\n", - "and x6 = \n", - " let v = L.copy x2 in\n", - " L.axpy ~alpha:3. x1 v;\n", - " v \n", - "\n", - " \n", - "let v1 = x1\n", - "and v2 = x2\n", - "and v3 = x3 \n", - "and v4 = x4 \n", - "and v5 = x5 \n", - "and v6 = x6 \n", - "\n", - " \n", - "let v1_s = of_vec x1\n", - "and v2_s = of_vec x2\n", - "and v3_s = of_vec x3\n", - "and v4_s = of_vec x4\n", - "and v5_s = of_vec x5\n", - "and v6_s = of_vec x6\n", - "\n", - " \n", - "let zero = L.Vec.make0 100\n", - "and zero_s = of_vec (L.Vec.make0 100)\n", - "\n", - " \n" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val test_conversion : unit -> unit = \n" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val test_operations : unit -> unit = \n" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val test_dot : unit -> unit = \n" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "text/plain": [ - "val test_case : unit -> (string * [> `Quick ] * (unit -> unit)) list = \n" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - " let test_conversion () =\n", - " Alcotest.(check bool) \"sparse -> dense 1\" true (to_vec v1_s = v1 );\n", - " Alcotest.(check bool) \"sparse -> dense 2\" true (to_vec v2_s = v2 );\n", - " Alcotest.(check bool) \"dense -> sparse 1\" true (of_vec v1 = v1_s);\n", - " Alcotest.(check bool) \"dense -> sparse 2\" true (of_vec v2 = v2_s)\n", - " \n", - " \n", - " let test_operations () =\n", - " Alcotest.(check bool) \"dense scale\" true (let w = L.copy v1 in L.scal 2. w ; w = v3);\n", - " Alcotest.(check bool) \"sparse scale\" true (scale 2. v1_s = v3_s);\n", - " \n", - " Alcotest.(check bool) \"dense dense add\" true (L.Vec.add v1 v2 = v4);\n", - " (*\n", - " Alcotest.(check bool) \"dense sparse add\" true (add v1 v2_s = v4_s);\n", - " Alcotest.(check bool) \"sparse dense add\" true (add v1_s v2 = v4_s);\n", - " Alcotest.(check bool) \"sparse dense add\" true (add v1 v2_s = v4_s);\n", - " *)\n", - " Alcotest.(check bool) \"sparse sparse add\" true (equal (add v1_s v2_s) v4_s);\n", - " \n", - " Alcotest.(check bool) \"dense dense sub\" true (L.Vec.sub v1 v2 = v5);\n", - " (*\n", - " Alcotest.(check bool) \"dense sparse sub\" true (sub v1 v2_s = v5_s);\n", - " Alcotest.(check bool) \"sparse dense sub\" true (sub v1_s v2 = v5_s);\n", - " Alcotest.(check bool) \"sparse dense sub\" true (sub v1 v2_s = v5_s);\n", - " *)\n", - " Alcotest.(check bool) \"sparse sparse sub\" true (equal (sub v1_s v2_s) v5_s);\n", - " \n", - " Alcotest.(check bool) \"dense dense sub\" true (L.Vec.sub v1 v1 = zero);\n", - " (*\n", - " Alcotest.(check bool) \"dense sparse sub\" true (sub v1 v1_s = zero_s);\n", - " Alcotest.(check bool) \"sparse dense sub\" true (sub v1_s v1 = zero_s);\n", - " *)\n", - " Alcotest.(check bool) \"sparse sparse sub\" true (equal (sub v1_s v1_s) zero_s);\n", - " \n", - " Alcotest.(check bool) \"dense dense axpy\" true (let w = L.copy v2 in L.axpy ~alpha:3. v1 w ; w = v6);\n", - " (*\n", - " Alcotest.(check bool) \"dense sparse axpy\" true (sub ~threshold:1.e-12 (axpy ~alpha:3. v1 v2_s) v6_s = zero_s);\n", - " Alcotest.(check bool) \"sparse dense axpy\" true (sub ~threshold:1.e-12 (axpy ~alpha:3. v1_s v2) v6_s = zero_s);\n", - " *)\n", - " Alcotest.(check bool) \"sparse sparse axpy\" true (equal (sub ~threshold:1.e-12 (axpy ~alpha:3. v1_s v2_s) v6_s) zero_s)\n", - " \n", - "let test_dot () = \n", - " let d1d2 = L.dot x1 x2\n", - " and d1d1 = L.dot x1 x1\n", - " and d2d2 = L.dot x2 x2 \n", - " in\n", - " (*\n", - " Alcotest.(check (float 1.e-10)) \"sparse x dense 1\" (dot v1_s v2 ) d1d2;\n", - " Alcotest.(check (float 1.e-10)) \"sparse x dense 2\" (dot v1_s v1 ) d1d1;\n", - " Alcotest.(check (float 1.e-10)) \"sparse x dense 3\" (dot v2_s v2 ) d2d2;\n", - " Alcotest.(check (float 1.e-10)) \"dense x sparse 1\" (dot v1 v2_s) d1d2;\n", - " Alcotest.(check (float 1.e-10)) \"dense x sparse 2\" (dot v1 v1_s) d1d1;\n", - " Alcotest.(check (float 1.e-10)) \"dense x sparse 3\" (dot v2 v2_s) d2d2;\n", - " *)\n", - " Alcotest.(check (float 1.e-10)) \"sparse x sparse 1\" (dot v1_s v2_s) d1d2;\n", - " Alcotest.(check (float 1.e-10)) \"sparse x sparse 2\" (dot v1_s v1_s) d1d1;\n", - " Alcotest.(check (float 1.e-10)) \"sparse x sparse 3\" (dot v2_s v2_s) d2d2\n", - " \n", - " \n", - "let test_case () = \n", - " [ \n", - " \"Conversion\", `Quick, test_conversion;\n", - " \"Operations\", `Quick, test_operations;\n", - " \"Dot product\", `Quick, test_dot;\n", - " ] " - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "File \"[28]\", line 1, characters 0-3:\n", - "Warning 1: this `(*' is the start of a comment.\n", - "Hint: Did you forget spaces when writing the infix operator `( * )'?\n" - ] - } - ], - "source": [ - "(*)\n", - "Alcotest.run ~argv:[|\"ignored\"|] \"Unit tests\" [\n", - " \"SpVec\", test_case ();\n", - "];;\n", - "Printf.printf \"%!\";;\n", - "*)" - ] - } - ], - "metadata": { - "celltoolbar": "Raw Cell Format", - "kernelspec": { - "display_name": "OCaml default", - "language": "OCaml", - "name": "ocaml-jupyter" - }, - "language_info": { - "codemirror_mode": "text/x-ocaml", - "file_extension": ".ml", - "mimetype": "text/x-ocaml", - "name": "OCaml", - "nbconverter_exporter": null, - "pygments_lexer": "OCaml", - "version": "4.07.1" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Notebooks/TemplateQCaml.ipynb b/Notebooks/TemplateQCaml.ipynb deleted file mode 100644 index 1f61dd1..0000000 --- a/Notebooks/TemplateQCaml.ipynb +++ /dev/null @@ -1,159 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "val png_image : string -> unit = \n" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "- : unit = ()\n", - "Findlib has been successfully loaded. Additional directives:\n", - " #require \"package\";; to load a package\n", - " #list;; to list the available packages\n", - " #camlp4o;; to load camlp4 (standard syntax)\n", - " #camlp4r;; to load camlp4 (revised syntax)\n", - " #predicates \"p,q,...\";; to set these predicates\n", - " Topfind.reset();; to force that packages will be reloaded\n", - " #thread;; to enable threads\n", - "\n", - "- : unit = ()\n" - ] - }, - { - "data": { - "text/plain": [ - "val png_image : string -> Jupyter_notebook.display_id = \n" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "let png_image = print_endline ;;\n", - "\n", - "(* --------- *)\n", - "\n", - "#cd \"/home/scemama/QCaml\";;\n", - "#use \"topfind\";;\n", - "#require \"jupyter.notebook\";;\n", - "\n", - "let png_image name = \n", - " Jupyter_notebook.display_file ~base64:true \"image/png\" (\"Notebooks/images/\"^name)\n", - ";;\n", - "\n", - "#require \"lacaml.top\";;\n", - "#require \"alcotest\";;\n", - "#require \"str\";;\n", - "#require \"bigarray\";;\n", - "#require \"zarith\";;\n", - "#require \"getopt\";;\n", - "#directory \"_build\";;\n", - "#directory \"_build/Basis\";;\n", - "#directory \"_build/CI\";;\n", - "#directory \"_build/MOBasis\";;\n", - "#directory \"_build/Nuclei\";;\n", - "#directory \"_build/Parallel\";;\n", - "#directory \"_build/Perturbation\";;\n", - "#directory \"_build/SCF\";;\n", - "#directory \"_build/Utils\";;\n" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "File Constants.cmo is not a bytecode object file.\n", - "File Util.cma is not a bytecode object file.\n", - "File Matrix.cmo is not a bytecode object file.\n", - "File Simulation.cmo is not a bytecode object file.\n", - "File Spindeterminant.cmo is not a bytecode object file.\n", - "File Determinant.cmo is not a bytecode object file.\n", - "File HartreeFock.cmo is not a bytecode object file.\n", - "File MOBasis.cmo is not a bytecode object file.\n", - "File F12CI.cmo is not a bytecode object file.\n" - ] - } - ], - "source": [ - "#load \"Constants.cmo\";;\n", - "#load_rec \"Util.cma\";;\n", - "#load_rec \"Matrix.cmo\";;\n", - "#load_rec \"Simulation.cmo\";;\n", - "#load_rec \"Spindeterminant.cmo\";;\n", - "#load_rec \"Determinant.cmo\";;\n", - "#load_rec \"HartreeFock.cmo\";;\n", - "#load_rec \"MOBasis.cmo\";;\n", - "#load_rec \"F12CI.cmo\";;" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "#install_printer AngularMomentum.pp_string ;;\n", - "#install_printer Basis.pp ;;\n", - "#install_printer Charge.pp ;;\n", - "#install_printer Coordinate.pp ;;\n", - "#install_printer Vector.pp;;\n", - "#install_printer Matrix.pp;;\n", - "#install_printer Util.pp_float_2darray;;\n", - "#install_printer Util.pp_float_array;;\n", - "#install_printer Util.pp_matrix;;\n", - "#install_printer HartreeFock.pp ;;\n", - "#install_printer Fock.pp ;;\n", - "#install_printer MOClass.pp ;;\n", - "let pp_mo ppf t = MOBasis.pp ~start:1 ~finish:0 ppf t ;;\n", - "#install_printer pp_mo;;\n", - "(*\n", - "#install_printer DeterminantSpace.pp;;\n", - "*)\n", - "#install_printer SpindeterminantSpace.pp;;\n", - "#install_printer Bitstring.pp;;\n", - "\n", - "(* --------- *)\n", - "\n", - "open Lacaml.D\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "OCaml default", - "language": "OCaml", - "name": "ocaml-jupyter" - }, - "language_info": { - "codemirror_mode": "text/x-ocaml", - "file_extension": ".ml", - "mimetype": "text/x-ocaml", - "name": "OCaml", - "nbconverter_exporter": null, - "pygments_lexer": "OCaml", - "version": "4.07.1" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/Notebooks/images/0_1_11.png b/Notebooks/images/0_1_11.png deleted file mode 100644 index b5433c9..0000000 Binary files a/Notebooks/images/0_1_11.png and /dev/null differ diff --git a/Notebooks/images/0_1_11.tikz b/Notebooks/images/0_1_11.tikz deleted file mode 100644 index 61ded10..0000000 --- a/Notebooks/images/0_1_11.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updna{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\upa{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\dn{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updna{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/0_1_22.png b/Notebooks/images/0_1_22.png deleted file mode 100644 index b202ba7..0000000 Binary files a/Notebooks/images/0_1_22.png and /dev/null differ diff --git a/Notebooks/images/0_1_22.tikz b/Notebooks/images/0_1_22.tikz deleted file mode 100644 index cad0952..0000000 --- a/Notebooks/images/0_1_22.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\upa{\XX}{2.0} -} -\emp{\XX}{1.5} -\dnb{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/0_2_22.png b/Notebooks/images/0_2_22.png deleted file mode 100644 index d426791..0000000 Binary files a/Notebooks/images/0_2_22.png and /dev/null differ diff --git a/Notebooks/images/0_2_22.tikz b/Notebooks/images/0_2_22.tikz deleted file mode 100644 index 5987dcc..0000000 --- a/Notebooks/images/0_2_22.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\updnab{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/1_1_11.png b/Notebooks/images/1_1_11.png deleted file mode 100644 index 9b8beba..0000000 Binary files a/Notebooks/images/1_1_11.png and /dev/null differ diff --git a/Notebooks/images/1_1_11.tikz b/Notebooks/images/1_1_11.tikz deleted file mode 100644 index d629dce..0000000 --- a/Notebooks/images/1_1_11.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updna{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\upa{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\dn{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\upa{\XX}{1.0} -\dn{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/1_1_12.png b/Notebooks/images/1_1_12.png deleted file mode 100644 index 518263a..0000000 Binary files a/Notebooks/images/1_1_12.png and /dev/null differ diff --git a/Notebooks/images/1_1_12.tikz b/Notebooks/images/1_1_12.tikz deleted file mode 100644 index 828d7bd..0000000 --- a/Notebooks/images/1_1_12.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\upa{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\dnb{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\dnb{\XX}{1.0} -\upa{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/1_1_21.png b/Notebooks/images/1_1_21.png deleted file mode 100644 index b9e01fd..0000000 Binary files a/Notebooks/images/1_1_21.png and /dev/null differ diff --git a/Notebooks/images/1_1_21.tikz b/Notebooks/images/1_1_21.tikz deleted file mode 100644 index 4975d88..0000000 --- a/Notebooks/images/1_1_21.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\upa{\XX}{2.0} -} -\emp{\XX}{1.5} -\dnb{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\dnb{\XX}{1.0} -\upa{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/1_1_22.png b/Notebooks/images/1_1_22.png deleted file mode 100644 index cf03c02..0000000 Binary files a/Notebooks/images/1_1_22.png and /dev/null differ diff --git a/Notebooks/images/1_1_22.tikz b/Notebooks/images/1_1_22.tikz deleted file mode 100644 index e0beb3d..0000000 --- a/Notebooks/images/1_1_22.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\upa{\XX}{2.0} -} -\emp{\XX}{1.5} -\dnb{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\dnb{\XX}{1.5} -\emp{\XX}{1.0} -\upa{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/1_2_22.png b/Notebooks/images/1_2_22.png deleted file mode 100644 index 1097d98..0000000 Binary files a/Notebooks/images/1_2_22.png and /dev/null differ diff --git a/Notebooks/images/1_2_22.tikz b/Notebooks/images/1_2_22.tikz deleted file mode 100644 index 196f5b5..0000000 --- a/Notebooks/images/1_2_22.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\updnab{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\dnb{\XX}{1.0} -\upa{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/2_1_12.png b/Notebooks/images/2_1_12.png deleted file mode 100644 index 9392d7e..0000000 Binary files a/Notebooks/images/2_1_12.png and /dev/null differ diff --git a/Notebooks/images/2_1_12.tikz b/Notebooks/images/2_1_12.tikz deleted file mode 100644 index 509b5d3..0000000 --- a/Notebooks/images/2_1_12.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\upa{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\dnb{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\updnab{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/2_1_21.png b/Notebooks/images/2_1_21.png deleted file mode 100644 index e4eb7ae..0000000 Binary files a/Notebooks/images/2_1_21.png and /dev/null differ diff --git a/Notebooks/images/2_1_21.tikz b/Notebooks/images/2_1_21.tikz deleted file mode 100644 index 6dfb7ae..0000000 --- a/Notebooks/images/2_1_21.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\upa{\XX}{2.0} -} -\emp{\XX}{1.5} -\dnb{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\updnab{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/2_1_22.png b/Notebooks/images/2_1_22.png deleted file mode 100644 index 6ff413e..0000000 Binary files a/Notebooks/images/2_1_22.png and /dev/null differ diff --git a/Notebooks/images/2_1_22.tikz b/Notebooks/images/2_1_22.tikz deleted file mode 100644 index 87936de..0000000 --- a/Notebooks/images/2_1_22.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\upa{\XX}{2.0} -} -\emp{\XX}{1.5} -\dnb{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\dnb{\XX}{1.5} -\upa{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/2_2_22.png b/Notebooks/images/2_2_22.png deleted file mode 100644 index 34aec64..0000000 Binary files a/Notebooks/images/2_2_22.png and /dev/null differ diff --git a/Notebooks/images/2_2_22.tikz b/Notebooks/images/2_2_22.tikz deleted file mode 100644 index 72eb4c4..0000000 --- a/Notebooks/images/2_2_22.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updn{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\updnab{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\updnab{\XX}{1.0} -\emp{\XX}{0.5} -\updn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/3_1_22.png b/Notebooks/images/3_1_22.png deleted file mode 100644 index f6c7d70..0000000 Binary files a/Notebooks/images/3_1_22.png and /dev/null differ diff --git a/Notebooks/images/3_1_22.tikz b/Notebooks/images/3_1_22.tikz deleted file mode 100644 index fd86140..0000000 --- a/Notebooks/images/3_1_22.tikz +++ /dev/null @@ -1,37 +0,0 @@ -\begin{tikzpicture} -\input{Electrons.tikz} - -% Det |I> -\renewcommand{\XX}{\XI} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\emp{\XX}{1.5} -\emp{\XX}{1.0} -\updnab{\XX}{0.5} -\updnc{\XX}{0.} - -% Det |alpha> -\renewcommand{\XX}{\XA} -\cabs{ -\emp{\XX}{2.5} -\upa{\XX}{2.0} -} -\emp{\XX}{1.5} -\dnb{\XX}{1.0} -\emp{\XX}{0.5} -\updnc{\XX}{0.} - -% Det |J> -\renewcommand{\XX}{\XJ} -\cabs{ -\emp{\XX}{2.5} -\emp{\XX}{2.0} -} -\upa{\XX}{1.5} -\updncb{\XX}{1.0} -\emp{\XX}{0.5} -\dn{\XX}{0.} - -\end{tikzpicture} diff --git a/Notebooks/images/Electrons.tikz b/Notebooks/images/Electrons.tikz deleted file mode 100644 index dccbecd..0000000 --- a/Notebooks/images/Electrons.tikz +++ /dev/null @@ -1,135 +0,0 @@ -% Documentation -% ------------- -% -% \up : up electron (black) -% \upr : up electron (red) -% \dn : down electron (black) -% \dnr : down electron (red) -% \updn : up electron (black), down electron (black) -% \updnrr : up electron (red ), down electron (red ) -% \updnrb : up electron (red ), down electron (black) -% \updnbr : up electron (black), down electron (red ) -% \emp : empty orbital -% \cabs{ } : CABS space inside -% -% Example -% ------- -% -% \input{Electrons.tikz} -% -% \cabs{ -% \emp{0.}{2.0} -% \emp{0.}{1.5} -% } -% \emp{0.}{1.0} -% \updnrb{0.}{0.5} -% \updn{0.}{0.} -% - -% Electron symbol -\newcommand{\upel}{$\uparrow$} -\newcommand{\dnel}{$\downarrow$} - -% Colors -\newcommand{\cabs}[1]{ { \color{lightgray}{#1} } } -\newcommand{\obs}[1]{ { \color{black}{#1} } } -\newcommand{\exca}[1]{ { \color{red}{#1} } } -\newcommand{\excb}[1]{ { \color{Cyan}{#1} } } -\newcommand{\excc}[1]{ { \color{Green}{#1} } } -\newcommand{\noexc}[1]{{ \color{black}{#1} } } - -% Spacing between the 3 diagrams -\newcommand{\XI}{-1.} -\newcommand{\XA}{0.} -\newcommand{\XJ}{1.} - -% Up electron -\newcommand{\up}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1-0.1,#2) {\noexc{\upel}}; -} - -\newcommand{\upa}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1-0.1,#2) {\exca{\upel}}; -} - -\newcommand{\upb}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1-0.1,#2) {\excb{\upel}}; -} - -\newcommand{\upc}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1-0.1,#2) {\excc{\upel}}; -} - -% Down electron -\newcommand{\dn}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1+0.1,#2) {\noexc{\dnel}}; -} - -\newcommand{\dna}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1+0.1,#2) {\exca{\dnel}}; -} - -\newcommand{\dnb}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1+0.1,#2) {\excb{\dnel}}; -} - -\newcommand{\dnc}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1+0.1,#2) {\excc{\dnel}}; -} - -% Up and Down electrons -\newcommand{\updn}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1+0.1,#2) {\noexc{\dnel}}; - \node at (#1-0.1,#2) {\noexc{\upel}}; -} - -\newcommand{\updnab}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1+0.1,#2) {\excb{\dnel}}; - \node at (#1-0.1,#2) {\exca{\upel}}; -} - -\newcommand{\updncb}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1+0.1,#2) {\excb{\dnel}}; - \node at (#1-0.1,#2) {\excc{\upel}}; -} - -\newcommand{\updna}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1+0.1,#2) {\noexc{\dnel}}; - \node at (#1-0.1,#2) {\exca{\upel}}; -} - -\newcommand{\updnb}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1-0.1,#2) {\noexc{\upel}}; - \node at (#1+0.1,#2) {\excb{\dnel}}; -} - -\newcommand{\updnc}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); - \node at (#1+0.1,#2) {\noexc{\dnel}}; - \node at (#1-0.1,#2) {\excc{\upel}}; -} - -% Empty orbital -\newcommand{\emp}[2]{ - \draw [-,thick] (-0.2+#1,#2) -- (0.2+#1,#2); -} - -% Determinant label -\node at (\XI,-0.7) {$\ket{I}$}; -\node at (\XA,-0.7) {$\ket{\alpha}$}; -\node at (\XJ,-0.7) {$\ket{J}$}; - -\newcommand{\XX}{0.} diff --git a/Nuclei/.merlin b/Nuclei/.merlin deleted file mode 100644 index 2ba6169..0000000 --- a/Nuclei/.merlin +++ /dev/null @@ -1 +0,0 @@ -REC diff --git a/Nuclei/Mass.ml b/Nuclei/Mass.ml deleted file mode 100644 index 5eb07ee..0000000 --- a/Nuclei/Mass.ml +++ /dev/null @@ -1,3 +0,0 @@ -(** Atomic mass. *) - -include NonNegativeFloat diff --git a/Nuclei/Mass.mli b/Nuclei/Mass.mli deleted file mode 100644 index d942ece..0000000 --- a/Nuclei/Mass.mli +++ /dev/null @@ -1,3 +0,0 @@ -(** Atomic mass. *) - -include module type of NonNegativeFloat diff --git a/Parallel_mpi/Farm.ml b/Parallel_mpi/Farm.ml deleted file mode 100644 index e7508eb..0000000 --- a/Parallel_mpi/Farm.ml +++ /dev/null @@ -1,246 +0,0 @@ -(********************************************************************) -(* Single process *) -(********************************************************************) - -let run_sequential f stream = - - let rec next _ = - try - let task = Stream.next stream in - Some (f task) - with Stream.Failure -> None - in - Stream.from next - - - - -(********************************************************************) -(* Server side *) -(********************************************************************) - -type task_id = int - -let debug _s = - if true then - () - else - Printf.eprintf "%d : %s : %s\n%!" (Mpi.comm_rank Mpi.comm_world) (Unix.gettimeofday () |> string_of_float) _s - -type status = - | Initializing - | Running - | Done - -let run_parallel_server ~comm ~ordered stream = - - (* [status.(rank)] is [Initializing] if rank has not yet obtained a task, - [Running] if rank is running a task and [Done] if [rank] is waiting at - the barrier. - *) - let status = Array.make (Mpi.comm_size comm) Initializing in - status.(0) <- Done; - - - (** Fetches a result coming from any client. Returns the result - as a (task_id * 'a) option and the rank of the client as an int. - *) - let fetch_result () : (task_id * 'a) option * int = - let (message, rank, _tag) : (task_id * 'a) option * int * int = - debug "Before receive_status"; - (* Avoid busy receive *) - let rec wait_and_receive () = - match Mpi.iprobe Mpi.any_source Mpi.any_tag comm with - | Some _ -> Mpi.receive_status Mpi.any_source Mpi.any_tag comm - | None -> (Unix.sleepf 0.001 ; (wait_and_receive [@tailcall]) ()) - in - wait_and_receive () - in - debug @@ Printf.sprintf "After receive_status %d %d" rank _tag; - message, rank - in - - - (** Pops a task from the stream and sends it to a client. - If no task is available, sends [None]. - The return value is a boolean telling if the stream is empty. - *) - let send_task (client_rank : int) : unit = - let task = - try - let task_id = Stream.count stream in - let element = Stream.next stream in - Some (task_id, element) - with Stream.Failure -> None - in - debug @@ Printf.sprintf "Sending to %d\n" client_rank; - Mpi.send task client_rank 0 comm; - debug @@ Printf.sprintf "Sent to %d : %s\n" client_rank - (if task = None then "None" else "Some"); - if task <> None then - status.(client_rank) <- Running - else - status.(client_rank) <- Done - in - - - let all_done () = - try - Array.iter (fun i -> if i <> Done then raise Exit) status; - true - with Exit -> false - in - - - - (** Main loop. - While [n_todo > 0], fetch a result from a client - and send it back a new task. If no more tasks are - available, send [None]. If the result of the task - is None, loop back into [get_result]. - *) - let rec get_result () : (task_id * 'a ) option = - if all_done () then - begin - debug "Before barrier"; - Mpi.barrier comm; - debug "After barrier"; - None - end - else - begin - let message, rank = fetch_result () in - send_task rank; - match message with - | None -> get_result () - | Some (task_id, result) -> Some (task_id, result) - end - in - - - (** Function from which the output stream is built. *) - let f = - - if not ordered then - (* If [ordered] is false, the values are popped out whenever they arrive - from the clients. - *) - - fun _ -> - match get_result () with - | Some (_, result) -> Some result - | None -> None - - else - (* If [ordered] is true, out into the stream when the next expected task has - been computed. - *) - - let buffer = - (* buffer of finished tasks with a task_id greater than the - current result_id. It allows to put back the results in - the correct order. - *) - Hashtbl.create 67 - in - - fun i -> - begin - match Hashtbl.find_opt buffer i with - | Some x -> - begin - Hashtbl.remove buffer i; - Some x - end - | None -> - let rec loop () = - match get_result () with - | None -> None - | Some (task_id, result) -> - if task_id = i then Some result - else (Hashtbl.add buffer task_id result; (loop [@tailcall]) () ) - in loop () - end - - in - Stream.from f - - - - -(********************************************************************) -(* Client side *) -(********************************************************************) - -let run_parallel_client ~comm f = - - (** Send a first message containing [None] to request a task *) - debug "Before send None"; - Mpi.send None 0 0 comm; - debug "After send None"; - - (** Main loop. - Receive a message. If the message is [None], there are no more - tasks to compute and we can go to the barrier. - If the message is not [None], apply [f] to the task, send the - result back to the server and loop. - *) - let rec run () = - - let message = - debug "Before receive"; - Mpi.receive 0 0 comm - in - debug "After receive" ; - - match message with - | None -> - ( debug "Before barrier"; - Mpi.barrier comm; - debug "After barrier";) - | Some (task_id, task) -> - let result = f task in - begin - debug @@ Printf.sprintf "Before send task_id %d" task_id ; - Mpi.send (Some (task_id, result)) 0 0 comm; - debug @@ Printf.sprintf "After send task_id %d" task_id ; - (run [@tailcall]) () - end - in - run (); - - (* The output is an empty stream so that the type of run_parallel_client - is the same as the type of the server function. - *) - Stream.of_list [] - - - - -let run_parallel ~comm ~ordered f stream = - match Mpi.comm_rank comm with - | 0 -> run_parallel_server ~comm ~ordered stream - | _ -> run_parallel_client ~comm f - - -let nested = ref false - -let run ?(ordered=true) ?(comm=Mpi.comm_world) ~f stream = - if !nested then - begin - let message = - "Nested parallel regions are not supported by Farm.ml" - in - Printf.eprintf "%s\n%!" message ; - failwith message - end; - nested := true; - let result = - match Mpi.comm_size comm with - | 1 -> run_sequential f stream - | _ -> run_parallel ~comm ~ordered f stream - in - nested := false; - result - - diff --git a/Parallel_mpi/Farm.mli b/Parallel_mpi/Farm.mli deleted file mode 100644 index 3226f5c..0000000 --- a/Parallel_mpi/Farm.mli +++ /dev/null @@ -1,18 +0,0 @@ -(** The Farm skeleton, similar to SklMl. - -The input is a stream of input data, and the output is a stream of data. -*) - - -val run_sequential : ('a -> 'b) -> 'a Stream.t -> 'b Stream.t - -val run : ?ordered:bool -> ?comm:Mpi.communicator -> - f:('a -> 'b) -> 'a Stream.t -> 'b Stream.t -(** Run the [f] function on every process by popping elements from the - input stream, and putting the results on the output stream. If [ordered] - (the default is [ordered = true], then the order of the output is kept - consistent with the order of the input. - [comm], within MPI is a communicator. It describes a subgroup of processes. -*) - - diff --git a/Parallel_mpi/Parallel.ml b/Parallel_mpi/Parallel.ml deleted file mode 100644 index e4f78f9..0000000 --- a/Parallel_mpi/Parallel.ml +++ /dev/null @@ -1,273 +0,0 @@ -(** Module for handling distributed parallelism *) - -let size = - let result = - Mpi.comm_size Mpi.comm_world - in - assert (result > 0); - result - - -let rank = - let result = - Mpi.comm_rank Mpi.comm_world - in - assert (result >= 0); - result - - -let master = rank = 0 - - -let barrier () = - Mpi.barrier Mpi.comm_world - - -let broadcast_generic broadcast x = - let x = - if master then Some (Lazy.force x) - else None - in - match broadcast x 0 Mpi.comm_world with - | Some x -> x - | None -> assert false - - -let broadcast x = broadcast_generic Mpi.broadcast x - -let broadcast_int x = - Mpi.broadcast_int x 0 Mpi.comm_world - -let broadcast_int_array x = - Mpi.broadcast_int_array x 0 Mpi.comm_world; - x - -let broadcast_float x = - Mpi.broadcast_float x 0 Mpi.comm_world - -let broadcast_float_array x = - Mpi.broadcast_float_array x 0 Mpi.comm_world; - x - -let broadcast_vec x = - let a = Lacaml.D.Vec.to_array x in - let a = broadcast_float_array a in - Lacaml.D.Vec.of_array a - - -module Node = struct - - let name = Unix.gethostname () - - let world_rank = rank - - let comm = - let _, color = - Mpi.allgather (name, world_rank) Mpi.comm_world - |> Array.to_list - |> List.sort compare - |> List.find (fun (n, r) -> n = name) - in - Mpi.(comm_split comm_world color world_rank) - - let rank = - Mpi.comm_rank comm - - let master = rank = 0 - - let broadcast_generic broadcast x = - let x = - if master then Some (Lazy.force x) - else None - in - match broadcast x 0 comm with - | Some x -> x - | None -> assert false - - let broadcast x = broadcast_generic Mpi.broadcast x - - let barrier () = Mpi.barrier comm - - let _ = barrier () - -end - - -module InterNode = struct - - let world_rank = rank - - let comm = - - let ranks = - let name = Unix.gethostname () in - - let rec aux accu old_name = function - | [] -> List.rev accu |> Array.of_list - | (new_name, r) :: rest when new_name <> old_name -> - aux (r::accu) new_name rest - | (new_name, r) :: rest -> aux accu new_name rest - in - - Mpi.allgather (name, world_rank) Mpi.comm_world - |> Array.to_list - |> List.sort compare - |> aux [] "" - in - - let world_group = - Mpi.comm_group Mpi.comm_world - in - - let new_group = - Mpi.group_incl world_group ranks - in - - Mpi.comm_create Mpi.comm_world new_group - - - let rank = - if Mpi.comm_is_null comm then 0 else - Mpi.comm_rank comm - - let master = rank = 0 - - let broadcast_generic broadcast x = - if Mpi.comm_is_null comm then - Lazy.force x - else - begin - let x = - if master then Some (Lazy.force x) - else None - in - match broadcast x 0 comm with - | Some x -> x - | None -> assert false - end - - let broadcast x = broadcast_generic Mpi.broadcast x - - let barrier () = - if Mpi.comm_is_null comm then () else - Mpi.barrier comm - - let _ = barrier () - -end - -module Vec = struct - - type t = - { - global_first : int ; (* Lower index in the global array *) - global_last : int ; (* Higher index in the global array *) - local_first : int ; (* Lower index in the local array *) - local_last : int ; (* Higher index in the local array *) - data : Lacaml.D.vec ; (* Lacaml vector containing the data *) - } - - let dim vec = - vec.global_last - vec.global_first + 1 - - let local_first vec = vec.local_first - let local_last vec = vec.local_last - let global_first vec = vec.global_first - let global_last vec = vec.global_last - let data vec = vec.data - - let pp ppf v = - Format.fprintf ppf "@[<2>"; - Format.fprintf ppf "@[ gf : %d@]@;" v.global_first; - Format.fprintf ppf "@[ gl : %d@]@;" v.global_last; - Format.fprintf ppf "@[ lf : %d@]@;" v.local_first; - Format.fprintf ppf "@[ ll : %d@]@;" v.local_last; - Format.fprintf ppf "@[ data : %a@]@;" (Lacaml.Io.pp_lfvec ()) v.data; - Format.fprintf ppf "@]@."; - () - - let create n = - let step = (n-1) / size + 1 in - let local_first = step * rank + 1 in - let local_last = min (local_first + step - 1) n in - { - global_first = 1 ; - global_last = n ; - local_first ; - local_last ; - data = Lacaml.D.Vec.create (max 0 (local_last - local_first + 1)) - } - - - let make n x = - let result = create n in - { result with data = - Lacaml.D.Vec.make - (Lacaml.D.Vec.dim result.data) - x - } - - - let make0 n = - make n 0. - - - let init n f = - let result = create n in - { result with data = - Lacaml.D.Vec.init - (Lacaml.D.Vec.dim result.data) - (fun i -> f (i+result.local_first-1)) - } - - - let of_array a = - let length_a = Array.length a in - let a = - let n = length_a mod size in - if n > 0 then - Array.concat [ a ; Array.make (size-n) 0. ] - else - a - in - let result = create length_a in - let a_local = Array.make ((Array.length a)/size) 0. in - let () = Mpi.scatter_float_array a a_local 0 Mpi.comm_world in - { result with data = Lacaml.D.Vec.of_array a_local } - - - let to_array vec = - let final_size = dim vec in - let buffer_size = (Lacaml.D.Vec.dim vec.data) * size in - let buffer = Array.make buffer_size 0. in - let data = Lacaml.D.Vec.to_array vec.data in - let () = Mpi.gather_float_array data buffer 0 Mpi.comm_world in - if final_size = buffer_size then - buffer - else - Array.init final_size (fun i -> buffer.(i)) - - - let of_vec a = - Lacaml.D.Vec.to_array a - |> of_array - - - let to_vec v = - to_array v - |> Lacaml.D.Vec.of_array - - -end - - - -let dot v1 v2 = - if Vec.dim v1 <> Vec.dim v2 then - invalid_arg "Incompatible dimensions"; - let local_dot = - Lacaml.D.dot (Vec.data v1) (Vec.data v2) - in - Mpi.reduce_float local_dot Mpi.Float_sum 0 Mpi.comm_world - - diff --git a/Parallel_mpi/Parallel.mli b/Parallel_mpi/Parallel.mli deleted file mode 100644 index 129ee50..0000000 --- a/Parallel_mpi/Parallel.mli +++ /dev/null @@ -1,171 +0,0 @@ -(** Module for handling distributed parallelism *) - -val size : int -(** Number of distributed processes. *) - -val rank : Mpi.rank -(** Rank of the current distributed processe. *) - -val master : bool -(** True if [rank = 0]. *) - -val barrier : unit -> unit -(** Wait for all processes to reach this point. *) - -val broadcast : 'a lazy_t -> 'a -(** Broadcasts data to all processes. *) - -val broadcast_int : int -> int -(** Broadcasts an [int] to all processes. *) - -val broadcast_float : float -> float -(** Broadcasts a [float] to all processes. *) - -val broadcast_int_array : int array -> int array -(** Broadcasts an [int array] to all processes. *) - -val broadcast_float_array : float array -> float array -(** Broadcasts a [float array] to all processes. *) - -val broadcast_vec : Lacaml.D.vec -> Lacaml.D.vec -(** Broadcasts a Lacaml vector to all processes. *) - - -(** {5 Intra-node operations} *) -module Node : sig - (** This module contains parallel primitives among processes - within the same compute node. - *) - - val name : string - (** Name of the current host *) - - val comm : Mpi.communicator - (** MPI Communicator containing the processes of the current node *) - - val rank : Mpi.rank - (** Rank of the current process in the node *) - - val master : bool - (** If true, master process of the node *) - - val broadcast : 'a lazy_t -> 'a - (** Broadcasts data to all the processes of the current node. *) - - val barrier : unit -> unit - (** Wait for all processes among the node to reach this point. *) -end - - -(** {5 Inter-node operations} *) -module InterNode : sig - - val comm : Mpi.communicator - (** MPI Communicator among the master processes of the each node *) - - val rank : Mpi.rank - (** Rank of the current process in the inter-node communicator *) - - val master : bool - (** If true, master process of the inter-node communicator *) - - val broadcast : 'a lazy_t -> 'a - (** Broadcasts data to all the processes of the inter-node communicator. *) - - val barrier : unit -> unit - (** Wait for all processes among the node to reach this point. *) -end - -(** {5 Vector operations} *) -module Vec : sig - - type t = private - { - global_first : int ; (* Lower index in the global array *) - global_last : int ; (* Higher index in the global array *) - local_first : int ; (* Lower index in the local array *) - local_last : int ; (* Higher index in the local array *) - data : Lacaml.D.vec ; (* Lacaml vector containing the data *) - } - - val pp : Format.formatter -> t -> unit - - (** {6 Creation/conversion of vectors} *) - - val create : int -> t - (** [create n] @return a distributed vector with [n] rows (not initialized). *) - - val make : int -> float -> t - (** [make n x] @return a distributed vector with [n] rows initialized with value [x]. *) - - val make0 : int -> t - (** [make0 n x] @return a distributed vector with [n] rows initialized with the zero - element. *) - - val init : int -> (int -> float) -> t - (** [init n f] @return a distributed vector containing [n] elements, where - each element at position [i] is initialized by the result of calling [f i]. *) - - val of_array : float array -> t - (** [of_array ar] @return a distributed vector initialized from array [ar]. *) - - val to_array : t -> float array - (** [to_array v] @return an array initialized from vector [v]. *) - - val of_vec : Lacaml.D.vec -> t - (** [of_vec vec] @return a distributed vector initialized from Lacaml vector [vec]. *) - - val to_vec : t -> Lacaml.D.vec - (** [to_vec v] @return a Lacaml vector initialized from vector [v]. *) - - - (** {6 Accessors } *) - - val dim : t -> int - (** [dim v] @return the dimension of the vector [v]. *) - - val global_first : t -> int - (** [global_first v] @return the index of the first element of [v]. *) - - val global_last : t -> int - (** [global_last v] @return the index of the last element of [v]. *) - - val local_first : t -> int - (** [local_first v] @return the index of the first element of the local piece of [v]. *) - - val global_last : t -> int - (** [local_last v] @return the index of the last element of the local piece of [v]. *) - - val data : t -> Lacaml.D.vec - (** [data v] @return the local Lacaml vector in which the piece of the vector [v] is stored. *) - -end - - -(* -module Mat : sig - - type t = - { - global_first_row : int ; (* Lower row index in the global array *) - global_last_row : int ; (* Higher row index in the global array *) - global_first_col : int ; (* Lower column index in the global array *) - global_last_col : int ; (* Higher column index in the global array *) - local_first_row : int ; (* Lower row index in the local array *) - local_last_row : int ; (* Higher row index in the local array *) - local_first_col : int ; (* Lower column index in the local array *) - local_last_col : int ; (* Higher column index in the local array *) - data : Lacaml.D.mat ; (* Lacaml matrix containing the data *) - } - -end - -val gemm : Mat.t -> Mat.t -> Mat.t -(* Distributed matrix-matrix product. The result is a distributed matrix. *) -*) - -val dot : Vec.t -> Vec.t-> float -(* Dot product between distributed vectors. *) - - - diff --git a/Parallel_mpi/SharedMemory.ml b/Parallel_mpi/SharedMemory.ml deleted file mode 100644 index 3b4878a..0000000 --- a/Parallel_mpi/SharedMemory.ml +++ /dev/null @@ -1,24 +0,0 @@ -let create ?(temp_dir="/dev/shm") data_type size_array = - let filename = - Parallel.Node.broadcast (lazy (Filename.temp_file ~temp_dir "4idx." ".tmp")) - in - - if Parallel.Node.master then - begin - let fd = Unix.openfile filename Unix.[O_RDWR ; O_CREAT] 0o777 in - let result = - Unix.map_file fd data_type Bigarray.fortran_layout true size_array - in - Bigarray.Genarray.fill result 0.; - Parallel.Node.barrier (); - at_exit (fun () -> Unix.close fd ; try Sys.remove filename with _ -> ()); - result - end - else - begin - Parallel.Node.barrier (); - let fd = Unix.openfile filename [Unix.O_RDONLY] 0o777 in - at_exit (fun () -> Unix.close fd ; try Sys.remove filename with _ -> ()); - Unix.map_file fd data_type Bigarray.fortran_layout false size_array - end - diff --git a/Parallel_serial/Farm.ml b/Parallel_serial/Farm.ml deleted file mode 100644 index ff3e777..0000000 --- a/Parallel_serial/Farm.ml +++ /dev/null @@ -1,13 +0,0 @@ -(* Single process function *) -let run_sequential f stream = - - let next _ = - try - let task = Stream.next stream in - Some (f task) - with Stream.Failure -> None in - Stream.from next - -let run ?(ordered=true) ?(comm) ~f stream = - run_sequential f stream - diff --git a/Parallel_serial/Farm.mli b/Parallel_serial/Farm.mli deleted file mode 100644 index 52523f6..0000000 --- a/Parallel_serial/Farm.mli +++ /dev/null @@ -1,16 +0,0 @@ -(** The Farm skeleton, similar to SklMl. - -The input is a stream of input data, and the output is a stream of data. -*) - - -val run : ?ordered:bool -> ?comm:'c -> - f:('a -> 'b) -> 'a Stream.t -> 'b Stream.t -(** Run the [f] function on every process by popping elements from the - input stream, and putting the results on the output stream. If [ordered] - (the default is [ordered = true], then the order of the output is kept - consistent with the order of the input. - In the non-parallel mode, the [comm] argument is unused. -*) - - diff --git a/Parallel_serial/Parallel.ml b/Parallel_serial/Parallel.ml deleted file mode 100644 index d8e9910..0000000 --- a/Parallel_serial/Parallel.ml +++ /dev/null @@ -1,155 +0,0 @@ -(** Module for handling distributed parallelism *) - -let size = 1 - -let rank = 0 - -let master = true - - -let barrier () = () - -let broadcast x = Lazy.force x - -let broadcast_int x = x - -let broadcast_int_array x = x - -let broadcast_float x = x - -let broadcast_float_array x = x - -let broadcast_vec x = x - -module Node = struct - - let name = Unix.gethostname () - - let comm = None - - let rank = 0 - - let master = true - - let broadcast x = Lazy.force x - - let barrier () = () - -end - -module InterNode = struct - - let comm = None - - let rank = 0 - - let master = true - - let broadcast x = Lazy.force x - - let barrier () = () - -end - - -module Vec = struct - - type t = - { - global_first : int ; (* Lower index in the global array *) - global_last : int ; (* Higher index in the global array *) - local_first : int ; (* Lower index in the local array *) - local_last : int ; (* Higher index in the local array *) - data : Lacaml.D.vec ; (* Lacaml vector containing the data *) - } - - let dim vec = - vec.global_last - vec.global_first + 1 - - let local_first vec = vec.local_first - let local_last vec = vec.local_last - let global_first vec = vec.global_first - let global_last vec = vec.global_last - let data vec = vec.data - - let pp ppf v = - Format.fprintf ppf "@[<2>"; - Format.fprintf ppf "@[ gf : %d@]@;" v.global_first; - Format.fprintf ppf "@[ gl : %d@]@;" v.global_last; - Format.fprintf ppf "@[ lf : %d@]@;" v.local_first; - Format.fprintf ppf "@[ ll : %d@]@;" v.local_last; - Format.fprintf ppf "@[ data : %a@]@;" (Lacaml.Io.pp_lfvec ()) v.data; - Format.fprintf ppf "@]@."; - () - - let create n = - { - global_first = 1 ; - global_last = n ; - local_first = 1 ; - local_last = n ; - data = Lacaml.D.Vec.create n - } - - - let make n x = - let result = create n in - { result with data = - Lacaml.D.Vec.make - (Lacaml.D.Vec.dim result.data) - x - } - - - let make0 n = - make n 0. - - - let init n f = - let result = create n in - { result with data = - Lacaml.D.Vec.init - (Lacaml.D.Vec.dim result.data) - (fun i -> f (i+result.local_first-1)) - } - - - let of_array a = - let length_a = Array.length a in - let a = - let n = length_a mod size in - if n > 0 then - Array.concat [ a ; Array.make (size-n) 0. ] - else - a - in - let result = create length_a in - let a_local = Array.make (Array.length a) 0. in - { result with data = Lacaml.D.Vec.of_array a_local } - - - let to_array vec = - Lacaml.D.Vec.to_array vec.data - |> Array.copy - - - let of_vec a = - Lacaml.D.Vec.to_array a - |> of_array - - - let to_vec v = - to_array v - |> Lacaml.D.Vec.of_array - - -end - - - -let dot v1 v2 = - if Vec.dim v1 <> Vec.dim v2 then - invalid_arg "Incompatible dimensions"; - Lacaml.D.dot (Vec.data v1) (Vec.data v2) - - diff --git a/Parallel_serial/Parallel.mli b/Parallel_serial/Parallel.mli deleted file mode 100644 index 77a6c8d..0000000 --- a/Parallel_serial/Parallel.mli +++ /dev/null @@ -1,167 +0,0 @@ -(** Module for handling distributed parallelism *) - -val size : int -(** Number of distributed processes. *) - -val rank : int -(** Rank of the current distributed processe. *) - -val master : bool -(** True if [rank = 0]. *) - -val barrier : unit -> unit -(** Wait for all processes to reach this point. *) - -val broadcast : 'a lazy_t -> 'a -(** Broadcasts data to all processes. *) - -val broadcast_int : int -> int -(** Broadcasts an [int] to all processes. *) - -val broadcast_float : float -> float -(** Broadcasts a [float] to all processes. *) - -val broadcast_int_array : int array -> int array -(** Broadcasts an [int array] to all processes. *) - -val broadcast_float_array : float array -> float array -(** Broadcasts a [float array] to all processes. *) - -val broadcast_vec : Lacaml.D.vec -> Lacaml.D.vec -(** Broadcasts a Lacaml vector to all processes. *) - - -(** {5 Intra-node operations} *) -module Node : sig - val name : string - (** Name of the current host *) - - val comm : 'a option - (** Always [None] *) - - val rank : int - (** Always zero *) - - val master : bool - (** Always true *) - - val broadcast : 'a lazy_t -> 'a - (** Same as Lazy.force *) - - val barrier : unit -> unit - (** Does nothing. *) -end - - -(** {5 Inter-node operations} *) -module InterNode : sig - - val comm : 'a option - (** Always [None] *) - - val rank : int - (** Always zero *) - - val master : bool - (** Always true *) - - val broadcast : 'a lazy_t -> 'a - (** Same as Lazy.force *) - - val barrier : unit -> unit - (** Does nothing. *) -end - -(** {5 Vector operations} *) -module Vec : sig - - type t = private - { - global_first : int ; (* Lower index in the global array *) - global_last : int ; (* Higher index in the global array *) - local_first : int ; (* Lower index in the local array *) - local_last : int ; (* Higher index in the local array *) - data : Lacaml.D.vec ; (* Lacaml vector containing the data *) - } - - val pp : Format.formatter -> t -> unit - - (** {6 Creation/conversion of vectors} *) - - val create : int -> t - (** [create n] @return a distributed vector with [n] rows (not initialized). *) - - val make : int -> float -> t - (** [make n x] @return a distributed vector with [n] rows initialized with value [x]. *) - - val make0 : int -> t - (** [make0 n x] @return a distributed vector with [n] rows initialized with the zero - element. *) - - val init : int -> (int -> float) -> t - (** [init n f] @return a distributed vector containing [n] elements, where - each element at position [i] is initialized by the result of calling [f i]. *) - - val of_array : float array -> t - (** [of_array ar] @return a distributed vector initialized from array [ar]. *) - - val to_array : t -> float array - (** [to_array v] @return an array initialized from vector [v]. *) - - val of_vec : Lacaml.D.vec -> t - (** [of_vec vec] @return a distributed vector initialized from Lacaml vector [vec]. *) - - val to_vec : t -> Lacaml.D.vec - (** [to_vec v] @return a Lacaml vector initialized from vector [v]. *) - - - (** {6 Accessors } *) - - val dim : t -> int - (** [dim v] @return the dimension of the vector [v]. *) - - val global_first : t -> int - (** [global_first v] @return the index of the first element of [v]. *) - - val global_last : t -> int - (** [global_last v] @return the index of the last element of [v]. *) - - val local_first : t -> int - (** [local_first v] @return the index of the first element of the local piece of [v]. *) - - val global_last : t -> int - (** [local_last v] @return the index of the last element of the local piece of [v]. *) - - val data : t -> Lacaml.D.vec - (** [data v] @return the local Lacaml vector in which the piece of the vector [v] is stored. *) - -end - - -(* -module Mat : sig - - type t = - { - global_first_row : int ; (* Lower row index in the global array *) - global_last_row : int ; (* Higher row index in the global array *) - global_first_col : int ; (* Lower column index in the global array *) - global_last_col : int ; (* Higher column index in the global array *) - local_first_row : int ; (* Lower row index in the local array *) - local_last_row : int ; (* Higher row index in the local array *) - local_first_col : int ; (* Lower column index in the local array *) - local_last_col : int ; (* Higher column index in the local array *) - data : Lacaml.D.mat ; (* Lacaml matrix containing the data *) - } - -end - -val gemm : Mat.t -> Mat.t -> Mat.t -(* Distributed matrix-matrix product. The result is a distributed matrix. *) -*) - -val dot : Vec.t -> Vec.t-> float -(* Dot product between distributed vectors. *) - - - diff --git a/Parallel_serial/SharedMemory.ml b/Parallel_serial/SharedMemory.ml deleted file mode 100644 index 134d6b5..0000000 --- a/Parallel_serial/SharedMemory.ml +++ /dev/null @@ -1,7 +0,0 @@ -let create ?(temp_dir="/dev/shm") data_type size_array = - let result = - Bigarray.Genarray.create data_type Bigarray.fortran_layout size_array - in - Bigarray.Genarray.fill result 0.; - result - diff --git a/Perturbation/.merlin b/Perturbation/.merlin deleted file mode 100644 index 2ba6169..0000000 --- a/Perturbation/.merlin +++ /dev/null @@ -1 +0,0 @@ -REC diff --git a/Perturbation/MP2.ml b/Perturbation/MP2.ml deleted file mode 100644 index 037cc94..0000000 --- a/Perturbation/MP2.ml +++ /dev/null @@ -1,60 +0,0 @@ -type t = float - -let make ~frozen_core hf = - let mo_basis = - MOBasis.of_hartree_fock hf - in - let epsilon = - MOBasis.mo_energies mo_basis - in - let mo_class = - MOClass.cas_sd mo_basis ~frozen_core 0 0 - |> MOClass.to_list - in - let eri = - MOBasis.ee_ints mo_basis - in - let inactives = - List.filter (fun i -> - match i with MOClass.Inactive _ -> true | _ -> false) mo_class - and virtuals = - List.filter (fun i -> - match i with MOClass.Virtual _ -> true | _ -> false) mo_class - in - - let rmp2 () = - List.fold_left (fun accu b -> - match b with MOClass.Virtual b -> - let eps = -. epsilon.{b} in - accu +. - List.fold_left (fun accu a -> - match a with MOClass.Virtual a -> - let eps = eps -. epsilon.{a} in - accu +. - List.fold_left (fun accu j -> - match j with MOClass.Inactive j -> - let eps = eps +. epsilon.{j} in - accu +. - List.fold_left (fun accu i -> - match i with MOClass.Inactive i -> - let eps = eps +. epsilon.{i} in - let ijab = ERI.get_phys eri i j a b - and abji = ERI.get_phys eri a b j i in - let abij = ijab in - accu +. ijab *. ( abij +. abij -. abji) /. eps - | _ -> accu - ) 0. inactives - | _ -> accu - ) 0. inactives - | _ -> accu - ) 0. virtuals - | _ -> accu - ) 0. virtuals - in - - - match HartreeFock.kind hf with - | HartreeFock.RHF -> rmp2 () - | _ -> failwith "Not implemented" - - diff --git a/README.md b/README.md index 8b4cadb..32a335f 100644 --- a/README.md +++ b/README.md @@ -3,15 +3,92 @@ QCaml (Quantum Camel) +QCaml is a quantum chemistry software written in OCaml. + Requirements ------------ -* MPI : Message Passing Interface * BLAS/LAPACK : Linear algebra * LaCaml : LAPACK OCaml interface * Zarith : Arbitrary-precision integers +* GetOpt : Parsing of command-line * gmp : GNU Multiple Precision arithmetic library * odoc-ltxhtml : https://github.com/akabe/odoc-ltxhtml * Alcotest : Lightweight testing framework +```bash +opam install dune lacaml getopt alcotest zarith +``` +To use the Intel MKL library: + +```bash +export LACAML_LIBS="-L${MKLROOT}/lib/intel64 -Wl,--no-as-needed -lmkl_rt -lpthread -lm -ldl" +opam install lacaml + + +odoc-ltxhtml allows to embed equations in the documentation generated by Ocamldoc. +Download the source code [here](https://github.com/scemama/odoc-ltxhtml). + +```bash +git clone https://github.com/scemama/odoc-ltxhtml +cd odoc-ltxhtml +make install +``` + +How to build the project +------------------------ + +Run `make` to compile the libraries and executables that are +meant to be installed. +``` +$ make +``` + +How to run tests +---------------- + +``` +$ make test +``` + +How to use local libraries interactively +---------------------------------------- + +Use `dune utop DIR` where DIR if the folder contains the `dune` +file for a library. For instance, our `sub2` sample library can be +used as follows: + +``` +$ dune utop sub2/lib +... +utop # Proj_sub2.A.do_something ();; +1525373137.245 seconds have elapsed since 1970-01-01T00:00:00. +- : unit = () +``` + +Installation +------------ + +The project can be installed with or without opam. +Without opam, you can run the following which relies directly on +dune: +``` +$ make install +``` +Similarly: +``` +$ make uninstall +``` + +With opam, you can install the current development version of your +project as a single opam package. It will override the currently +installed package of the same name, if any: +``` +$ opam pin add proj . +``` +For more information on `opam pin`, please consult the opam documentation. + +The advantage of the opam-based method is that other opam packages can +depend on this one, and opam will recompile them automatically as +necessary. diff --git a/SCF/Fock.ml b/SCF/Fock.ml deleted file mode 100644 index 2508f43..0000000 --- a/SCF/Fock.ml +++ /dev/null @@ -1,244 +0,0 @@ -open Lacaml.D -open Simulation -open Constants -open Util - - -type t = - { - fock : Mat.t ; - core : Mat.t ; - coulomb : Mat.t ; - exchange : Mat.t ; - } - - -let fock t = t.fock -let core t = t.core -let coulomb t = t.coulomb -let exchange t = t.exchange - - -module Ao = AOBasis - -let make_rhf ~density ?(threshold=Constants.epsilon) ao_basis = - let m_P = density - and m_T = Ao.kin_ints ao_basis |> KinInt.matrix - and m_V = Ao.eN_ints ao_basis |> NucInt.matrix - and m_G = Ao.ee_ints ao_basis - in - let nBas = Mat.dim1 m_T - in - - let m_Hc = Mat.add m_T m_V - and m_J = Array.make_matrix nBas nBas 0. - and m_K = Array.make_matrix nBas nBas 0. - in - - for sigma = 1 to nBas do - let m_Ksigma = m_K.(sigma-1) in - for nu = 1 to nBas do - let m_Jnu = m_J.(nu-1) in - for lambda = 1 to nBas do - let pJ = m_P.{lambda,sigma} - and pK = 0.5 *. m_P.{lambda,nu} - in - match (abs_float pJ > threshold , abs_float pK > threshold, nu < sigma) with - | (false, false, _) -> () - | (true , true , true) -> - begin - for mu = 1 to nu do - let integral = - ERI.get_phys m_G mu lambda nu sigma - in - if (integral <> 0.) then begin - m_Jnu.(mu-1) <- m_Jnu.(mu-1) +. pJ *. integral; - m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *. integral - end - done; - for mu = nu+1 to sigma do - m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *. - ERI.get_phys m_G mu lambda nu sigma - done - end - | (true , true , false) -> - begin - for mu = 1 to sigma do - let integral = - ERI.get_phys m_G mu lambda nu sigma - in - if (integral <> 0.) then begin - m_Jnu.(mu-1) <- m_Jnu.(mu-1) +. pJ *. integral; - m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *. integral - end - done; - for mu = sigma+1 to nu do - m_Jnu.(mu-1) <- - m_Jnu.(mu-1) +. pJ *. ERI.get_phys m_G mu lambda nu sigma - done - end - | (false, true , _) -> - for mu = 1 to sigma do - m_Ksigma.(mu-1) <- - m_Ksigma.(mu-1) +. pK *. ERI.get_phys m_G mu lambda nu sigma - done - | (true , false, _) -> - for mu = 1 to nu do - m_Jnu.(mu-1) <- - m_Jnu.(mu-1) +. pJ *. ERI.get_phys m_G mu lambda nu sigma - done - done - done; - for mu = 1 to sigma-1 do - m_K.(mu-1).(sigma-1) <- m_Ksigma.(mu-1); - done - done; - for nu = 1 to nBas do - let m_Jnu = m_J.(nu-1) in - for mu = 1 to nu-1 do - m_J.(mu-1).(nu-1) <- m_Jnu.(mu-1) - done - done; - - let m_J = Mat.of_array m_J - and m_K = Mat.of_array m_K - in - { fock = Mat.add m_Hc (Mat.sub m_J m_K) ; - core = m_Hc ; coulomb = m_J ; exchange = m_K } - - - -let make_uhf ~density_same ~density_other ?(threshold=Constants.epsilon) ao_basis = - let m_P_a = density_same - and m_P_b = density_other - and m_T = Ao.kin_ints ao_basis |> KinInt.matrix - and m_V = Ao.eN_ints ao_basis |> NucInt.matrix - and m_G = Ao.ee_ints ao_basis - in - let nBas = Mat.dim1 m_T - in - - let m_Hc = Mat.add m_T m_V - and m_J = Array.make_matrix nBas nBas 0. - and m_K = Array.make_matrix nBas nBas 0. - in - - for sigma = 1 to nBas do - let m_Ksigma = m_K.(sigma-1) in - for nu = 1 to nBas do - let m_Jnu = m_J.(nu-1) in - for lambda = 1 to nBas do - let pJ = m_P_a.{lambda,sigma} +. m_P_b.{lambda,sigma} - and pK = m_P_a.{lambda,nu} - in - match (abs_float pJ > threshold , abs_float pK > threshold, nu < sigma) with - | (false, false, _) -> () - | (true , true , true) -> - begin - for mu = 1 to nu do - let integral = - ERI.get_phys m_G mu lambda nu sigma - in - if (integral <> 0.) then begin - m_Jnu.(mu-1) <- m_Jnu.(mu-1) +. pJ *. integral; - m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *. integral - end - done; - for mu = nu+1 to sigma do - m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *. - ERI.get_phys m_G mu lambda nu sigma - done - end - | (true , true , false) -> - begin - for mu = 1 to sigma do - let integral = - ERI.get_phys m_G mu lambda nu sigma - in - if (integral <> 0.) then begin - m_Jnu.(mu-1) <- m_Jnu.(mu-1) +. pJ *. integral; - m_Ksigma.(mu-1) <- m_Ksigma.(mu-1) +. pK *. integral - end - done; - for mu = sigma+1 to nu do - m_Jnu.(mu-1) <- - m_Jnu.(mu-1) +. pJ *. ERI.get_phys m_G mu lambda nu sigma - done - end - | (false, true , _) -> - for mu = 1 to sigma do - m_Ksigma.(mu-1) <- - m_Ksigma.(mu-1) +. pK *. ERI.get_phys m_G mu lambda nu sigma - done - | (true , false, _) -> - for mu = 1 to nu do - m_Jnu.(mu-1) <- - m_Jnu.(mu-1) +. pJ *. ERI.get_phys m_G mu lambda nu sigma - done - done - done; - for mu = 1 to sigma-1 do - m_K.(mu-1).(sigma-1) <- m_Ksigma.(mu-1); - done - done; - for nu = 1 to nBas do - let m_Jnu = m_J.(nu-1) in - for mu = 1 to nu-1 do - m_J.(mu-1).(nu-1) <- m_Jnu.(mu-1) - done - done; - - let m_J = Mat.of_array m_J - and m_K = Mat.of_array m_K - in - { fock = Mat.add m_Hc (Mat.sub m_J m_K) ; - core = m_Hc ; coulomb = m_J ; exchange = m_K } - - - - - - - -let op ~f f1 f2 = - assert (f1.core = f2.core); - let m_Hc = f1.core - and m_J = f f1.coulomb f2.coulomb - and m_K = f f1.exchange f2.exchange - in - { - fock = Mat.add m_Hc (Mat.sub m_J m_K); - core = m_Hc; - coulomb = m_J; - exchange = m_K; - } - - -let add = op ~f:(fun a b -> Mat.add a b) - -let sub = op ~f:(fun a b -> Mat.sub a b) - -let scale alpha f1 = - let m_Hc = f1.core - and m_J = lacpy f1.coulomb - and m_K = lacpy f1.exchange - in - Mat.scal alpha m_J; - Mat.scal alpha m_K; - { - fock = Mat.add m_Hc (Mat.sub m_J m_K); - core = m_Hc; - coulomb = m_J; - exchange = m_K; - } - - - -let pp ppf a = - Format.fprintf ppf "@[<2>"; - Format.fprintf ppf "@[ Fock matrix:@[<2>@[%a@]@.]@]" pp_matrix a.fock; - Format.fprintf ppf "@[ Core Hamiltonian:@[<2>@[%a@]@.]@]" pp_matrix a.core; - Format.fprintf ppf "@[ Coulomb matrix:@[<2>@[%a@]@.]@]" pp_matrix a.coulomb; - Format.fprintf ppf "@[ Exchange matrix:@[<2>@[%a@]@.]@]" pp_matrix a.exchange; - Format.fprintf ppf "@]" - diff --git a/SCF/Fock.mli b/SCF/Fock.mli deleted file mode 100644 index cf87500..0000000 --- a/SCF/Fock.mli +++ /dev/null @@ -1,50 +0,0 @@ -(** Type for the Fock operator in AO basis. *) - -open Lacaml.D - - -type t - -(** {1 Accessors} *) - -val fock : t -> Mat.t -(** Fock matrix in AO basis *) - -val core : t -> Mat.t -(** Core Hamiltonian : {% $\langle i | \hat{h} | j \rangle$ %} *) - -val coulomb : t -> Mat.t -(** Coulomb matrix : {% $\langle i | J | j \rangle$ %} *) - -val exchange : t -> Mat.t -(** Exchange matrix : {% $\langle i | K | j \rangle$ %} *) - - -(** {1 Creators} *) - -val make_rhf : density:Mat.t -> ?threshold:float -> AOBasis.t -> t -(** Create a Fock operator in the RHF formalism. Expected density is - {% $2 \mathbf{C\, C}^\dagger$ %}. [threshold] is a threshold on the - integrals. *) - -val make_uhf : density_same: Mat.t -> density_other:Mat.t -> ?threshold:float -> - AOBasis.t -> t -(** Create a Fock operator in the UHF formalism. Expected density is - {% $\mathbf{C\, C}^\dagger$ %}. When building the {% $\alpha$ %} Fock - operator, [density_same] is the {% $\alpha$ %} density and [density_other] - is the {% $\beta$ %} density. [threshold] is a threshold on the integrals. *) - - -(** {1 Operations} *) - -val add : t -> t -> t -(** Add two Fock operators sharing the same core Hamiltonian. *) - -val sub : t -> t -> t -(** Subtract two Fock operators sharing the same core Hamiltonian. *) - - -(** {1 Printers} *) - -val pp : Format.formatter -> t -> unit - diff --git a/SCF/Guess.ml b/SCF/Guess.ml deleted file mode 100644 index 5e96d6c..0000000 --- a/SCF/Guess.ml +++ /dev/null @@ -1,82 +0,0 @@ -open Lacaml.D -open Util - -type guess = -| Hcore of Mat.t -| Huckel of Mat.t -| Matrix of Mat.t - -type t = guess - -module Ao = AOBasis -module El = Electrons -module Ov = Overlap - -let hcore_guess ao_basis = - let eN_ints = Ao.eN_ints ao_basis |> NucInt.matrix - and kin_ints = Ao.kin_ints ao_basis |> KinInt.matrix - in - Mat.add eN_ints kin_ints - - -let huckel_guess ao_basis = - let c = 0.5 *. 1.75 in - let eN_ints = Ao.eN_ints ao_basis |> NucInt.matrix - and kin_ints = Ao.kin_ints ao_basis |> KinInt.matrix - in - let m_F = - Mat.add eN_ints kin_ints - in - let ao_num = Ao.basis ao_basis |> Basis.size - and overlap = Ao.overlap ao_basis |> Ov.matrix - in - let diag = Vec.init ao_num (fun i -> - m_F.{i,i} ) - in - - function - | 0 -> invalid_arg "Huckel guess needs a non-zero number of occupied MOs." - | nocc -> - Mat.init_cols ao_num ao_num (fun i j -> - if (i<>j) then - if (diag.{i} +. diag.{j}) < 0. then - c *. overlap.{i,j} *. (diag.{i} +. diag.{j}) +. m_F.{i,j} (*TODO Pseudo *) - else - m_F.{i,j} (*TODO Pseudo *) - else - diag.{i} - ) - - -let make ?(nocc=0) ~guess ao_basis = - match guess with - | `Hcore -> Hcore (hcore_guess ao_basis) - | `Huckel -> Huckel (huckel_guess ao_basis nocc) - | `Matrix m -> Matrix m - - - -let test_case ao_basis = - - let test_hcore () = - match make ~guess:`Hcore ao_basis with - | Hcore matrix -> - let a = Lacaml.D.Mat.to_array matrix in - let reference = - Lacaml.D.Mat.add - (AOBasis.eN_ints ao_basis |> NucInt.matrix) - (AOBasis.kin_ints ao_basis |> KinInt.matrix) - |> Lacaml.D.Mat.to_array - in - Array.iteri (fun i x -> - let message = - Printf.sprintf "Guess line %d" (i) - in - Alcotest.(check (array (float 1.e-15))) message a.(i) x) reference - | _ -> assert false - - in - [ - "HCore", `Quick, test_hcore; - ] - diff --git a/SCF/Guess.mli b/SCF/Guess.mli deleted file mode 100644 index 3961adc..0000000 --- a/SCF/Guess.mli +++ /dev/null @@ -1,18 +0,0 @@ -open Lacaml.D - -(** Guess for Hartree-Fock calculations. *) - -type guess = -| Hcore of Mat.t (* Core Hamiltonian Matrix *) -| Huckel of Mat.t (* Huckel Hamiltonian Matrix *) -| Matrix of Mat.t (* Guess Eigenvectors *) - -type t = guess - - -val make : ?nocc:int -> guess:[ `Hcore | `Huckel | `Matrix of Mat.t ] -> AOBasis.t -> t - - -(** {2 Tests} *) - -val test_case : AOBasis.t -> unit Alcotest.test_case list diff --git a/SCF/HartreeFock.ml b/SCF/HartreeFock.ml deleted file mode 100644 index 907eb9a..0000000 --- a/SCF/HartreeFock.ml +++ /dev/null @@ -1,725 +0,0 @@ -open Lacaml.D -open Util -open Constants - - -type hartree_fock_data = - { - iteration : int ; - coefficients : Mat.t option ; - eigenvalues : Vec.t option ; - error : float option ; - diis : DIIS.t option ; - energy : float option ; - density : Mat.t option ; - density_a : Mat.t option ; - density_b : Mat.t option ; - fock : Fock.t option ; - fock_a : Fock.t option ; - fock_b : Fock.t option ; - } - -type hartree_fock_kind = -| RHF (** Restricted Hartree-Fock *) -| ROHF (** Restricted Open-shell Hartree-Fock *) -| UHF (** Unrestricted Hartree-Fock *) - -type t = - { - kind : hartree_fock_kind; - simulation : Simulation.t; - guess : Guess.t; - data : hartree_fock_data option lazy_t array; - nocc : int ; - } - - -let empty = - { - iteration = 0 ; - coefficients = None ; - eigenvalues = None ; - error = None ; - diis = None ; - energy = None ; - density = None ; - density_a = None ; - density_b = None ; - fock = None ; - fock_a = None ; - fock_b = None ; - } - - - - - - -module Si = Simulation -module El = Electrons -module Ao = AOBasis -module Ov = Overlap - - -let kind t = t.kind -let simulation t = t.simulation -let guess t = t.guess -let nocc t = t.nocc - - - -let n_iterations t = - Array.fold_left (fun accu x -> - match Lazy.force x with - | Some x -> accu + 1 - | None -> accu - ) 0 t.data - - -let last_iteration t = - of_some @@ Lazy.force (t.data.(n_iterations t - 1)) - -let eigenvectors t = - let data = last_iteration t in - of_some data.coefficients - -let eigenvalues t = - let data = last_iteration t in - of_some data.eigenvalues - -let density t = - let data = last_iteration t in - match kind t with - | RHF -> of_some data.density - | ROHF -> Mat.add (of_some data.density_a) (of_some data.density_b) - | _ -> failwith "Not implemented" - -let occupation t = - let n_alfa, n_beta = - El.n_alfa @@ Simulation.electrons @@ simulation t, - El.n_beta @@ Simulation.electrons @@ simulation t - in - match kind t with - | RHF -> Vec.init (Mat.dim2 @@ eigenvectors t) (fun i -> - if i <= nocc t then 2.0 else 0.0) - | ROHF -> Vec.init (Mat.dim2 @@ eigenvectors t) (fun i -> - if i <= n_beta then 2.0 else - if i <= n_alfa then 1.0 else - 0.0) - | _ -> failwith "Not implemented" - - -let energy t = - let data = last_iteration t in - of_some data.energy - - -let nuclear_repulsion t = - Si.nuclear_repulsion (simulation t) - - -let ao_basis t = - Si.ao_basis (simulation t) - - -let kin_energy t = - let m_T = - ao_basis t - |> Ao.kin_ints - |> KinInt.matrix - in - let m_P = density t in - Mat.gemm_trace m_P m_T - - -let eN_energy t = - let m_V = - ao_basis t - |> Ao.eN_ints - |> NucInt.matrix - in - let m_P = density t in - Mat.gemm_trace m_P m_V - - -let coulomb_energy t = - let data = - last_iteration t - in - match kind t with - | RHF -> let m_P = of_some data.density in - let fock = of_some data.fock in - let m_J = Fock.coulomb fock in - 0.5 *. Mat.gemm_trace m_P m_J - - | ROHF -> let m_P_a = of_some data.density_a in - let m_P_b = of_some data.density_b in - let fock_a = of_some data.fock_a in - let fock_b = of_some data.fock_b in - let m_J_a = Fock.coulomb fock_a in - let m_J_b = Fock.coulomb fock_b in - 0.5 *. ( (Mat.gemm_trace m_P_a m_J_a) +. (Mat.gemm_trace m_P_b m_J_b) ) - - | _ -> failwith "Not implemented" - - -let exchange_energy t = - let data = - last_iteration t - in - match kind t with - | RHF -> let m_P = of_some data.density in - let fock = of_some data.fock in - let m_K = Fock.exchange fock in - -. 0.5 *. Mat.gemm_trace m_P m_K - - | ROHF -> let m_P_a = of_some data.density_a in - let m_P_b = of_some data.density_b in - let fock_a = of_some data.fock_a in - let fock_b = of_some data.fock_b in - let m_K_a = Fock.exchange fock_a in - let m_K_b = Fock.exchange fock_b in - -. 0.5 *. ( (Mat.gemm_trace m_P_a m_K_a) +. (Mat.gemm_trace m_P_b m_K_b) ) - - | _ -> failwith "Not implemented" - - - - - - -let make - ?kind - ?guess:(guess=`Huckel) - ?max_scf:(max_scf=64) - ?level_shift:(level_shift=0.2) - ?threshold_SCF:(threshold_SCF=1.e-8) - simulation = - - - (* Number of occupied MOs *) - let n_alfa, n_beta = - El.n_alfa @@ Si.electrons simulation, - El.n_beta @@ Si.electrons simulation - in - - let nocc = n_alfa in - - let kind = - match kind with - | Some kind -> kind - | None -> if (n_alfa = n_beta) then RHF else ROHF - in - - let nuclear_repulsion = - Si.nuclear_repulsion simulation - in - - let ao_basis = - Si.ao_basis simulation - in - - - (* Orthogonalization matrix *) - let m_X = - Ao.ortho ao_basis - in - - (* Overlap matrix *) - let m_S = - Ao.overlap ao_basis - |> Ov.matrix - in - - (* Level shift in MO basis *) - let m_LSmo = - Array.init (Mat.dim2 m_X) (fun i -> - if i > nocc then level_shift else 0.) - |> Vec.of_array - |> Mat.of_diag - in - - (* Guess coefficients *) - let guess = - Guess.make ~nocc ~guess ao_basis - in - - let m_C = - let c_of_h m_H = - let m_Hmo = xt_o_x m_H m_X in - let m_C', _ = diagonalize_symm m_Hmo in - gemm m_X m_C' - in - match guess with - | Guess.Hcore m_H -> c_of_h m_H - | Guess.Huckel m_H -> c_of_h m_H - | Guess.Matrix m_C -> m_C - in - - (* A single SCF iteration *) - let scf_iteration_rhf data = - - let nSCF = data.iteration + 1 - and m_C = of_some data.coefficients - and m_P_prev = data.density - and fock_prev = data.fock - and diis = - match data.diis with - | Some diis -> diis - | None -> DIIS.make () - and threshold = - match data.error with - | Some error -> error - | None -> threshold_SCF *. 2. - in - - (* Density matrix over nocc occupied MOs *) - let m_P = - gemm ~alpha:2. ~transb:`T ~k:nocc m_C m_C - in - - (* Fock matrix in AO basis *) - let fock = - match fock_prev, m_P_prev, threshold > 100. *. threshold_SCF with - | Some fock_prev, Some m_P_prev, true -> - let threshold = 1.e-8 in - Fock.make_rhf ~density:(Mat.sub m_P m_P_prev) ~threshold ao_basis - |> Fock.add fock_prev - | _ -> Fock.make_rhf ~density:m_P ao_basis - in - - let m_F0, m_Hc, m_J, m_K = - let x = fock in - Fock.(fock x, core x, coulomb x, exchange x) - in - - (* Add level shift in AO basis *) - let m_F = - let m_SC = - gemm m_S m_C - in - gemm m_SC (gemm m_LSmo m_SC ~transb:`T) - |> Mat.add m_F0 - in - - - (* Fock matrix in orthogonal basis *) - let m_F_ortho = - xt_o_x m_F m_X - in - - let error_fock = - let fps = - gemm m_F (gemm m_P m_S) - and spf = - gemm m_S (gemm m_P m_F) - in - xt_o_x (Mat.sub fps spf) m_X - in - - let diis, m_F_diis = - let diis = - DIIS.append ~p:(Mat.as_vec m_F_ortho) ~e:(Mat.as_vec error_fock) diis - in - - try - let m_F_diis = - let x = - Bigarray.genarray_of_array1 (DIIS.next diis) - in - Bigarray.reshape_2 x (Mat.dim1 m_F_ortho) (Mat.dim2 m_F_ortho) - in - diis, m_F_diis - - with Failure _ -> (* Failure in DIIS.next *) - DIIS.make (), m_F_ortho - in - let diis = - DIIS.append ~p:(Mat.as_vec m_F_ortho) ~e:(Mat.as_vec error_fock) diis - in - - - (* MOs in orthogonal MO basis *) - let m_C', _ = - diagonalize_symm m_F_diis - in - - (* Re-compute eigenvalues to remove level-shift *) - let eigenvalues = - let m_F_ortho = - xt_o_x m_F0 m_X - in - xt_o_x m_F_ortho m_C' - |> Mat.copy_diag - in - - (* MOs in AO basis *) - let m_C = - gemm m_X m_C' - |> Conventions.rephase - in - - (* Hartree-Fock energy *) - let energy = - nuclear_repulsion +. 0.5 *. - Mat.gemm_trace m_P (Mat.add m_Hc m_F) - in - - (* Convergence criterion *) - let error = - error_fock - |> Mat.as_vec - |> amax - |> abs_float - in - - { empty with - iteration = nSCF ; - eigenvalues = Some eigenvalues ; - coefficients = Some m_C ; - error = Some error ; - diis = Some diis ; - energy = Some energy ; - density = Some m_P ; - fock = Some fock ; - } - - in - - let scf_iteration_rohf data = - - let nSCF = data.iteration + 1 - and m_C = of_some data.coefficients - and m_P_a_prev = data.density_a - and m_P_b_prev = data.density_b - and fock_a_prev = data.fock_a - and fock_b_prev = data.fock_b - and diis = - match data.diis with - | Some diis -> diis - | None -> DIIS.make () - and threshold = - match data.error with - | Some error -> error - | None -> threshold_SCF *. 2. - in - - (* Density matrix *) - let m_P_a = - gemm ~alpha:1. ~transb:`T ~k:n_alfa m_C m_C - in - - let m_P_b = - gemm ~alpha:1. ~transb:`T ~k:n_beta m_C m_C - in - - let m_P = - Mat.add m_P_a m_P_b - in - - (* Fock matrix in AO basis *) - let fock_a = - match fock_a_prev, threshold > 100. *. threshold_SCF with - | Some fock_a_prev, true -> - let threshold = 1.e-8 in - Fock.make_uhf ~density_same:(Mat.sub m_P_a @@ of_some m_P_a_prev) ~density_other:(Mat.sub m_P_b @@ of_some m_P_b_prev) ~threshold ao_basis - |> Fock.add fock_a_prev - | _ -> Fock.make_uhf ~density_same:m_P_a ~density_other:m_P_b ao_basis - in - - let fock_b = - match fock_b_prev, threshold > 100. *. threshold_SCF with - | Some fock_b_prev, true -> - let threshold = 1.e-8 in - Fock.make_uhf ~density_same:(Mat.sub m_P_b @@ of_some m_P_b_prev) ~density_other:(Mat.sub m_P_a @@ of_some m_P_a_prev) ~threshold ao_basis - |> Fock.add fock_b_prev - | _ -> Fock.make_uhf ~density_same:m_P_b ~density_other:m_P_a ao_basis - in - - let m_F_a, m_Hc_a, m_J_a, m_K_a = - let x = fock_a in - Fock.(fock x, core x, coulomb x, exchange x) - in - - let m_F_b, m_Hc_b, m_J_b, m_K_b = - let x = fock_b in - Fock.(fock x, core x, coulomb x, exchange x) - in - - - let m_F_mo_a = - xt_o_x ~o:m_F_a ~x:m_C - in - - let m_F_mo_b = - xt_o_x ~o:m_F_b ~x:m_C - in - - let m_F_mo = - let space k = - if k <= n_beta then - `Core - else if k <= n_alfa then - `Active - else - `Virtual - in - Array.init (Mat.dim2 m_F_mo_a) (fun i -> - let i = i+1 in - Array.init (Mat.dim1 m_F_mo_a) (fun j -> - let j = j+1 in - match (space i), (space j) with - | `Core , `Core -> - 0.5 *. (m_F_mo_a.{i,j} +. m_F_mo_b.{i,j}) -. - (m_F_mo_b.{i,j} -. m_F_mo_a.{i,j}) - - | `Active , `Core - | `Core , `Active -> - m_F_mo_b.{i,j} - - | `Core , `Virtual - | `Virtual , `Core - | `Active , `Active -> - 0.5 *. (m_F_mo_a.{i,j} +. m_F_mo_b.{i,j}) - - | `Virtual , `Active - | `Active , `Virtual -> - m_F_mo_a.{i,j} - - | `Virtual , `Virtual -> - 0.5 *. (m_F_mo_a.{i,j} +. m_F_mo_b.{i,j}) +. - (m_F_mo_b.{i,j} -. m_F_mo_a.{i,j}) - ) ) - |> Mat.of_array - in - - let m_SC = - gemm m_S m_C - in - - let m_F0 = - x_o_xt ~x:m_SC ~o:m_F_mo - in - - - (* Add level shift in AO basis *) - let m_F = - x_o_xt ~x:m_SC ~o:m_LSmo - |> Mat.add m_F0 - in - - (* Fock matrix in orthogonal basis *) - let m_F_ortho = - xt_o_x m_F m_X - in - - let error_fock = - let fps = - gemm m_F (gemm m_P m_S) - and spf = - gemm m_S (gemm m_P m_F) - in - xt_o_x (Mat.sub fps spf) m_X - in - - let diis, m_F_diis = - let diis = - DIIS.append ~p:(Mat.as_vec m_F_ortho) ~e:(Mat.as_vec error_fock) diis - in - - try - let m_F_diis = - let x = - Bigarray.genarray_of_array1 (DIIS.next diis) - in - Bigarray.reshape_2 x (Mat.dim1 m_F_ortho) (Mat.dim2 m_F_ortho) - in - diis, m_F_diis - - with Failure _ -> (* Failure in DIIS.next *) - DIIS.make (), m_F_ortho - in - - - (* MOs in orthogonal MO basis *) - let m_C', eigenvalues = - diagonalize_symm m_F_diis - in - - (* Re-compute eigenvalues to remove level-shift *) - let eigenvalues = - let m_F_ortho = - xt_o_x m_F0 m_X - in - xt_o_x m_F_ortho m_C' - |> Mat.copy_diag - in - - (* MOs in AO basis *) - let m_C = - gemm m_X m_C' - |> Conventions.rephase - in - - (* Hartree-Fock energy *) - let energy = - nuclear_repulsion +. 0.5 *. ( Mat.gemm_trace m_P_a (Mat.add m_Hc_a m_F_a) +. - Mat.gemm_trace m_P_b (Mat.add m_Hc_b m_F_b) ) - in - - (* Convergence criterion *) - let error = - error_fock - |> Mat.as_vec - |> amax - |> abs_float - in - { empty with - iteration = nSCF ; - eigenvalues = Some eigenvalues ; - coefficients = Some m_C ; - error = Some error ; - diis = Some diis ; - energy = Some energy ; - density_a = Some m_P_a ; - density_b = Some m_P_b ; - fock_a = Some fock_a ; - fock_b = Some fock_b ; - } - - in - - - let scf_iteration data = - match kind with - | RHF -> scf_iteration_rhf data - | ROHF -> scf_iteration_rohf data - | _ -> failwith "Not implemented" - in - - let array_data = - - let storage = - Array.make max_scf None - in - - let rec iteration = function - | 0 -> Some (scf_iteration { empty with coefficients = Some m_C }) - | n -> begin - match storage.(n) with - | Some result -> Some result - | None -> - begin - let data = iteration (n-1) in - match data with - | None -> None - | Some data -> - begin - (** Check convergence *) - let converged, error = - match data.error with - | None -> false, 0. - | Some error -> (data.iteration = max_scf || error < threshold_SCF), error - in - if converged then - None - else - begin - storage.(n-1) <- Some { empty with - iteration = data.iteration; - energy = data.energy ; - eigenvalues = data.eigenvalues ; - error = data.error ; - }; - storage.(n) <- Some (scf_iteration data); - storage.(n); - end - end - end - end - in - Array.init max_scf (fun i -> lazy (iteration i)) - in - { - kind; - simulation; - guess ; - data = array_data; - nocc; - } - - - - - - - - - - -let linewidth = 60 - -let pp_iterations ppf t = - Format.fprintf ppf "@[%4s%s@]@." "" (Printing.line linewidth); - Format.fprintf ppf "@[%4s@[%5s@]@,@[%16s@]@,@[%16s@]@,@[%11s@]@]@." - "" "#" "HF energy " "Convergence" "HOMO-LUMO"; - Format.fprintf ppf "@[%4s%s@]@." "" (Printing.line linewidth); - let nocc = nocc t in - Array.iter (fun data -> - let data = Lazy.force data in - match data with - | None -> () - | Some data -> - let e = of_some data.eigenvalues in - let gap = e.{nocc+1} -. e.{nocc} in - begin - Format.fprintf ppf "@[%4s@[%5d@]@,@[%16.8f@]@,@[%16.4e@]@,@[%11.4f@]@]@." "" - (data.iteration) (of_some data.energy) (of_some data.error) gap; - end - ) t.data; - Format.fprintf ppf "@[%4s%s@]@." "" (Printing.line linewidth) - - -let pp_summary ppf t = - let print text value = - Format.fprintf ppf "@[@[%30s@]@,@[%16.10f@]@]@;" text value; - and line () = - Format.fprintf ppf "@[ %s @]@;" (Printing.line (linewidth-4)); - in - let ha_to_ev = Constants.ha_to_ev in - let e = eigenvalues t in - - Format.fprintf ppf "@[%s@]@;" (Printing.line ~c:'=' linewidth) - ; Format.fprintf ppf "@[" - ; print "One-electron energy" (kin_energy t +. eN_energy t) - ; print "Kinetic" (kin_energy t) - ; print "Potential" (eN_energy t) - ; line () - ; print "Two-electron energy" (coulomb_energy t +. exchange_energy t) - ; print "Coulomb" (coulomb_energy t) - ; print "Exchange" (exchange_energy t) - ; line () - ; print "HF HOMO" (ha_to_ev *. e.{nocc t}) - ; print "HF LUMO" (ha_to_ev *. e.{nocc t + 1}) - ; print "HF LUMO-LUMO" (ha_to_ev *. (e.{nocc t + 1} -. e.{nocc t })) - ; line () - ; print "Electronic energy" (energy t -. nuclear_repulsion t) - ; print "Nuclear repulsion" (nuclear_repulsion t) - ; print "Hartree-Fock energy" (energy t) - ; Format.fprintf ppf "@]" - ; Format.fprintf ppf "@[%s@]@;" (Printing.line ~c:'=' linewidth) - ; Util.debug_matrix "MOs" (eigenvectors t) - - - - -let pp ppf t = - Format.fprintf ppf "@.@[%s@]@." (Printing.line ~c:'=' 70); - Format.fprintf ppf "@[%34s %-34s@]@." (match t.kind with - | UHF -> "Unrestricted" - | RHF -> "Restricted" - | ROHF -> "Restricted Open-shell") "Hartree-Fock"; - Format.fprintf ppf "@[%s@]@.@." (Printing.line ~c:'=' 70); - Format.fprintf ppf "@[%a@]@." pp_iterations t; - Format.fprintf ppf "@[@;%a@]@." pp_summary t - diff --git a/SCF/HartreeFock.mli b/SCF/HartreeFock.mli deleted file mode 100644 index 9197046..0000000 --- a/SCF/HartreeFock.mli +++ /dev/null @@ -1,77 +0,0 @@ -open Lacaml.D - -(** Data structure representing the output of a Hartree-Fock caculation *) - -type hartree_fock_data - -type hartree_fock_kind = -| RHF (** Restricted Hartree-Fock *) -| ROHF (** Restricted Open-shell Hartree-Fock *) -| UHF (** Unrestricted Hartree-Fock *) - - -type t - -val kind : t -> hartree_fock_kind -(** Kind of simulation : RHF, ROHF or UHF. *) - -val simulation : t -> Simulation.t -(** Simulation which was used for HF calculation *) - -val guess : t -> Guess.t -(** Initial guess *) - -val eigenvectors : t -> Mat.t -(** Final eigenvectors *) - -val eigenvalues : t -> Vec.t -(** Final eigenvalues *) - -val occupation : t -> Vec.t -(** Diagonal of the density matrix *) - -val energy : t -> float -(** Final energy *) - -val nuclear_repulsion : t -> float -(** Nucleus-Nucleus potential energy *) - -val kin_energy : t -> float -(** Kinetic energy *) - -val eN_energy : t -> float -(** Electron-nucleus potential energy *) - -val coulomb_energy : t -> float -(** Electron-Electron potential energy *) - -val exchange_energy : t -> float -(** Exchange energy *) - -val nocc : t -> int -(** Number of occupied MOs *) - -val empty: hartree_fock_data -(** Empty data *) - - -val make : - ?kind:hartree_fock_kind -> - ?guess:[ `Hcore | `Huckel | `Matrix of Mat.t ] -> - ?max_scf:int -> - ?level_shift:float -> ?threshold_SCF:float -> - Simulation.t -> t - - -(** {1 Printers} *) - -val pp : Format.formatter -> t -> unit - -val pp_iterations : Format.formatter -> t -> unit - -val pp_summary : Format.formatter -> t -> unit - -(* -val pp_mos : Format.formatter -> t -> unit -#*) - diff --git a/Simulation.ml b/Simulation.ml deleted file mode 100644 index b1bc241..0000000 --- a/Simulation.ml +++ /dev/null @@ -1,62 +0,0 @@ -type t = { - charge : Charge.t; - electrons : Electrons.t; - nuclei : Nuclei.t; - basis : Basis.t; - ao_basis : AOBasis.t; - nuclear_repulsion : float; -} - -let nuclei t = t.nuclei -let charge t = t.charge -let electrons t = t.electrons -let basis t = t.basis -let ao_basis t = t.ao_basis -let nuclear_repulsion t = t.nuclear_repulsion -let range_separation t = Basis.range_separation t.basis -let f12 t = Basis.f12 t.basis - -let make ?cartesian:(cartesian=false) - ?multiplicity:(multiplicity=1) - ?charge:(charge=0) - ~nuclei - basis - = - - (* Tune Garbage Collector *) - let gc = Gc.get () in - Gc.set { gc with space_overhead = 1000 }; - - let electrons = - Electrons.make ~multiplicity ~charge nuclei - in - - let charge = - Charge.(Nuclei.charge nuclei + Electrons.charge electrons) - in - - let ao_basis = - AOBasis.make ~basis ~cartesian nuclei - in - - let nuclear_repulsion = - Nuclei.repulsion nuclei - in - - { - charge ; basis ; nuclei ; electrons ; ao_basis ; - nuclear_repulsion ; - } - - -let of_filenames ?(cartesian=false) ?(multiplicity=1) ?(charge=0) ?f12 ?range_separation ~nuclei ?(aux_basis_filenames=[]) basis_filename = - let nuclei = - Nuclei.of_filename nuclei - in - let basis = - Basis.of_nuclei_and_basis_filenames ?f12 ?range_separation ~nuclei (basis_filename :: aux_basis_filenames) - in - - lazy (make ~cartesian ~charge ~multiplicity ~nuclei basis) - |> Parallel.broadcast - diff --git a/Simulation.mli b/Simulation.mli deleted file mode 100644 index c14df69..0000000 --- a/Simulation.mli +++ /dev/null @@ -1,45 +0,0 @@ -type t - -val nuclei : t -> Nuclei.t -(** Nuclear coordinates used in the smiulation *) - -val charge : t -> Charge.t -(** Total charge (electrons + nuclei) *) - -val electrons : t -> Electrons.t -(** Electrons used in the simulation *) - -val basis : t -> Basis.t -(** Basis set used to build the AOs *) - -val ao_basis : t -> AOBasis.t -(** Atomic basis set *) - -val nuclear_repulsion : t -> float -(** Nuclear repulsion energy *) - -val f12 : t -> F12factor.t option -(** f12 correlation factor *) - -val range_separation : t -> float option -(** Range-separation parameter of the electron repulsion integrals potential *) - -(** {1 Creation} *) - -val make : - ?cartesian:bool -> - ?multiplicity:int -> - ?charge:int -> - nuclei:Nuclei.t -> - Basis.t -> t - -val of_filenames : - ?cartesian:bool -> - ?multiplicity:int -> - ?charge:int -> - ?f12:F12factor.t -> - ?range_separation: float -> - nuclei:string -> - ?aux_basis_filenames:string list -> - string -> t - diff --git a/Utils/Cholesky.ml b/Utils/Cholesky.ml deleted file mode 100644 index a1924f7..0000000 --- a/Utils/Cholesky.ml +++ /dev/null @@ -1,240 +0,0 @@ -open Lacaml.D - -let full_ldl m_A = - - let n = Mat.dim1 m_A in - - assert (Mat.dim2 m_A = n); - - let v_D = Vec.make0 n in - - let m_Lt = Mat.identity n in - - let v_D_inv = Vec.make0 n in - - - let compute_d j = - let l_jk = - Mat.col m_Lt j - in - let l_jk__d_k = - Vec.mul ~n:(j-1) l_jk v_D - in - m_A.{j,j} -. dot ~n:(j-1) l_jk l_jk__d_k - in - - - let compute_l i = - let l_ik__d_k = - Mat.col m_Lt i - |> Vec.mul ~n:(i-1) v_D - in - fun j -> - assert (i > j); - let l_jk = - Mat.col m_Lt j - in - v_D_inv.{j} *. ( m_A.{j,i} -. dot ~n:(j-1) l_ik__d_k l_jk ) - in - - - for i=1 to n do - for j=1 to (i-1) do - m_Lt.{j,i} <- compute_l i j; - done; - let d_i = compute_d i in - v_D.{i} <- d_i; - v_D_inv.{i} <- 1. /. d_i; - done; - m_Lt, v_D - - - - -let pivoted_ldl threshold m_A = -(** {% $P A P^\dagger = L D L^\dagger$. %} - Input : Matrix $A$ - Output : Matrices $L, D, P$. -*) - - let n = Mat.dim1 m_A in - assert (Mat.dim2 m_A = n); - - let pi = Array.init (n+1) (fun i -> i) in - - let v_D = Vec.init n (fun i -> abs_float m_A.{i,i}) in - let m_Lt = Mat.identity n in - - let v_D_inv = Vec.make0 n in - - let compute_d i = - let l_ik = - Mat.col m_Lt i - in - let l_ik__d_k = - Vec.mul ~n:(i-1) l_ik v_D - in - m_A.{pi.(i),pi.(i)} -. dot ~n:(i-1) l_ik l_ik__d_k - in - - let compute_l i = - let l_ik__d_k = - Mat.col m_Lt i - |> Vec.mul ~n:(i-1) v_D - in - fun j -> - assert (i > j); - let l_jk = - Mat.col m_Lt j - in - v_D_inv.{j} *. ( m_A.{pi.(j),pi.(i)} -. dot ~n:(j-1) l_ik__d_k l_jk ) - in - - - let maxloc v i = - let rec aux pos value i = - if i > n then - pos - else if v_D.{i} > value then - (aux [@tailcall]) i v_D.{i} (i+1) - else - (aux [@tailcall]) pos value (i+1) - in - aux i v.{i} (i+1) - in - - - let pivot i = - let j = maxloc v_D i in - let p_i, p_j = pi.(i), pi.(j) in - pi.(i) <- p_j; - pi.(j) <- p_i; - in - - - - - let () = - try - for i=1 to n do - pivot i; - for j=1 to (i-1) do - m_Lt.{j,i} <- compute_l i j; - done; - let d_i = compute_d i in - if abs_float d_i < threshold then - raise Exit; - v_D.{i} <- d_i; - v_D_inv.{i} <- 1. /. d_i; - done - with Exit -> () - in - m_Lt, v_D, pi - - - - -let make_ldl ?(threshold=Constants.epsilon) m_A = - pivoted_ldl m_A - - - - - - - - -let test_case () = - - let matrix_diff m_A m_B = - Mat.syrk_trace (Mat.sub m_A m_B) - in - - let vector_diff v_A v_B = - let v = Vec.sub v_A v_B in - dot v v - in - - let m_A = Mat.random 1000 1000 in - let m_A = Mat.add m_A (Mat.transpose_copy m_A) in - - let test_full_small () = - let m_A = - Mat.of_array [| [| 4. ; 12. ; -16. |] ; - [| 12. ; 37. ; -43. |] ; - [| -16. ; -43. ; 98. |] |] - in - - let m_L_ref = - Mat.of_array [| [| 1. ; 0. ; 0. |] ; - [| 3. ; 1. ; 0. |] ; - [| -4. ; 5. ; 1. |] |] - in - - let m_Lt_ref = - Mat.transpose_copy m_L_ref - in - - let v_D_ref = - Vec.of_array [| 4. ; 1. ; 9. |] - in - - let m_Lt, v_D = full_ldl m_A in - Alcotest.(check (float 1.e-15)) "full L" 0. (matrix_diff m_Lt m_Lt_ref); - Alcotest.(check (float 1.e-15)) "full D" 0. (vector_diff v_D v_D_ref); - let m_D = Mat.of_diag v_D in - let m_B = gemm ~transa:`T m_Lt @@ gemm m_D m_Lt in - Alcotest.(check (float 1.e-15)) "full L" 0. (matrix_diff m_A m_B); - () - in - - let test_full () = - let m_Lt, v_D = full_ldl m_A in - let m_D = Mat.of_diag v_D in - let m_B = gemm ~transa:`T m_Lt @@ gemm m_D m_Lt in - Alcotest.(check (float 1.e-15)) "full D" 0. (matrix_diff m_A m_B); - () - in - - let test_pivoted () = - let m_Lt, v_D, pi = pivoted_ldl 0. m_A in - let n = Mat.dim1 m_A in - let m_P = Mat.make0 n n in - for i=1 to n do - m_P.{i,pi.(i)} <- 1. - done; - let m_D = Mat.of_diag v_D in - let m_B = - gemm ~transa:`T m_P @@ - gemm ~transa:`T m_Lt @@ - gemm m_D @@ - gemm m_Lt m_P - in - Alcotest.(check (float 1.e-14)) "pivoted D" 0. (matrix_diff m_A m_B); - () - in - - let test_truncated () = - let m_Lt, v_D, pi = pivoted_ldl 0.001 m_A in - let n = Mat.dim1 m_Lt in - let m_P = Mat.make0 n n in - for i=1 to n do - m_P.{i,pi.(i)} <- 1. - done; - let m_D = Mat.of_diag v_D in - let m_B = - gemm ~transa:`T m_P @@ - gemm ~transa:`T m_Lt @@ - gemm m_D @@ - gemm m_Lt m_P - in - Alcotest.(check (float 1.e-3)) "full D" 0. (matrix_diff m_A m_B); - () - in - [ - "Small", `Quick, test_full_small; - "Full", `Quick, test_full; - "Pivoted", `Quick, test_pivoted ; - "Truncated", `Quick, test_truncated ; - ] - diff --git a/Utils/Conventions.ml b/Utils/Conventions.ml deleted file mode 100644 index e70918c..0000000 --- a/Utils/Conventions.ml +++ /dev/null @@ -1,30 +0,0 @@ -(** Contains the conventions relative to the program. - - The phase convention is given by: - {% $\sum_i c_i > 0$ %} or {% $\min_i c_i \ge 0$ %} - -*) - -open Lacaml.D - -let in_phase vec = - let s = Vec.sum vec in - if s = 0. then - let rec first_non_zero k = - if k > Vec.dim vec then - k-1 - else if vec.{k} = 0. then - first_non_zero (k+1) - else k - in - let k = first_non_zero 1 in - vec.{k} >= 0. - else - s > 0. - - -let rephase mat = - Mat.to_col_vecs mat - |> Array.map (fun v -> if in_phase v then v else Vec.neg v) - |> Mat.of_col_vecs - diff --git a/Utils/Conventions.mli b/Utils/Conventions.mli deleted file mode 100644 index e32613f..0000000 --- a/Utils/Conventions.mli +++ /dev/null @@ -1,16 +0,0 @@ -(** Contains the conventions relative to the program. - - The phase convention is given by: - {% $\sum_i c_i > 0$ %} or {% $\min_i c_i \ge 0$ %} - -*) - -open Lacaml.D - - -val in_phase : Vec.t -> bool -(** Checks if one MO respects the phase convention *) - -val rephase : Mat.t -> Mat.t -(** Apply the phase convention to the MOs. *) - diff --git a/Utils/Davidson.ml b/Utils/Davidson.ml deleted file mode 100644 index 8d5c85a..0000000 --- a/Utils/Davidson.ml +++ /dev/null @@ -1,165 +0,0 @@ -open Lacaml.D - -type t - -let make - ?guess - ?(n_states=1) - ?(n_iter=8) - ?(threshold=1.e-7) - diagonal - matrix_prod - = - - (* Size of the matrix to diagonalize *) - let n = Vec.dim diagonal in - - let m = n_states in - - (* Create guess vectors u, with unknown vectors initialized to unity. *) - let init_vectors m = - let init_vector k = - Vector.sparse_of_assoc_list n [ (k,1.0) ] - in - Array.init m (fun i -> init_vector (i+1)) - |> Matrix.sparse_of_vector_array - |> Matrix.to_mat - in - - let guess = - match guess with - | Some vectors -> vectors - | None -> init_vectors m - in - - let guess = - if Mat.dim2 guess = n_states then guess - else - (Mat.to_col_vecs_list guess) @ - (Mat.to_col_vecs_list (init_vectors (m-(Mat.dim2 guess))) ) - |> Mat.of_col_vecs_list - in - - let pick_new u = - Mat.to_col_vecs_list u - |> Util.list_pack m - |> List.rev - |> List.hd - in - - let u_new = Mat.to_col_vecs_list guess in - - let rec iteration u u_new w iter macro = - (* u is a list of orthonormal vectors, on which the operator has - been applied : w = op.u - u_new is a list of vectors which will increase the size of the - space. - *) - (* Orthonormalize input vectors u_new *) - let u_new_ortho = - List.concat [u ; u_new] - |> Mat.of_col_vecs_list - |> Util.qr_ortho - |> pick_new - in - - (* Apply the operator to the m last vectors *) - let w_new = - matrix_prod ( - u_new_ortho - |> Mat.of_col_vecs_list - |> Matrix.dense_of_mat ) - |> Matrix.to_mat - |> Mat.to_col_vecs_list - in - - (* Data for the next iteration *) - let u_next = - List.concat [ u ; u_new_ortho ] - and w_next = - List.concat [ w ; w_new ] - in - - (* Build the small matrix h = *) - let m_U = - Mat.of_col_vecs_list u_next - and m_W = - Mat.of_col_vecs_list w_next - in - let m_h = - gemm ~transa:`T m_U m_W - in - - (* Diagonalize h *) - let y, lambda = - Util.diagonalize_symm m_h - in - - (* Express m lowest eigenvectors of h in the large basis *) - let m_new_U = - gemm ~n:m m_U y - and m_new_W = - gemm ~n:m m_W y - in - - (* Compute the residual as proposed new vectors *) - let u_proposed = - Mat.init_cols n m (fun i k -> - let delta = lambda.{k} -. diagonal.{i} in - let delta = - if abs_float delta > 1.e-2 then delta - else if delta > 0. then 1.e-2 - else (-1.e-2) - in - (lambda.{k} *. m_new_U.{i,k} -. m_new_W.{i,k}) /. delta - ) - |> Mat.to_col_vecs_list - in - - - let residual_norms = List.rev @@ List.rev_map nrm2 u_proposed in - let residual_norm = - List.fold_left (fun accu i -> accu +. i *. i) 0. residual_norms - |> sqrt - in - - if Parallel.master then - begin - Printf.printf "%3d " iter; - Vec.iteri (fun i x -> if (i<=m) then Printf.printf "%16.10f " x) lambda; - Printf.printf "%16.8e%!\n" residual_norm - end; - - (* Make new vectors sparse *) - - let u_proposed = - Mat.of_col_vecs_list u_proposed - in - let maxu = lange u_proposed ~norm:`M in - let thr = maxu *. 0.00001 in - let u_proposed = - Mat.map (fun x -> if abs_float x < thr then 0. else x) u_proposed - |> Mat.to_col_vecs_list - in - (* - Format.printf "%a@." Matrix.pp_matrix @@ Matrix.dense_of_mat m_new_U; - *) - - - if residual_norm > threshold && macro > 0 then - let u_next, w_next, iter, macro = - if iter = n_iter then - m_new_U |> pick_new, - m_new_W |> pick_new, - 0, (macro-1) - else - u_next, w_next, (iter+1), macro - in - (iteration [@tailcall]) u_next u_proposed w_next iter macro - else - (m_new_U |> pick_new |> Mat.of_col_vecs_list), lambda - - in - iteration [] u_new [] 1 30 - - diff --git a/Utils/FourIdxStorage.ml b/Utils/FourIdxStorage.ml deleted file mode 100644 index d2dc3de..0000000 --- a/Utils/FourIdxStorage.ml +++ /dev/null @@ -1,693 +0,0 @@ -open Util -open Lacaml.D -open Constants - -let max_index = 1 lsl 14 - -type index_pair = { first : int ; second : int } - -type array2 = (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array2.t - -type storage_t = - | Dense of array2 - | Svd of Vec.t * array2 * array2 - | Sparse of (int, float) Hashtbl.t - -type t = - { - size : int ; - two_index : array2; - two_index_anti : array2; - three_index : array2; - three_index_anti : array2; - four_index : storage_t ; - } - -let key_of_indices ~r1 ~r2 = - let { first=i ; second=k } = r1 and { first=j ; second=l } = r2 in - let f i k = - let p, r = - if i <= k then i, k else k, i - in p + (r*(r-1))/2 - in - let p = f i k and q = f j l in - f p q - - -let check_bounds r1 r2 t = - let { first=i ; second=k } = r1 and { first=j ; second=l } = r2 in - let size = t.size in - assert ( (i lor j lor k lor l) > 0 ); - assert ( i <= size && j <= size && k <= size && l <= size ) - - -let dense_index i j size = - (j-1)*size + i - - -let sym_index i j = - if i < j then - (j*(j-1))/2 + i - else - (i*(i-1))/2 + j - - -let unsafe_get_four_index ~r1 ~r2 t = - - let open Bigarray.Array2 in - let { first=i ; second=k } = r1 and { first=j ; second=l } = r2 in - - if i=k then - if j=l then - unsafe_get t.two_index i j - else - unsafe_get t.three_index (dense_index j l t.size) i - else if j=l then - unsafe_get t.three_index (dense_index i k t.size) j - - else if i=l then - if k=j then - unsafe_get t.two_index_anti i j - else - unsafe_get t.three_index_anti (dense_index j k t.size) i - - else if j=k then - unsafe_get t.three_index_anti (dense_index i l t.size) j - - else if i=j then - if k=l then - unsafe_get t.two_index_anti i k - else - unsafe_get t.three_index_anti (dense_index k l t.size) i - - else if k=l then - (* *) - unsafe_get t.three_index_anti (dense_index i j t.size) k - - else - match t.four_index with - | Dense a -> unsafe_get a (dense_index i k t.size) (sym_index j l) - | Svd _ -> assert false - | Sparse a -> let key = key_of_indices ~r1 ~r2 in - try Hashtbl.find a key - with Not_found -> 0. - - -let get_four_index ~r1 ~r2 t = - check_bounds r1 r2 t; - unsafe_get_four_index ~r1 ~r2 t - - -let unsafe_set_four_index ~r1 ~r2 ~value t = - - - let open Bigarray.Array2 in - let { first=i ; second=k } = r1 and { first=j ; second=l } = r2 in - - let () = - - if i=k then - begin - if j=l then - begin - unsafe_set t.two_index i j value; - unsafe_set t.two_index j i value; - unsafe_set t.three_index (dense_index i i t.size) j value; - end; - unsafe_set t.three_index (dense_index j l t.size) i value; - unsafe_set t.three_index (dense_index l j t.size) i value; - end - else if j=l then - begin - unsafe_set t.three_index (dense_index i k t.size) j value; - unsafe_set t.three_index (dense_index k i t.size) j value; - end - - else if i=l then - begin - if j=k then - begin - unsafe_set t.two_index_anti i j value; - unsafe_set t.two_index_anti j i value; - unsafe_set t.three_index_anti (dense_index i i t.size) j value; - end; - unsafe_set t.three_index_anti (dense_index j k t.size) i value; - unsafe_set t.three_index_anti (dense_index k j t.size) i value; - end - else if j=k then - begin - unsafe_set t.three_index_anti (dense_index i l t.size) j value; - unsafe_set t.three_index_anti (dense_index l i t.size) j value; - end - - else if i=j then - begin - if k=l then - begin - unsafe_set t.two_index_anti i k value; - unsafe_set t.two_index_anti k i value; - unsafe_set t.three_index_anti (dense_index i i t.size) k value; - end; - unsafe_set t.three_index_anti (dense_index k l t.size) i value; - unsafe_set t.three_index_anti (dense_index l k t.size) i value; - end - - else if k=l then - (* *) - begin - unsafe_set t.three_index_anti (dense_index i j t.size) k value; - unsafe_set t.three_index_anti (dense_index j i t.size) k value; - end - in - - match t.four_index with - | Dense a -> let ik = (dense_index i k t.size) - and jl = (dense_index j l t.size) - and ki = (dense_index k i t.size) - and lj = (dense_index l j t.size) - and ik_s = (sym_index i k) - and jl_s = (sym_index j l) - in - begin - unsafe_set a ik jl_s value; - unsafe_set a ki jl_s value; - unsafe_set a jl ik_s value; - unsafe_set a lj ik_s value; - end - | Sparse a -> let key = key_of_indices ~r1 ~r2 in - Hashtbl.replace a key value - | Svd _ -> assert false - - -let set_four_index ~r1 ~r2 ~value t = - check_bounds r1 r2 t; - unsafe_set_four_index ~r1 ~r2 ~value t - - -let unsafe_increment_four_index ~r1 ~r2 ~value t = - let updated_value = - value +. unsafe_get_four_index ~r1 ~r2 t - in - unsafe_set_four_index ~r1 ~r2 ~value:updated_value t - - -let increment_four_index ~r1 ~r2 ~value t = - check_bounds r1 r2 t; - unsafe_increment_four_index ~r1 ~r2 ~value t - - -let get ~r1 ~r2 a = - get_four_index ~r1 ~r2 a - -let set ~r1 ~r2 ~value = - match classify_float value with - | FP_normal -> set_four_index ~r1 ~r2 ~value - | FP_zero - | FP_subnormal -> fun _ -> () - | FP_infinite - | FP_nan -> - let msg = - Printf.sprintf "FourIdxStorage.ml : set : r1 = (%d,%d) ; r2 = (%d,%d)" - r1.first r1.second r2.first r2.second - in - raise (Invalid_argument msg) - - -let increment ~r1 ~r2 = - increment_four_index ~r1 ~r2 - -let create ~size ?(temp_dir="/dev/shm") sparsity = - assert (size < max_index); - let two_index = - SharedMemory.create ~temp_dir Float64 [| size ; size |] - |> Bigarray.array2_of_genarray - in - let two_index_anti = - SharedMemory.create ~temp_dir Float64 [| size ; size |] - |> Bigarray.array2_of_genarray - in - let three_index = - SharedMemory.create ~temp_dir Float64 [| size * size ; size |] - |> Bigarray.array2_of_genarray - in - let three_index_anti = - SharedMemory.create ~temp_dir Float64 [| size * size ; size |] - |> Bigarray.array2_of_genarray - in - let four_index = - match sparsity with - | `Dense -> let result = - SharedMemory.create ~temp_dir Float64 [| size*size ; (size*(size+1))/2 |] - |> Bigarray.array2_of_genarray - in - Dense result - | `Sparse -> let result = Hashtbl.create (size*size+13) in - Sparse result - in - { size ; two_index ; two_index_anti ; three_index ; three_index_anti ; four_index } - - -let size t = t.size - -(** TODO : remove epsilons *) - - -let get_chem t i j k l = get ~r1:{ first=i ; second=j } ~r2:{ first=k ; second=l } t -let get_phys t i j k l = get ~r1:{ first=i ; second=k } ~r2:{ first=j ; second=l } t - -let set_chem t i j k l value = set ~r1:{ first=i ; second=j } ~r2:{ first=k ; second=l } ~value t -let set_phys t i j k l value = set ~r1:{ first=i ; second=k } ~r2:{ first=j ; second=l } ~value t - -let increment_chem t i j k l value = increment ~r1:{ first=i ; second=j } ~r2:{ first=k ; second=l } ~value t -let increment_phys t i j k l value = increment ~r1:{ first=i ; second=k } ~r2:{ first=j ; second=l } ~value t - - - -type element = (** Element for the stream *) -{ - i_r1: int ; - j_r2: int ; - k_r1: int ; - l_r2: int ; - value: float -} - - -let get_phys_all_i d ~j ~k ~l = - Vec.init d.size (fun i -> get_phys d i j k l) - - -let get_chem_all_i d ~j ~k ~l = - Vec.init d.size (fun i -> get_chem d i j k l) - - -let get_phys_all_ij d ~k ~l = - Mat.init_cols d.size d.size (fun i j -> get_phys d i j k l) - - -let get_chem_all_ij d ~k ~l = - - if k = l then - - let result = - Mat.col d.three_index k - |> Bigarray.genarray_of_array1 - in - Bigarray.reshape_2 result d.size d.size - - else - - match d.four_index with - | Dense a -> - let kl = sym_index k l in - let result = - Mat.col a kl - |> Bigarray.genarray_of_array1 - in - Bigarray.reshape_2 result d.size d.size - | Sparse a -> - Mat.init_cols d.size d.size (fun i j -> get_chem d i j k l) - | Svd _ -> assert false - - - -let to_stream d = - - let i = ref 0 - and j = ref 1 - and k = ref 1 - and l = ref 1 - in - let f_dense _ = - incr i; - if !i > !k then begin - i := 1; - incr j; - if !j > !l then begin - j := 1; - incr k; - if !k > !l then begin - k := 1; - incr l; - end; - end; - end; - if !l <= d.size then - Some { i_r1 = !i ; j_r2 = !j ; - k_r1 = !k ; l_r2 = !l ; - value = get_phys d !i !j !k !l - } - else - None - in - Stream.from f_dense - - -(** Write all integrals to a file with the convention *) -let to_file ?(cutoff=Constants.integrals_cutoff) ~filename data = - let oc = open_out filename in - to_stream data - |> Stream.iter (fun {i_r1 ; j_r2 ; k_r1 ; l_r2 ; value} -> - if (abs_float value > cutoff) then - Printf.fprintf oc " %5d %5d %5d %5d%20.15f\n" i_r1 j_r2 k_r1 l_r2 value); - close_out oc - - - -let of_file ~size ~sparsity filename = - let result = create ~size sparsity in - let ic = Scanf.Scanning.open_in filename in - let rec read_line () = - let result = - try - Some (Scanf.bscanf ic " %d %d %d %d %f" (fun i j k l v -> - set_phys result i j k l v)) - with End_of_file -> None - in - match result with - | Some () -> (read_line [@tailcall]) () - | None -> () - in - read_line (); - Scanf.Scanning.close_in ic; - result - - -let to_list data = - let s = - to_stream data - in - let rec append accu = - let d = - try Some (Stream.next s) with - | Stream.Failure -> None - in - match d with - | None -> List.rev accu - | Some d -> (append [@tailcall]) (d :: accu) - in - append [] - - - -let broadcast t = - let size = - Parallel.InterNode.broadcast (lazy t.size) - in - let bufsize = size * size * size in - let stream = to_stream t in - let rec iterate () = - let buffer = - Parallel.InterNode.broadcast (lazy ( - if Stream.peek stream = None then None else - Some (Array.init bufsize (fun _ -> - try Some (Stream.next stream) - with _ -> None - )) - ) ) - in - match buffer with - | None -> () - | Some buffer -> - begin - if not Parallel.InterNode.master then - Array.iter (fun x -> - match x with - | Some {i_r1 ; j_r2 ; k_r1 ; l_r2 ; value} -> - set_phys t i_r1 j_r2 k_r1 l_r2 value - | None -> () ) buffer; - (iterate [@tailcall]) () - end - in iterate (); - t - - - -let four_index_transform_dense_sparse ds coef source = - - let mo_num = Mat.dim2 coef in - let destination = create ~size:mo_num ds in - - let ao_num = Mat.dim1 coef in - let mo_num_2 = mo_num * mo_num in - let ao_num_2 = ao_num * ao_num in - let ao_mo_num = ao_num * mo_num in - - let range_mo = list_range 1 mo_num in - let range_ao = list_range 1 ao_num in - - let u = Mat.create mo_num_2 mo_num - and o = Mat.create ao_num ao_num_2 - and p = Mat.create ao_num_2 mo_num - and q = Mat.create ao_mo_num mo_num - in - - if Parallel.master then Printf.eprintf "4-idx transformation \n%!"; - - let task delta = - Mat.fill u 0.; - - List.iter (fun l -> - if abs_float coef.{l,delta} > epsilon then - begin - let jk = ref 1 in - List.iter (fun k -> - get_chem_all_ij source ~k ~l - |> lacpy ~b:o ~bc:!jk - |> ignore; - jk := !jk + ao_num; - ) range_ao; - (* o_i_jk *) - - let p = - gemm ~transa:`T ~c:p o coef - (* p_jk_alpha = \sum_i o_i_jk c_i_alpha *) - in - let p' = - Bigarray.reshape_2 (Bigarray.genarray_of_array2 p) ao_num ao_mo_num - (* p_j_kalpha *) - in - - let q = - gemm ~transa:`T ~c:q p' coef - (* q_kalpha_beta = \sum_j p_j_kalpha c_j_beta *) - in - let q' = - Bigarray.reshape_2 (Bigarray.genarray_of_array2 q) ao_num mo_num_2 - (* q_k_alphabeta = \sum_j p_j_kalpha c_j_beta *) - in - - ignore @@ - gemm ~transa:`T ~beta:1. ~alpha:coef.{l,delta} ~c:u q' coef ; - (* u_alphabeta_gamma = \sum_k q_k_alphabeta c_k_gamma *) - end - ) range_ao; - let u = - Bigarray.reshape - (Bigarray.genarray_of_array2 u) - [| mo_num ; mo_num ; mo_num |] - |> Bigarray.array3_of_genarray - in - let result = ref [] in - List.iter (fun gamma -> - List.iter (fun beta -> - List.iter (fun alpha -> - let x = u.{alpha,beta,gamma} in - if abs_float x > Constants.integrals_cutoff then - result := (alpha, beta, gamma, delta, x) :: !result; - ) (list_range 1 beta) - ) range_mo - ) (list_range 1 delta); - Array.of_list !result - in - - - let n = ref 0 in - Stream.of_list range_mo - |> Farm.run ~f:task ~ordered:true ~comm:Parallel.Node.comm - |> Stream.iter (fun l -> - if Parallel.master then (incr n ; Printf.eprintf "\r%d / %d%!" !n mo_num); - Array.iter (fun (alpha, beta, gamma, delta, x) -> - set_chem destination alpha beta gamma delta x) l); - - if Parallel.master then Printf.eprintf "\n%!"; - broadcast destination - - -let svd_of_dense t = - let four_index = - let f = - match t.four_index with - | Dense a -> a - | _ -> invalid_arg "svd_of_dense expects a Dense storage" - in - let size = t.size in - let b = Mat.create (size*size) (size*size) in - for k = 1 to size do - for l = 1 to size do - let ac = sym_index k l in - lacpy f ~n:1 ~ac ~b ~bc:(dense_index k l size) - |> ignore; - lacpy f ~n:1 ~ac ~b ~bc:(dense_index l k size) - |> ignore - done - done; - let d, u, v = gesdd b in - let rank = - let w = copy d in - scal (1. /. d.{1}) w; - let rec aux i = - if i = Vec.dim w then i else - if w.{i} < epsilon_float then i else - aux (i+1) - in aux 1 - in - let d = copy d ~n:rank in - let u = lacpy ~n:rank u in - let v = lacpy ~m:rank v in - Svd (d,u,v) - in - { t with four_index } - - -let dense_of_svd t = - let four_index = - let d, u, v = - match t.four_index with - | Svd (d, u, v) -> d, u, v - | _ -> invalid_arg "dense_of_svd expects a Svd storage" - in - let f = - gemm u @@ gemm (Mat.of_diag d) v - in - let size = t.size in - let b = Mat.create (size*size) ((size*(size+1))/2) in - for k = 1 to size do - for l = 1 to k do - let bc = sym_index k l in - lacpy f ~ac:(dense_index l k size) ~n:1 ~bc ~b - |> ignore - done - done; - Dense b - in - { t with four_index } - - -let four_index_transform_svd coef source = - let t0 = Unix.gettimeofday () in - let svd = svd_of_dense source in - Printf.printf "Computed SVD in %f seconds\n%!" (Unix.gettimeofday () -. t0); - - let u0, d0, v0 = - match svd.four_index with - | Svd (d, u, v) -> u, d, (Mat.transpose_copy v) - | _ -> assert false - in - - let t0 = Unix.gettimeofday () in - - let ao_num = Mat.dim1 coef in - let mo_num = Mat.dim2 coef in - let svd_num = Vec.dim d0 in - - let destination = create ~size:mo_num `Dense in - - let mo_num_2 = mo_num * mo_num in - - if Parallel.master then Printf.eprintf "4-idx transformation \n%!"; - - let u_vecs = Mat.to_col_vecs u0 - and v_vecs = Mat.to_col_vecs v0 - in - - - Printf.printf "%d %d %d %d\n" (Mat.dim1 u0) (Mat.dim2 u0) (Mat.dim1 v0) (Mat.dim2 v0); - let task a = - let o = - Bigarray.reshape_2 (Bigarray.genarray_of_array1 u_vecs.(a-1)) ao_num ao_num - in - - let u = - let p = gemm ~transa:`T coef @@ gemm o coef in - Bigarray.reshape_1 (Bigarray.genarray_of_array2 p) mo_num_2 - in - - let o = - Bigarray.reshape_2 (Bigarray.genarray_of_array1 v_vecs.(a-1)) ao_num ao_num - in - - let v = - let p = gemm ~transa:`T coef @@ gemm o coef in - Bigarray.reshape_1 (Bigarray.genarray_of_array2 p) mo_num_2 - in - (u, v) - in - - - (* - let four_index = Svd (d,u'',v'') in - let t = make_from_four_index - - { source with - size = mo_num; - two_index; - two_index_anti; - three_index; - three_index_anti; - four_index - } - *) - - let n = ref 0 in - let u_list = ref [] - and v_list = ref [] - in - Util.list_range 1 svd_num - |> Stream.of_list - |> Farm.run ~f:task ~ordered:true ~comm:Parallel.Node.comm - |> Stream.iter (fun (u,v) -> - if Parallel.master then (incr n ; Printf.eprintf "\r%d / %d%!" !n mo_num); - u_list := u :: !u_list; - v_list := v :: !v_list); - - let u = Mat.of_col_vecs_list (List.rev !u_list) - and v = Mat.of_col_vecs_list (List.rev !v_list) - in - Printf.printf "Computed 4-idx in %f seconds\n%!" (Unix.gettimeofday () -. t0); - - let result = - let p = gemm u @@ gemm ~transb:`T (Mat.of_diag d0) v in - Bigarray.reshape (Bigarray.genarray_of_array2 p) [| mo_num ; mo_num ; mo_num ; mo_num |] - in - for a=1 to mo_num do - for b=a to mo_num do - for c=1 to mo_num do - for d=c to mo_num do - let x = result.{a,b,c,d} in - if abs_float x > Constants.integrals_cutoff then - set_chem destination a b c d x; - done - done - done - done; - - Printf.printf "Computed 4-idx in %f seconds\n%!" (Unix.gettimeofday () -. t0); - - if Parallel.master then Printf.eprintf "\n%!"; - broadcast destination - - - - - - - - - -let four_index_transform coef source = - match source.four_index with - | Sparse _ -> four_index_transform_dense_sparse `Sparse coef source - | Svd _ -> assert false (* four_index_transform_svd coef source *) - | Dense _ -> four_index_transform_dense_sparse `Dense coef source - diff --git a/Utils/Matrix.ml b/Utils/Matrix.ml deleted file mode 100644 index 2d38e70..0000000 --- a/Utils/Matrix.ml +++ /dev/null @@ -1,869 +0,0 @@ -open Lacaml.D - -type sparse_matrix = - { - m: int; - n: int; - v: Vector.t array; - } - -type computed = - { - m: int; - n: int; - f: int -> int -> float; - } - -type t = -| Dense of Mat.t -| Sparse of sparse_matrix -| Computed of computed - -let epsilon = Constants.epsilon - -let is_computed = function - | Computed _ -> true - | _ -> false - -let is_sparse = function - | Sparse _ -> true - | _ -> false - -let is_dense = function - | Dense _ -> true - | _ -> false - - -let dim1 = function - | Dense m -> Mat.dim1 m - | Sparse {m ; _} -> m - | Computed {m ; _} -> m - - -let dim2 = function - | Dense m -> Mat.dim2 m - | Sparse {n ; _} -> n - | Computed {n ; _} -> n - - -let check_bounds m n i j = - if (i <= 0 || i > m || j <= 0 || j > n) then - raise (Invalid_argument "Index out of bounds") - -let get = function - | Dense m -> (fun i j -> m.{i,j}) - | Sparse { m ; n ; v } -> (fun i j -> Vector.get v.(j-1) i) - | Computed { m ; n ; f } -> (fun i j -> check_bounds m n i j ; f i j) - - -let sparse_of_dense ?(threshold=epsilon) = function - | Dense m' -> - let m = Mat.dim1 m' - and n = Mat.dim2 m' - and v = - Mat.to_col_vecs m' - |> Array.map (fun v -> Vector.sparse_of_vec ~threshold v) - in Sparse {m ; n ; v} - | _ -> invalid_arg "Expected a dense matrix" - - -let dense_of_sparse = function - | Sparse {m ; n ; v} -> - let m' = - Array.map (fun v -> Vector.to_vec v) v - |> Mat.of_col_vecs - in Dense m' - | _ -> invalid_arg "Expected a sparse matrix" - - -let sparse_of_computed ?(threshold=epsilon) = function - | Computed {m ; n ; f} -> - Sparse { m ; n ; v=Array.init n (fun j -> - Util.list_range 1 m - |> List.rev_map (fun i -> - let x = f i (j+1) in - if abs_float x > threshold then Some (i, x) - else None) - |> Util.list_some - |> List.rev - |> Vector.sparse_of_assoc_list m - ) } - | _ -> invalid_arg "Expected a computed matrix" - -let dense_of_computed x = dense_of_sparse @@ sparse_of_computed x - -let dense_of_mat m = Dense m - -let of_fun m n f = Computed {m ; n ; f} - -let rec to_vector_array ?(threshold=epsilon) = function - | Sparse {m ; n ; v} -> v - | Dense m -> to_vector_array (sparse_of_dense ~threshold (Dense m)) - | Computed m -> to_vector_array (sparse_of_computed ~threshold (Computed m)) - - -let identity n = - Sparse { n ; m=n ; - v = Array.init n (fun i -> Vector.sparse_of_assoc_list n [(i+1,1.0)]) - } - -let sparse_of_mat ?(threshold=epsilon) m = - dense_of_mat m - |> sparse_of_dense ~threshold - - -let sparse_of_vector_array v = - let m = - Array.fold_left (fun accu v' -> - if Vector.dim v' <> accu then - invalid_arg "Inconsistent dimension" - else accu) (Vector.dim v.(0)) v - and n = Array.length v - in - Sparse {m ; n ; v} - - -let rec to_mat = function - | Dense m -> m - | Sparse m -> - dense_of_sparse (Sparse m) - |> to_mat - | Computed m -> sparse_of_computed (Computed m) |> dense_of_sparse |> to_mat - -let transpose = function - | Dense m -> Dense (Mat.transpose_copy m) - | Sparse {m ; n ; v} -> - begin - let v' = Array.init m (fun i -> ref []) in - Array.iteri (fun j v_j -> - Vector.to_assoc_list v_j - |> List.iter (fun (i, v_ij) -> - v'.(i-1) := (j+1, v_ij) :: !(v'.(i-1)) - ) - ) v; - let v' = - Array.map (fun x -> Vector.sparse_of_assoc_list n (List.rev !x) ) v' - in - Sparse {m=n ; n=m ; v=v'} - end - | Computed {m ; n ; f} -> - let f' i j = f j i in - Computed { m=n ; n=m ; f=f' } - - -let outer_product ?(threshold=epsilon) v1 v2 = - match Vector.(is_dense v1, is_dense v2) with - | (true, true) -> - let v1 = Vector.to_vec v1 - and v2 = Vector.to_vec v2 - in - let a = Mat.make0 (Vec.dim v1) (Vec.dim v2) in - ger v1 v2 a; - Dense a - | (true, false) -> - let v = Vector.to_vec v1 - and v' = Vector.to_vec v2 - in - let v = - Array.init (Vector.dim v2) (fun j -> - Vec.map (fun x -> x *. v'.{j+1}) v - |> Vector.sparse_of_vec) - in - Sparse {m=Vector.dim v1 ; n=Vector.dim v2 ; v} - | (false, true) - | (false, false) -> - let v = Vector.to_assoc_list v1 - and v' = Vector.to_vec v2 - in - let v = - Array.init (Vector.dim v2) (fun j -> - List.rev_map (fun (i, x) -> - let z = x *. v'.{j+1} in - if abs_float z < threshold then - None - else - Some (i, z) - ) v - |> Util.list_some - |> List.rev - |> Vector.sparse_of_assoc_list (Vector.dim v1) - ) - in - Sparse {m=Vector.dim v1 ; n=Vector.dim v2 ; v} - - - -let rec mm ?(transa=`N) ?(transb=`N) ?(threshold=epsilon) a b = - - let f, f' = - match transa, transb with - | `N, `N -> dim2, dim1 - | `T, `N -> dim1, dim1 - | `T, `T -> dim1, dim2 - | `N, `T -> dim2, dim2 - in - if f a <> f' b then - Printf.sprintf "%d %d : Inconsistent dimensions" (f a) (f' b) - |> invalid_arg; - - (* Dense x sparse *) - let mmsp transa transb a b = - let a = - match transa with - | `N -> Mat.transpose_copy a - | `T -> a - in - let m' = Mat.dim2 a in - let a = - Mat.to_col_vecs a - |> Array.map (fun v -> Vector.dense_of_vec v) - in - let {m ; n ; v} = - if transb = `T then - match transpose (Sparse b) with - | Sparse x -> x - | _ -> assert false - else - b - in - let v' = - Array.map (fun b_j -> - Array.map (fun a_i -> - Vector.dot a_i b_j) a - |> Vec.of_array - |> Vector.sparse_of_vec - ) v - in - Sparse {m=m' ; n ; v=v'} - in - - (* Sparse x dense *) - let spmm transa transb a b = - let b = - match transb with - | `N -> b - | `T -> Mat.transpose_copy b - in - let n' = Mat.dim2 b in - let b = - Mat.to_col_vecs b - |> Array.map (fun v -> Vector.dense_of_vec v) - in - let m, n, v = - if transa = `N then - match transpose (Sparse a) with - | Sparse {m ; n ; v} -> n, m, v - | _ -> assert false - else - match Sparse a with - | Sparse {m ; n ; v} -> n, m, v - | _ -> assert false - in - let v' = - Array.map (fun b_j -> - Array.map (fun a_i -> - Vector.dot a_i b_j) v - |> Vec.of_array - |> Vector.sparse_of_vec - ) b - in - Sparse {m ; n=n' ; v=v'} - in - - (* Sparse x Sparse *) - let mmspmm transa transb a b = - let {m ; n ; v} = - if transb = `T then - match transpose (Sparse b) with - | Sparse x -> x - | _ -> assert false - else - b - in - let m', n', v' = - if transa = `N then - match transpose (Sparse a) with - | Sparse {m ; n ; v} -> n, m, v - | _ -> assert false - else - match Sparse a with - | Sparse {m ; n ; v} -> n, m, v - | _ -> assert false - in - let v'' = - Array.map (fun b_j -> - Array.map (fun a_i -> - Vector.dot a_i b_j) v' - |> Vec.of_array - |> Vector.sparse_of_vec - ) v - in - Sparse {m=m' ; n=n ; v=v''} - in - - let mmcc transa transb a b = - let {m ; n ; f} = - if transb = `T then - match transpose (Computed b) with - | Computed x -> x - | _ -> assert false - else - b - in - let m', n', f' = - if transa = `T then - match transpose (Computed a) with - | Computed {m ; n ; f} -> m, n, f - | _ -> assert false - else - let {m ; n ; f} = a in - m, n, f - in - if n' <> m then - invalid_arg "Inconsistent dimensions"; - let g i j = - let result = ref 0. in - for k=1 to m do - let a = f k j in - if a <> 0. then - result := !result +. (f' i k) *. a ; - done; - !result - in - Computed {m=m' ; n=n ; f=g} - in - - let mmccde transa transb a b = - let m', n', f' = - if transa = `T then - match transpose (Computed a) with - | Computed {m ; n ; f} -> m, n, f - | _ -> assert false - else - let {m ; n ; f} = a in - m, n, f - in - let m, n = - match transb with - | `N -> Mat.dim1 b , Mat.dim2 b - | `T -> Mat.dim2 b , Mat.dim1 b - in - if n' <> m then - invalid_arg "Inconsistent dimensions"; - - let matrix = - Array.init n (fun j -> - let bj = - if transb = `T then - (Mat.copy_row b (j+1)) - else - (Mat.to_col_vecs b).(j) - in - let accu = Vec.make0 m' in - let v = Vec.make0 m' in - let bj = Vec.to_array bj in - Array.iteri (fun k a -> - if a <> 0. then - begin - for i = 1 to m' do - v.{i} <- (f' i (k+1)); - done; - axpy ~alpha:a v accu - end - ) bj; - accu - ) - |> Mat.of_col_vecs - in - Dense matrix - in - match a, b with - | (Dense a), (Dense b) -> Dense (gemm ~transa ~transb a b) - | (Sparse a), (Dense b) -> spmm transa transb a b - | (Dense a), (Sparse b) -> mmsp transa transb a b - | (Sparse a), (Sparse b) -> mmspmm transa transb a b - | (Computed a), (Computed b) -> mmcc transa transb a b - | (Computed a), (Dense b) -> mmccde transa transb a b - | (Computed a), (Sparse _) -> - let b = { m = dim1 b ; n = dim2 b ; f = get b } in - mmcc transa transb a b - |> sparse_of_computed ~threshold - | _, (Computed _) -> - begin - match transa, transb with - | `N, `N -> mm ~transa:`T ~transb:`T ~threshold b a - | `N, `T -> mm ~transa:`N ~transb:`T ~threshold b a - | `T, `N -> mm ~transa:`T ~transb:`N ~threshold b a - | `T, `T -> mm ~transa:`N ~transb:`N ~threshold b a - end |> transpose - - -let mv ?(sparse=false) ?(trans=`N) ?(threshold=epsilon) a b = - - let f = - match trans with - | `N -> dim2 - | `T -> dim1 - in - if f a <> Vector.dim b then - invalid_arg "Inconsistent dimensions"; - - let spmv a b = - let {m ; n ; v} = - if trans = `N then - match transpose (Sparse a) with - | Sparse x -> x - | _ -> assert false - else - a - in - Array.map (fun row_a -> Vector.dot row_a b) v - |> Vec.of_array - in - - let mv a b = - let f_a = - match trans with - | `N -> (fun i -> Mat.copy_row a i) - | `T -> (fun i -> Mat.col a i) - in - Vec.init (Mat.dim1 a) (fun i -> - Vector.dense_of_vec (f_a i) - |> Vector.dot b ) - in - - let cmv a b = - match trans with - | `N -> Vec.init a.m (fun i -> - let accu = ref 0. in - for j=1 to a.n do - accu := !accu +. a.f i j *. Vector.get b j - done; - !accu) - | `T -> Vec.init a.m (fun i -> - let accu = ref 0. in - for j=1 to a.n do - accu := !accu +. a.f j i *. Vector.get b j - done; - !accu) - in - - let dense_result = - match a, Vector.is_dense b with - | Dense a, true -> gemv ~trans a (Vector.to_vec b) - | Dense a, false -> mv a b - | Sparse a, _ -> spmv a b - | Computed a, _ -> cmv a b - in - - if sparse then - Vector.sparse_of_vec dense_result - else - Vector.dense_of_vec dense_result - - -let rec op2 dense_op sparse_op a b = - if dim1 a <> dim1 b || dim2 a <> dim2 b then - failwith "Inconsistent dimensions"; - - match a, b with - | (Dense a), (Dense b) -> Dense (dense_op a b) - | (Dense _), (Sparse _) -> op2 dense_op sparse_op (sparse_of_dense a) b - | (Sparse _), (Dense _) -> op2 dense_op sparse_op a (sparse_of_dense b) - | (Sparse a), (Sparse b) -> Sparse - { m=a.m ; n=a.n ; - v = Array.map2 sparse_op a.v b.v - } - | _ -> failwith "Not implemented" - -let add = op2 (fun a b -> Mat.add a b) (fun a b -> Vector.add a b) -let sub = op2 (fun a b -> Mat.sub a b) (fun a b -> Vector.sub a b) - -let scale f = function - | Dense a -> let b = lacpy a in (Mat.scal f b ; Dense b) - | Sparse a -> Sparse - { a with - v = if f = 1.0 then a.v - else Array.map (fun v -> Vector.scale f v) a.v } - | _ -> failwith "Not implemented" - -let frobenius_norm = function - | Dense a -> lange ~norm:`F a - | Sparse a -> - Array.fold_left (fun accu v -> accu +. Vector.dot v v) 0. a.v - |> sqrt - | _ -> failwith "Not implemented" - - - -let split_cols nrows = function - | Dense a -> - begin - Mat.to_col_vecs a - |> Array.to_list - |> Util.list_pack nrows - |> List.rev_map (fun l -> - Dense (Mat.of_col_vecs @@ Array.of_list l) ) - |> List.rev - end - | Sparse a -> - begin - Array.to_list a.v - |> Util.list_pack nrows - |> List.rev_map Array.of_list - |> List.rev_map (fun v -> Sparse { m=a.m ; n= Array.length v ; v }) - end - | Computed a -> - begin - Util.list_range 0 (a.n-1) - |> Util.list_pack nrows - |> List.rev_map Array.of_list - |> List.rev_map (fun v -> Computed { m=a.m ; n= Array.length v ; f = (fun i j -> a.f i (j+v.(0)) ) }) - end - - -let join_cols l = - let rec aux_dense accu = function - | [] -> Dense (Mat.of_col_vecs_list (List.concat accu)) - | (Dense a) :: rest -> aux_dense ((Mat.to_col_vecs_list a) :: accu) rest - | _ -> assert false - - and aux_sparse m n accu = function - | [] -> Sparse { m ; n ; v=Array.of_list (List.concat accu) } - | (Sparse a) :: rest -> aux_sparse a.m (n+a.n) ((Array.to_list a.v)::accu) rest - | _ -> assert false - - and aux = function - | [] -> Sparse { m=0 ; n=0 ; v=[| |] } - | (Dense a) :: rest -> aux_dense [] ((Dense a) :: rest) - | (Sparse a) :: rest -> aux_sparse 0 0 [] ((Sparse a) :: rest) - | (Computed a) :: rest -> aux_sparse 0 0 [] - (List.rev_map sparse_of_computed ( (Computed a) :: rest ) - |> List.rev) - - in aux (List.rev l) - - - - - -let ax_eq_b_conj_grad ?x a b = - (* /!\ : A needs to be positive definite and symmetric *) - let x = - match x with - | Some x0 -> x0 - | None -> b - in - let r = Vector.sub b (mv a x) in - let p = r in - let rsold = Vector.dot r r in - let rec aux rsold r p x = function - | 0 -> x - | i -> - let ap = mv a p in - let alpha = rsold /. (Vector.dot p ap) in - let x = Vector.add x (Vector.scale alpha p) in - let r = Vector.sub r (Vector.scale alpha ap) in - let rsnew = Vector.dot r r in - if rsnew < Constants.epsilon then - x - else - let p = - Vector.add r (Vector.scale (rsnew /. (rsold +. 1.e-12) ) p) - in - (aux [@tailcall]) rsnew r p x (i-1) - in - aux rsold r p x (Vector.dim b *2) - - - -let rec ax_eq_b ?(trans=`N) a b = - match a, b with - | (Dense a), (Dense b) -> - let a = lacpy a in - let x = lacpy b in - (getrs ~trans a x; Dense x) - | (Dense _), (Sparse _) -> - let b = dense_of_sparse b in - ax_eq_b ~trans a b - | _ -> - let ata, atb = - if trans = `N then - mm ~transa:`T a a, mm ~transa:`T a b - else - mm ~transa:`N a a, mm ~transa:`N a b - in - Sparse { m=dim1 b ; n=dim2 b ; - v=Array.map (fun v -> ax_eq_b_conj_grad ata v) (to_vector_array atb) - } - - -(* ------- Parallel routines ---------- *) - -let rec parallel_mm ?(transa=`N) ?(transb=`N) ?(threshold=epsilon) a b = - - let m = - match transa with - | `N -> dim2 a - | `T -> dim1 a - in - let b = - match transb with - | `T -> transpose b - | `N -> b - in - assert (m = dim1 b); - let n = 1 + (m / (Parallel.size * 7)) in - let chunks = - split_cols n b - in - - let result = - Stream.of_list chunks - |> Farm.run ~ordered:true ~f:(fun b -> - match a, b with - | Computed _, Computed _ -> - mm ~transa ~threshold a b - |> sparse_of_computed ~threshold - | _ -> - mm ~transa ~threshold a b - ) - |> Util.stream_to_list - |> join_cols - in - - result - - -(* ------------ Printers ------------ *) - -let rec pp ppf = function - | Dense m -> Util.pp_matrix ppf m - | Sparse m -> pp ppf @@ dense_of_sparse (Sparse m) - | Computed m -> pp ppf @@ dense_of_computed (Computed m) - - - - - - -(* ---------- Unit tests ------------ *) - -let test_case () = - - let d1 = 30 - and d2 = 40 - and d3 = 50 - in - - let x1 = Mat.map (fun x -> if abs_float x < 0.6 then 0. else x) (Mat.random d1 d2) - and x2 = Mat.map (fun x -> if abs_float x < 0.3 then 0. else x) (Mat.random d2 d3) - in - - let m1 = dense_of_mat x1 - and m2 = dense_of_mat x2 - in - - let m1_s = sparse_of_mat x1 - and m2_s = sparse_of_mat x2 - in - - let norm_diff m1 m2 = - (Mat.sub (to_mat m1) (to_mat m2) - |> Mat.syrk_trace) - in - - let test_dimensions () = - Alcotest.(check int) "dim1 1" d1 (dim1 m1 ); - Alcotest.(check int) "dim1 2" d1 (dim1 m1_s); - Alcotest.(check int) "dim2 3" d2 (dim2 m1 ); - Alcotest.(check int) "dim2 4" d2 (dim2 m1_s); - Alcotest.(check int) "dim1 5" d2 (dim1 m2 ); - Alcotest.(check int) "dim1 6" d2 (dim1 m2_s); - Alcotest.(check int) "dim2 7" d3 (dim2 m2 ); - Alcotest.(check int) "dim2 8" d3 (dim2 m2_s); - in - - let test_conversion () = - Alcotest.(check bool) "sparse -> dense 1" true (dense_of_sparse m1_s = m1 ); - Alcotest.(check bool) "sparse -> dense 2" true (dense_of_sparse m2_s = m2 ); - Alcotest.(check bool) "dense -> sparse 1" true (sparse_of_dense m1 = m1_s); - Alcotest.(check bool) "dense -> sparse 3" true (sparse_of_dense m2 = m2_s); - in - - let test_transpose () = - let m1t = Mat.transpose_copy x1 |> dense_of_mat - and m2t = Mat.transpose_copy x2 |> dense_of_mat - in - Alcotest.(check bool) "dense 1" true (transpose m1 = m1t); - Alcotest.(check bool) "dense 2" true (transpose m2 = m2t); - Alcotest.(check bool) "sparse 1" true (transpose m1_s = sparse_of_dense m1t); - Alcotest.(check bool) "sparse 2" true (transpose m2_s = sparse_of_dense m2t); - in - - let test_outer () = - let x1 = Vec.init d1 (fun i -> float_of_int i) - and x2 = Vec.init d2 (fun i -> float_of_int i -. 0.3) - in - let v1 = Vector.dense_of_vec x1 - and v2 = Vector.dense_of_vec x2 - in - let v1_s = Vector.sparse_of_vec x1 - and v2_s = Vector.sparse_of_vec x2 - in - let m1 = - Dense (Mat.init_cols d1 d2 (fun i j -> (float_of_int i) *. (float_of_int j -. 0.3))) - in - let m1_s = - sparse_of_dense m1 - in - Alcotest.(check (float 1.e-10)) "dense dense " 0. (norm_diff m1 (outer_product v1 v2)); - Alcotest.(check (float 1.e-10)) "sparse dense " 0. (norm_diff m1_s (outer_product v1_s v2)); - Alcotest.(check (float 1.e-10)) "dense sparse" 0. (norm_diff m1_s (outer_product v1 v2_s)); - Alcotest.(check (float 1.e-10)) "sparse sparse" 0. (norm_diff m1_s (outer_product v1_s v2_s)); - in - - let test_add_sub () = - let x2 = Mat.map (fun x -> if abs_float x < 0.3 then 0. else x) (Mat.random d1 d2) in - let m2 = dense_of_mat x2 in - let m3 = Mat.add x1 x2 |> dense_of_mat in - let m4 = Mat.sub x1 x2 |> dense_of_mat in - let m2_s = sparse_of_mat x2 in - let m3_s = Mat.add x1 x2 |> sparse_of_mat in - let m4_s = Mat.sub x1 x2 |> sparse_of_mat in - Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (add m1 m2) m3); - Alcotest.(check (float 1.e-10)) "dense dense 2" 0. (norm_diff (sub m1 m2) m4); - Alcotest.(check (float 1.e-10)) "dense sparse 3" 0. (norm_diff (add m1 m2_s) m3_s); - Alcotest.(check (float 1.e-10)) "dense sparse 4" 0. (norm_diff (sub m1 m2_s) m4_s); - Alcotest.(check (float 1.e-10)) "sparse dense 5" 0. (norm_diff (add m1_s m2) m3); - Alcotest.(check (float 1.e-10)) "sparse dense 6" 0. (norm_diff (sub m1_s m2) m4); - Alcotest.(check (float 1.e-10)) "dense sparse 7" 0. (norm_diff (add m1_s m2_s) m3_s); - Alcotest.(check (float 1.e-10)) "dense sparse 8" 0. (norm_diff (sub m1_s m2_s) m4_s); - Alcotest.(check (float 1.e-10)) "dense sparse 9" (frobenius_norm m1_s) (frobenius_norm m1); - in - - let test_mv () = - let y = Vec.random d2 in - let z = Vec.random d1 in - let x3 = gemv x1 y in - let x4 = gemv ~trans:`T x1 z in - let v = Vector.dense_of_vec y in - let v2 = Vector.dense_of_vec z in - let v3 = Vector.dense_of_vec x3 in - let v4 = Vector.dense_of_vec x4 in - let v_s = Vector.sparse_of_vec y in - let v2_s = Vector.sparse_of_vec z in - let norm_diff v1 v2 = - Vec.sub (Vector.to_vec v1) (Vector.to_vec v2) - |> nrm2 - in - Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (mv m1 v) v3); - Alcotest.(check (float 1.e-10)) "dense dense 2" 0. (norm_diff (mv ~trans:`T m1 v2) v4); - - Alcotest.(check (float 1.e-10)) "dense sparse 3" 0. (norm_diff (mv m1 v_s) v3); - Alcotest.(check (float 1.e-10)) "dense sparse 4" 0. (norm_diff (mv ~trans:`T m1 v2_s) v4); - - Alcotest.(check (float 1.e-10)) "sparse dense 5" 0. (norm_diff (mv m1_s v) v3); - Alcotest.(check (float 1.e-10)) "sparse dense 6" 0. (norm_diff (mv ~trans:`T m1_s v2) v4); - - Alcotest.(check (float 1.e-10)) "sparse sparse 7" 0. (norm_diff (mv m1_s v_s) v3); - Alcotest.(check (float 1.e-10)) "sparse sparse 8" 0. (norm_diff (mv ~trans:`T m1_s v2_s) v4); - in - - let test_mm () = - let x3 = gemm x1 x2 in - let m3 = dense_of_mat x3 - and m3_s = sparse_of_mat x3 - and m4 = dense_of_mat x1 |> transpose - and m4_s = sparse_of_mat x1 |> transpose - and m5 = dense_of_mat x2 |> transpose - and m5_s = sparse_of_mat x2 |> transpose - in - let c1 = of_fun (Mat.dim1 x1) (Mat.dim2 x1) (fun i j -> x1.{i,j}) in - let c2 = of_fun (Mat.dim1 x2) (Mat.dim2 x2) (fun i j -> x2.{i,j}) in - let c3 = of_fun (Mat.dim1 x3) (Mat.dim2 x3) (fun i j -> x3.{i,j}) in - let c4 = of_fun (dim1 m4) (dim2 m4) (fun i j -> get m4 i j ) in - let c5 = of_fun (dim1 m5) (dim2 m5) (fun i j -> get m5 i j ) in - Alcotest.(check (float 1.e-10)) "dense dense 0" 0. (norm_diff m3 c3); - Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (mm m1 m2) m3); - Alcotest.(check (float 1.e-10)) "dense dense 2" 0. (norm_diff (mm c1 c2) m3); - Alcotest.(check (float 1.e-10)) "dense dense 3" 0. (norm_diff (mm c1 m2) m3); - Alcotest.(check (float 1.e-10)) "dense dense 4" 0. (norm_diff (mm c1 m2_s) m3); - Alcotest.(check (float 1.e-10)) "dense dense 5" 0. (norm_diff (mm m1 c2) m3); - Alcotest.(check (float 1.e-10)) "dense dense 6" 0. (norm_diff (mm m1_s c2) m3); - Alcotest.(check (float 1.e-10)) "dense dense 7" 0. (norm_diff (mm ~transa:`T m4 m2) m3); - Alcotest.(check (float 1.e-10)) "dense dense 8" 0. (norm_diff (mm ~transa:`T c4 m2) m3); - Alcotest.(check (float 1.e-10)) "dense dense 9" 0. (norm_diff (mm ~transb:`T m1 m5) m3); - Alcotest.(check (float 1.e-10)) "dense dense 10" 0. (norm_diff (mm ~transb:`T m1 c5) m3); - Alcotest.(check (float 1.e-10)) "dense dense 11" 0. (norm_diff (mm ~transa:`T ~transb:`T m2 m1) (transpose m3)); - - Alcotest.(check (float 1.e-10)) "dense sparse 12" 0. (norm_diff (mm m1 m2_s) m3_s); - Alcotest.(check (float 1.e-10)) "dense sparse 13" 0. (norm_diff (mm ~transa:`T m4 m2_s) m3_s); - Alcotest.(check (float 1.e-10)) "dense sparse 14" 0. (norm_diff (mm ~transa:`T c4 m2_s) m3_s); - Alcotest.(check (float 1.e-10)) "dense sparse 15" 0. (norm_diff (mm ~transb:`T m1 m5_s) m3_s); - Alcotest.(check (float 1.e-10)) "dense sparse 16" 0. (norm_diff (transpose (mm m2 m1_s ~transa:`T ~transb:`T)) m3_s); - - Alcotest.(check (float 1.e-10)) "sparse dense 17" 0. (norm_diff (mm m1_s m2) m3_s); - Alcotest.(check (float 1.e-10)) "sparse dense 18" 0. (norm_diff (mm ~transa:`T m4_s m2) m3_s); - Alcotest.(check (float 1.e-10)) "sparse dense 19" 0. (norm_diff (mm ~transb:`T m1_s m5) m3_s); - Alcotest.(check (float 1.e-10)) "sparse dense 20" 0. (norm_diff (mm ~transb:`T m1_s c5) m3_s); - Alcotest.(check (float 1.e-10)) "sparse dense 21" 0. (norm_diff (transpose (mm m2_s m1 ~transa:`T ~transb:`T)) m3_s); - - Alcotest.(check (float 1.e-10)) "sparse sparse 22" 0. (norm_diff (mm m1_s m2_s) m3_s); - Alcotest.(check (float 1.e-10)) "sparse sparse 23" 0. (norm_diff (mm ~transa:`T m4_s m2_s) m3_s); - Alcotest.(check (float 1.e-10)) "sparse sparse 24" 0. (norm_diff (mm ~transb:`T m1_s m5_s) m3_s); - Alcotest.(check (float 1.e-10)) "sparse sparse 25" 0. (norm_diff (transpose (mm m2_s m1_s ~transa:`T ~transb:`T)) m3_s); - in - - let test_solve () = - let x1 = Mat.map (fun x -> if abs_float x < 0.6 then 0. else x) (Mat.random 30 30) - and x2 = Mat.map (fun x -> if abs_float x < 0.3 then 0. else x) (Mat.random 30 5) - in - - let m1 = dense_of_mat x1 - and m2 = dense_of_mat x2 - in - - let m1_s = sparse_of_mat x1 - and m2_s = sparse_of_mat x2 - in - - let a = m1 and b = m2 in - let x = ax_eq_b a b in - Alcotest.(check (float 1.e-10)) "dense dense 1" 0. (norm_diff (mm a x) b); - - let a = m1 and b = m2_s in - let x = ax_eq_b a b in - Alcotest.(check (float 1.e-10)) "dense sparse 2" 0. (norm_diff (mm a x) b); - - let a = m1_s and b = m2 in - let x = ax_eq_b a b in - Alcotest.(check (float 1.e-10)) "sparse dense 3" 0. (norm_diff (mm a x) b); - - let a = m1_s and b = m2_s in - let x = ax_eq_b a b in - Alcotest.(check (float 1.e-10)) "sparse sparse 4" 0. (norm_diff (mm a x) b); - in - - let test_split_join () = - let m1_split = split_cols 7 m1 in - let m1_s_split = split_cols 7 m1_s in - let m2 = join_cols m1_split in - let m2_s = join_cols m1_s_split in - Alcotest.(check int) "length" 6 (List.length m1_split); - Alcotest.(check int) "length" 6 (List.length m1_s_split); - Alcotest.(check bool) "join" true (m1 = m2); - Alcotest.(check bool) "join" true (m1_s = m2_s); - in - [ - "Conversion", `Quick, test_conversion; - "Dimensions", `Quick, test_dimensions; - "Transposition", `Quick, test_transpose; - "Outer product", `Quick, test_outer; - "Add sub", `Quick, test_add_sub; - "Matrix Vector", `Quick, test_mv; - "Matrix Matrix", `Quick, test_mm; - "Linear solve", `Quick, test_solve; - "split_join", `Quick, test_split_join; - ] - diff --git a/Utils/Matrix.mli b/Utils/Matrix.mli deleted file mode 100644 index 971b3f3..0000000 --- a/Utils/Matrix.mli +++ /dev/null @@ -1,101 +0,0 @@ -(* Sparse or dense matrices *) - -open Lacaml.D - -type t - -(** {1 Accessors} *) - -val is_sparse : t -> bool -(** True is the matrix is sparse. *) - -val is_dense : t -> bool -(** True is the matrix is dense. *) - -val dim1 : t -> int -(** First dimension of the matrix *) - -val dim2 : t -> int -(** Secons dimension of the matrix *) - -val get : t -> int -> int -> float -(** [get m i j] returns {% $\mathbf{m}_{ij}$ %}. *) - - -(** {1 Converters } *) - -val to_mat : t -> Mat.t -(** Convert into a Lacaml Mat. *) - -val to_vector_array : ?threshold:float -> t -> Vector.t array -(** Convert the matrix into an array of column vectors. *) - -val of_fun : int -> int -> (int -> int -> float) -> t -(** [of_fun m n f] creates a computed matrix of dimension m times n, where the function - [f i j] is called to evaluate element [i j] *) - -val sparse_of_dense : ?threshold:float -> t -> t -(** Creates a sparse matrix from a dense matrix. Default threshold is {!Constants.epsilon}. *) - -val sparse_of_computed : ?threshold:float -> t -> t -(** Creates a sparse matrix from a computed matrix. *) - -val dense_of_computed : t -> t -(** Creates a dense matrix from a computed matrix. *) - -val dense_of_sparse : t -> t -(** Creates a dense matrix from a sparse matrix. *) - -val dense_of_mat : Mat.t -> t -(** Create a dense matrix from a Lacaml Mat *) - -val sparse_of_mat : ?threshold:float -> Lacaml.D.Mat.t -> t -(** Create a sparse matrix from a Lacaml Mat. Default threshold is {!Constants.epsilon}. *) - -val sparse_of_vector_array : Vector.t array -> t -(** Create a sparse matrix from an array of column vectors. *) - -val transpose : t -> t -(** Returns the transposed matrix. *) - -val split_cols : int -> t -> t list -(** [split_cols n m_M] Split the matrix [m_M] by packs of [n] columns *) - -val join_cols : t list -> t -(** [join_cols l] Joins the list of matrices into a single matrix (along columns). *) - - -(** {1 Operations} *) - -val outer_product : ?threshold:float -> Vector.t -> Vector.t -> t -(** Creates the matrix formed by the outer product of two vectors. *) - -val mm : ?transa:trans3 -> ?transb:trans3 -> ?threshold:float -> t -> t -> t -(** Matrix multiplication *) - -val mv : ?sparse:bool -> ?trans:trans3 -> ?threshold:float -> t -> Vector.t -> Vector.t -(** Matrix Vector product *) - -val ax_eq_b : ?trans:trans3 -> t -> t -> t -(** Solves A.X = B or A'.X = B *) - -val add : t -> t -> t -(** Add two matrices *) - -val sub : t -> t -> t -(** Subtract two matrices *) - - -(** {1 Parallel routines } *) - -val parallel_mm : ?transa:trans3 -> ?transb:trans3 -> ?threshold:float -> t -> t -> t -(** Matrix multiplication, parallelized by splitting b along the columns. *) - -(** {1 Printers } *) - -val pp : Format.formatter -> t -> unit - - -(** {1 Unit testing} *) - -val test_case : unit -> (string * [> `Quick ] * (unit -> unit)) list diff --git a/Utils/Point.mli b/Utils/Point.mli deleted file mode 100644 index 8ccd5aa..0000000 --- a/Utils/Point.mli +++ /dev/null @@ -1,10 +0,0 @@ -(** A point in a 3D space. Used by {!Angstrom.t} and {!Bohr.t}. - *) - -type t = { - x : float ; - y : float ; - z : float ; -} - - diff --git a/Utils/Printing.ml b/Utils/Printing.ml deleted file mode 100644 index 74afb7e..0000000 --- a/Utils/Printing.ml +++ /dev/null @@ -1,7 +0,0 @@ -let line ?(c='-') n = - String.make n c - -let ppf_dev_null = - let oc = open_out "/dev/null" in - Format.formatter_of_out_channel oc - diff --git a/Utils/Vector.ml b/Utils/Vector.ml deleted file mode 100644 index b6334b9..0000000 --- a/Utils/Vector.ml +++ /dev/null @@ -1,330 +0,0 @@ -open Lacaml.D - -let epsilon = Constants.epsilon - -type index_value = - { - index: int; - value: float - } - -type sparse_vector = - { - n: int; - v: index_value array - } - -type t = - | Dense of Vec.t - | Sparse of sparse_vector - - -let is_sparse = function - | Sparse _ -> true - | Dense _ -> false - - -let is_dense = function - | Sparse _ -> false - | Dense _ -> true - - -exception Found of float - -let get = function - | Dense v -> (fun i -> v.{i}) - | Sparse { n ; v } -> (fun i -> - if i < 1 || i > n then invalid_arg "index out of bounds"; - try - Array.iter (fun {index ; value} -> - if index=i then - raise (Found value)) v; - raise Not_found - with - | Not_found -> 0. - | Found x -> x - ) - - - -let dim = function - | Dense v -> Vec.dim v - | Sparse {n ; v} -> n - - -let sparse_of_dense ?(threshold=epsilon) = function - | Sparse _ -> invalid_arg "Expected a dense vector" - | Dense v -> - let rec aux accu = function - | 0 -> accu |> Array.of_list - | i -> - let x = v.{i} in - if abs_float x < threshold then - (aux [@tailcall]) accu (i-1) - else - (aux [@tailcall]) ({index=i ; value=x}::accu) (i-1) - in - let n = Vec.dim v in - Sparse { n ; v=aux [] n } - - -let rec to_assoc_list ?(threshold=epsilon) = function - | Sparse {n ; v} -> Array.map (fun {index ; value} -> (index, value)) v |> Array.to_list - | Dense v -> to_assoc_list @@ sparse_of_dense ~threshold (Dense v) - - -let dense_of_sparse = function - | Dense _ -> invalid_arg "Expected a sparse vector" - | Sparse {n ; v} -> - let v' = Vec.make0 n in - Array.iter (fun {index ; value} -> v'.{index} <- value) v; - Dense v' - - -let dense_of_vec v = Dense v - - -let sparse_of_vec ?(threshold=epsilon) v = - dense_of_vec v - |> sparse_of_dense ~threshold - - -let sparse_of_assoc_list n v = - Sparse { n ; - v = Array.of_list v - |> Array.map (fun (index, value) -> {index ; value}) - } - - -let rec to_vec = function - | Dense v -> v - | Sparse v -> dense_of_sparse (Sparse v) |> to_vec - - - -let scale ?(threshold=epsilon) x = function - | Dense v -> let v' = copy v in (scal x v'; Dense v') - | Sparse {n ; v} -> - Sparse {n ; v = Array.map (fun {index ; value} -> { index ; value=x *. value} ) v } - - -let rec neg = function - | Dense v -> Dense (Vec.neg v) - | Sparse {n ; v} -> - Sparse {n ; v = Array.map (fun {index ; value} -> {index ; value = -. value}) v} - - - -let axpy ?(threshold=epsilon) ?(alpha=1.) x y = - if dim x <> dim y then - invalid_arg "Inconsistent dimensions"; - - match x, y with - | Dense x , Dense y -> Dense (let y = copy y in axpy ~alpha x y ; y) - | Sparse {n ; v}, Dense y -> - begin - let v' = copy y in - Array.iter (fun {index ; value} -> v'.{index} <- v'.{index} +. alpha *. value) v; - sparse_of_vec ~threshold v' - end - | Dense x , Sparse {n ; v} -> - begin - let v' = copy x in - scal alpha v'; - Array.iter (fun {index ; value} -> v'.{index} <- v'.{index} +. value) v; - sparse_of_vec ~threshold v' - end - | Sparse {n ; v}, Sparse {n=n' ; v=v'} -> - begin - let rec aux accu k l = - match k < Array.length v, l < Array.length v' with - | true, true -> - begin - let {index=i ; value=x} = v.(k) - and {index=j ; value=y} = v'.(l) - in - match compare i j with - | -1 -> - let z = alpha *. x in - let new_accu = - if abs_float z > threshold then - {index=i ; value=z} :: accu - else - accu - in (aux [@tailcall]) new_accu (k+1) l - | 1 -> - let new_accu = - if abs_float y > threshold then - {index=j ; value=y} :: accu - else - accu - in (aux [@tailcall]) new_accu k (l+1) - | 0 -> - let z = alpha *. x +. y in - let new_accu = - if abs_float z > threshold then - {index=i ; value=z} :: accu - else - accu - in (aux [@tailcall]) new_accu (k+1) (l+1) - | _ -> assert false - end - - | true, false -> - let {index=i ; value=x} = v.(k) in - (aux [@tailcall]) ({index=i ; value=alpha *. x}::accu) (k+1) l - - | false, true -> - (aux [@tailcall]) (v'.(l)::accu) k (l+1) - - | false, false -> {n ; v=List.rev accu |> Array.of_list} - in - Sparse (aux [] 0 0) - end - -let add = axpy ~alpha:1. - -let sub ?(threshold=epsilon) x y = add ~threshold x @@ neg y - -let pp ppf = function - | Dense m -> Util.pp_float_array ppf @@ Vec.to_array m - | Sparse {n ; v} -> - begin - Format.fprintf ppf "@[[ %d | " n; - Array.iter (fun {index ; value} -> Format.fprintf ppf "@[(%d, %f); @]" index value) v; - Format.fprintf ppf "]@]" - end - - - -let dot v v' = - - let d_d v v' = - dot v v' - in - - let d_sp v' {n ; v} = - if n <> Vec.dim v' then - invalid_arg "Inconsistent dimensions"; - Array.fold_left (fun accu {index ; value} -> accu +. value *. v'.{index}) 0. v - in - - let sp_sp {n ; v} {n=n' ; v=v'} = - if n <> n' then - invalid_arg "Inconsistent dimensions"; - - let rec aux accu k l = - match Array.length v > k, Array.length v' > l with - | true, true -> - let {index=i ; value=x} = v.(k) - and {index=j ; value=y} = v'.(l) - in - begin - match compare i j with - | -1 -> (aux [@tailcall]) accu (k+1) l - | 1 -> (aux [@tailcall]) accu k (l+1) - | 0 -> (aux [@tailcall]) (accu +. x *. y) (k+1) (l+1) - | _ -> assert false - end - | _ -> accu - in - aux 0. 0 0 - in - - match v, v' with - | (Dense v), (Dense v') -> d_d v v' - | (Sparse v), (Sparse v') -> sp_sp v v' - | (Dense v), (Sparse v') -> d_sp v v' - | (Sparse v), (Dense v') -> d_sp v' v - - -let norm v = sqrt @@ dot v v - -let test_case () = - - let x1 = Vec.map (fun x -> if abs_float x < 0.6 then 0. else x) (Vec.random 100) - and x2 = Vec.map (fun x -> if abs_float x < 0.3 then 0. else x) (Vec.random 100) - in - let x3 = Vec.map (fun x -> 2. *. x) x1 - and x4 = Vec.add x1 x2 - and x5 = Vec.sub x1 x2 - and x6 = - let v = copy x2 in - Lacaml.D.axpy ~alpha:3. x1 v; - v - in - - let v1 = dense_of_vec x1 - and v2 = dense_of_vec x2 - and v3 = dense_of_vec x3 - and v4 = dense_of_vec x4 - and v5 = dense_of_vec x5 - and v6 = dense_of_vec x6 - in - - let v1_s = sparse_of_vec x1 - and v2_s = sparse_of_vec x2 - and v3_s = sparse_of_vec x3 - and v4_s = sparse_of_vec x4 - and v5_s = sparse_of_vec x5 - and v6_s = sparse_of_vec x6 - in - - let zero = dense_of_vec (Vec.make0 100) - and zero_s = sparse_of_vec (Vec.make0 100) - in - - let test_conversion () = - Alcotest.(check bool) "sparse -> dense 1" true (dense_of_sparse v1_s = v1 ); - Alcotest.(check bool) "sparse -> dense 2" true (dense_of_sparse v2_s = v2 ); - Alcotest.(check bool) "dense -> sparse 1" true (sparse_of_dense v1 = v1_s); - Alcotest.(check bool) "dense -> sparse 2" true (sparse_of_dense v2 = v2_s); - in - let test_operations () = - Alcotest.(check bool) "dense scale" true (scale 2. v1 = v3); - Alcotest.(check bool) "sparse scale" true (scale 2. v1_s = v3_s); - - Alcotest.(check bool) "dense dense add" true (add v1 v2 = v4); - Alcotest.(check bool) "dense sparse add" true (add v1 v2_s = v4_s); - Alcotest.(check bool) "sparse dense add" true (add v1_s v2 = v4_s); - Alcotest.(check bool) "sparse dense add" true (add v1 v2_s = v4_s); - Alcotest.(check bool) "sparse sparse add" true (add v1_s v2_s = v4_s); - - Alcotest.(check bool) "dense dense sub" true (sub v1 v2 = v5); - Alcotest.(check bool) "dense sparse sub" true (sub v1 v2_s = v5_s); - Alcotest.(check bool) "sparse dense sub" true (sub v1_s v2 = v5_s); - Alcotest.(check bool) "sparse dense sub" true (sub v1 v2_s = v5_s); - Alcotest.(check bool) "sparse sparse sub" true (sub v1_s v2_s = v5_s); - - Alcotest.(check bool) "dense dense sub" true (sub v1 v1 = zero); - Alcotest.(check bool) "dense sparse sub" true (sub v1 v1_s = zero_s); - Alcotest.(check bool) "sparse dense sub" true (sub v1_s v1 = zero_s); - Alcotest.(check bool) "sparse sparse sub" true (sub v1_s v1_s = zero_s); - - Alcotest.(check bool) "dense dense axpy" true (axpy ~alpha:3. v1 v2 = v6); - Alcotest.(check bool) "dense sparse axpy" true (sub ~threshold:1.e-12 (axpy ~alpha:3. v1 v2_s) v6_s = zero_s); - Alcotest.(check bool) "sparse dense axpy" true (sub ~threshold:1.e-12 (axpy ~alpha:3. v1_s v2) v6_s = zero_s); - - Alcotest.(check bool) "sparse sparse axpy" true (sub ~threshold:1.e-12 (axpy ~alpha:3. v1_s v2_s) v6_s = zero_s); - in - let test_dot () = - let d1d2 = Lacaml.D.dot x1 x2 - and d1d1 = Lacaml.D.dot x1 x1 - and d2d2 = Lacaml.D.dot x2 x2 - in - Alcotest.(check (float 1.e-10)) "sparse x dense 1" (dot v1_s v2 ) d1d2; - Alcotest.(check (float 1.e-10)) "sparse x dense 2" (dot v1_s v1 ) d1d1; - Alcotest.(check (float 1.e-10)) "sparse x dense 3" (dot v2_s v2 ) d2d2; - Alcotest.(check (float 1.e-10)) "dense x sparse 1" (dot v1 v2_s) d1d2; - Alcotest.(check (float 1.e-10)) "dense x sparse 2" (dot v1 v1_s) d1d1; - Alcotest.(check (float 1.e-10)) "dense x sparse 3" (dot v2 v2_s) d2d2; - Alcotest.(check (float 1.e-10)) "sparse x sparse 1" (dot v1_s v2_s) d1d2; - Alcotest.(check (float 1.e-10)) "sparse x sparse 2" (dot v1_s v1_s) d1d1; - Alcotest.(check (float 1.e-10)) "sparse x sparse 3" (dot v2_s v2_s) d2d2; - in - [ - "Conversion", `Quick, test_conversion; - "Operations", `Quick, test_operations; - "Dot product", `Quick, test_dot; - ] - diff --git a/Utils/Vector.mli b/Utils/Vector.mli deleted file mode 100644 index 5c3b537..0000000 --- a/Utils/Vector.mli +++ /dev/null @@ -1,78 +0,0 @@ -(* Sparse or dense vectors *) - -open Lacaml.D - -type t - -(** {1 Accessors} *) - -val is_sparse : t -> bool -(** True is the vector is sparse. *) - -val is_dense : t -> bool -(** True is the vector is dense. *) - -val get : t -> int -> float -(** [get v i] returns the i-th element of [v]. *) - -val dim : t -> int -(** Dimension of the vector *) - - -(** {1 Converters } *) - -val to_vec : t -> Vec.t -(** Convert into a Lacaml Vec. *) - -val to_assoc_list : ?threshold:float -> t -> (int * float) list -(** Convert into an association list. *) - -val sparse_of_dense : ?threshold:float -> t -> t -(** Creates a sparse vector from a dense vector. Default threshold is {!Constants.epsilon}. *) - -val dense_of_sparse : t -> t -(** Creates a dense vector from a sparse vector. *) - -val dense_of_vec : Vec.t -> t -(** Create a dense vector from a Lacaml Vec *) - -val sparse_of_vec : ?threshold:float -> Vec.t -> t -(** Create a sparse vector from a Lacaml Vec. Default threshold is {!Constants.epsilon}. *) - -val sparse_of_assoc_list : int -> (int * float) list -> t -(** Create a sparse vector from an association list [(index,value)]. The first integer is - the size of the vector. *) - - - -(** {1 Operations} *) - -val neg : t -> t -(** Returns the negative of the vector. *) - -val scale : ?threshold:float -> float -> t -> t -(** Scale a vector by a constant *) - -val add : ?threshold:float -> t -> t -> t -(** Add two vectors *) - -val sub : ?threshold:float -> t -> t -> t -(** Subtract two vectors *) - -val axpy : ?threshold:float -> ?alpha:float -> t -> t -> t -(** {% $a \mathbf{x} + \mathbf{y}$ %} *) - -val dot : t -> t -> float -(** Dot product. *) - -val norm : t -> float -(** l2-norm of the vector : {% $\sqrt{\sum_i x_i^2}$ %} *) - -(** {1 Printers } *) - -val pp : Format.formatter -> t -> unit - - -(** {1 Unit testing} *) - -val test_case : unit -> (string * [> `Quick ] * (unit -> unit)) list diff --git a/_tags b/_tags deleted file mode 100644 index 94195d5..0000000 --- a/_tags +++ /dev/null @@ -1,13 +0,0 @@ -not <**/*.cma> : linkdep(Utils/math_functions.o), package(str,unix,bigarray,lacaml,alcotest,zarith,getopt) -<**/*.byte> : custom -<**/*.native> : linkdep(Utils/math_functions.o) - : not_hygienic - : include - : include - : include - : include - : include - : include - : include - : include - : include diff --git a/Utils/AngularMomentum.ml b/common/lib/angular_momentum.ml similarity index 93% rename from Utils/AngularMomentum.ml rename to common/lib/angular_momentum.ml index 9345de4..f988c91 100644 --- a/Utils/AngularMomentum.ml +++ b/common/lib/angular_momentum.ml @@ -1,6 +1,6 @@ open Powers -exception AngularMomentumError of string +exception Angular_momentum_error of string type t = | S | P | D | F | G | H | I | J | K | L | M | N | O @@ -14,7 +14,7 @@ let of_char = function | 'k' | 'K' -> K | 'l' | 'L' -> L | 'm' | 'M' -> M | 'n' | 'N' -> N | 'o' | 'O' -> O - | c -> raise (AngularMomentumError (String.make 1 c)) + | c -> raise (Angular_momentum_error (String.make 1 c)) let to_string = function | S -> "S" | P -> "P" @@ -32,7 +32,7 @@ let to_char = function | I -> 'I' | J -> 'J' | K -> 'K' | L -> 'L' | M -> 'M' | N -> 'N' - | O -> 'O' | Int i -> '_' + | O -> 'O' | Int _ -> '_' let to_int = function | S -> 0 | P -> 1 @@ -80,17 +80,17 @@ let zkey_array a = Powers.of_int_tuple (x,y,l-(x+y)) in let rec create_y accu xyz = - let { x ; y ; z } = xyz in + let { x ; y ; z ;_ } = xyz in match y with | 0 -> (create_z xyz)::accu - | i -> let ynew = y-1 in + | _ -> let ynew = y-1 in (create_y [@tailcall]) ( (create_z xyz)::accu) (Powers.of_int_tuple (x,ynew,z)) in let rec create_x accu xyz = - let { x ; y ; z } = xyz in + let { x ; z ;_ } = xyz in match x with | 0 -> (create_y [] xyz)@accu - | i -> let xnew = x-1 in + | _ -> let xnew = x-1 in let ynew = l-xnew in (create_x [@tailcall]) ((create_y [] xyz)@accu) (Powers.of_int_tuple (xnew, ynew, z)) in diff --git a/Utils/AngularMomentum.mli b/common/lib/angular_momentum.mli similarity index 75% rename from Utils/AngularMomentum.mli rename to common/lib/angular_momentum.mli index 4e23e52..0206eef 100644 --- a/Utils/AngularMomentum.mli +++ b/common/lib/angular_momentum.mli @@ -4,26 +4,26 @@ type t = | S | P | D | F | G | H | I | J | K | L | M | N | O | Int of int -exception AngularMomentumError of string -(** Raised when the {!AngularMomentum.t} element can't be created. +exception Angular_momentum_error of string +(** Raised when the {!Angular_momentum.t} element can't be created. *) val of_char : char -> t -(** Returns an {!AngularMomentum.t} when a shell is given as a character (case +(** Returns an {!Angular_momentum.t} when a shell is given as a character (case insensitive). Example: {[ - AngularMomentum.of_char 'p' -> AngularMomentum.P + Angular_momentum.of_char 'p' -> Angular_momentum.P ]} *) val to_string : t -> string (** {[ - AngularMomentum.(to_string D) -> "D" + Angular_momentum.(to_string D) -> "D" ]} *) @@ -31,7 +31,7 @@ val to_string : t -> string val to_char : t -> char (** {[ - AngularMomentum.(to_char D) -> 'D' + Angular_momentum.(to_char D) -> 'D' ]} *) @@ -43,7 +43,7 @@ val to_int : t -> int Example: {[ - AngularMomentum.to_int D -> 2 + Angular_momentum.to_int D -> 2 ]} *) @@ -54,7 +54,7 @@ val of_int : int -> t Example: {[ - AngularMomentum.of_int 3 -> AngularMomentum.F + Angular_momentum.of_int 3 -> Angular_momentum.F ]} *) @@ -71,7 +71,7 @@ val n_functions : t -> int Example: {[ - AngularMomentum.n_functions D -> 6 + Angular_momentum.n_functions D -> 6 ]} *) @@ -83,7 +83,7 @@ val zkey_array : kind -> Zkey.t array Example: {[ - AngularMomentum.( zkey_array Doublet (P,S) ) -> + Angular_momentum.( zkey_array Doublet (P,S) ) -> [| {Zkey.left = 0; right = 1125899906842624} ; {Zkey.left = 0; right = 1099511627776} ; {Zkey.left = 0; right = 1073741824} |] diff --git a/Utils/Bitstring.ml b/common/lib/bitstring.ml similarity index 67% rename from Utils/Bitstring.ml rename to common/lib/bitstring.ml index 066e5ed..889ffdd 100644 --- a/Utils/Bitstring.ml +++ b/common/lib/bitstring.ml @@ -181,7 +181,7 @@ let rec to_list ?(accu=[]) = function Bit twiddling hacks}. Example: {[ - bit_permtutations 2 4 = [ 0011 ; 0101 ; 0110 ; 1001 ; 1010 ; 1100 ] + permtutations 2 4 = [ 0011 ; 0101 ; 0110 ; 1001 ; 1010 ; 1100 ] ]} *) let permtutations m n = @@ -203,43 +203,4 @@ let permtutations m n = aux (Util.binom n m) (minus_one (shift_left_one n m)) [] -(*-----------------------------------------------------------------------------------*) - -let test_case () = - - let test_one_many () = - let x = 8745687 in - let z = Z.of_int 8745687 in - let one_x = One x in - let many_x = Many z in - Alcotest.(check bool) "of_x" true (one_x = (of_int x)); - Alcotest.(check bool) "of_z" true (one_x = (of_z z)); - Alcotest.(check bool) "shift_left1" true (One (x lsl 3) = shift_left one_x 3); - Alcotest.(check bool) "shift_left2" true (Many (Z.shift_left z 3) = shift_left many_x 3); - Alcotest.(check bool) "shift_left3" true (Many (Z.shift_left z 100) = shift_left many_x 100); - Alcotest.(check bool) "shift_right1" true (One (x lsr 3) = shift_right one_x 3); - Alcotest.(check bool) "shift_right2" true (Many (Z.shift_right z 3) = shift_right many_x 3); - Alcotest.(check bool) "shift_left_one1" true (One (1 lsl 3) = shift_left_one 4 3); - Alcotest.(check bool) "shift_left_one2" true (Many (Z.shift_left Z.one 200) = shift_left_one 300 200); - Alcotest.(check bool) "testbit1" true (testbit (One 8) 3); - Alcotest.(check bool) "testbit2" false (testbit (One 8) 2); - Alcotest.(check bool) "testbit3" false (testbit (One 8) 4); - Alcotest.(check bool) "testbit4" true (testbit (Many (Z.of_int 8)) 3); - Alcotest.(check bool) "testbit5" false (testbit (Many (Z.of_int 8)) 2); - Alcotest.(check bool) "testbit6" false (testbit (Many (Z.of_int 8)) 4); - Alcotest.(check bool) "logor1" true (One (1 lor 2) = logor (One 1) (One 2)); - Alcotest.(check bool) "logor2" true (Many (Z.of_int (1 lor 2)) = logor (Many Z.one) (Many (Z.of_int 2))); - Alcotest.(check bool) "logxor1" true (One (1 lxor 2) = logxor (One 1) (One 2)); - Alcotest.(check bool) "logxor2" true (Many (Z.of_int (1 lxor 2)) = logxor (Many Z.one) (Many (Z.of_int 2))); - Alcotest.(check bool) "logand1" true (One (1 land 2) = logand (One 1) (One 2)); - Alcotest.(check bool) "logand2" true (Many (Z.of_int (1 land 2)) = logand (Many Z.one) (Many (Z.of_int 2))); - Alcotest.(check bool) "to_list" true ([ 1 ; 3 ; 4 ; 6 ] = (to_list (One 45))); - in - - [ - "One-many", `Quick, test_one_many; - ] - - - diff --git a/Utils/Charge.ml b/common/lib/charge.ml similarity index 100% rename from Utils/Charge.ml rename to common/lib/charge.ml diff --git a/Utils/Charge.mli b/common/lib/charge.mli similarity index 100% rename from Utils/Charge.mli rename to common/lib/charge.mli diff --git a/Utils/Command_line.ml b/common/lib/command_line.ml similarity index 98% rename from Utils/Command_line.ml rename to common/lib/command_line.ml index 1dd5789..ca89677 100644 --- a/Utils/Command_line.ml +++ b/common/lib/command_line.ml @@ -166,7 +166,7 @@ let set_specs specs_in = let cmd_specs = List.filter (fun x -> x.short != ' ') !specs - |> List.map (fun { short ; long ; opt ; doc ; arg } -> + |> List.map (fun { short ; long ; arg ; _ } -> match arg with | With_arg _ -> (short, long, None, Some (fun x -> Hashtbl.replace dict long x) ) diff --git a/Utils/Constants.ml b/common/lib/constants.ml similarity index 100% rename from Utils/Constants.ml rename to common/lib/constants.ml diff --git a/Utils/Constants.mli b/common/lib/constants.mli similarity index 100% rename from Utils/Constants.mli rename to common/lib/constants.mli diff --git a/Utils/Coordinate.ml b/common/lib/coordinate.ml similarity index 100% rename from Utils/Coordinate.ml rename to common/lib/coordinate.ml diff --git a/Utils/Coordinate.mli b/common/lib/coordinate.mli similarity index 100% rename from Utils/Coordinate.mli rename to common/lib/coordinate.mli diff --git a/common/lib/dune b/common/lib/dune new file mode 100644 index 0000000..777cb5b --- /dev/null +++ b/common/lib/dune @@ -0,0 +1,17 @@ +; name = name of the supermodule that will wrap all source files as submodules +; public_name = name of the library for ocamlfind and opam +(library + (name qcaml_common) + (public_name qcaml.common) + (libraries + zarith + getopt + ) + (c_names + math_functions + ) + (c_flags + (:standard) + -Ofast -march=native -fPIC + ) + (synopsis "General utilities used in all QCaml libraries.")) diff --git a/Utils/math_functions.c b/common/lib/math_functions.c similarity index 100% rename from Utils/math_functions.c rename to common/lib/math_functions.c diff --git a/Utils/NonNegativeFloat.ml b/common/lib/non_negative_float.ml similarity index 100% rename from Utils/NonNegativeFloat.ml rename to common/lib/non_negative_float.ml diff --git a/Utils/NonNegativeFloat.mli b/common/lib/non_negative_float.mli similarity index 100% rename from Utils/NonNegativeFloat.mli rename to common/lib/non_negative_float.mli diff --git a/Utils/Powers.ml b/common/lib/powers.ml similarity index 100% rename from Utils/Powers.ml rename to common/lib/powers.ml diff --git a/Utils/Powers.mli b/common/lib/powers.mli similarity index 100% rename from Utils/Powers.mli rename to common/lib/powers.mli diff --git a/common/lib/qcaml.ml b/common/lib/qcaml.ml new file mode 100644 index 0000000..dcccf10 --- /dev/null +++ b/common/lib/qcaml.ml @@ -0,0 +1,17 @@ +let name = "QCaml" + + +let root = + let rec chop = function + | [] -> raise Not_found + | x :: _ as l when x = name -> l + | _ :: rest -> chop rest + in + String.split_on_char Filename.dir_sep.[0] (Sys.getcwd ()) + |> List.rev + |> chop + |> List.rev + |> String.concat Filename.dir_sep + + + diff --git a/common/lib/qcaml.mli b/common/lib/qcaml.mli new file mode 100644 index 0000000..025fa67 --- /dev/null +++ b/common/lib/qcaml.mli @@ -0,0 +1,6 @@ + +val name : string +(** Name of the QCaml source directory on the file system. *) + +val root : string +(** Path to the QCaml source directory. *) diff --git a/Utils/Range.ml b/common/lib/range.ml similarity index 100% rename from Utils/Range.ml rename to common/lib/range.ml diff --git a/Utils/Range.mli b/common/lib/range.mli similarity index 100% rename from Utils/Range.mli rename to common/lib/range.mli diff --git a/Utils/Spin.ml b/common/lib/spin.ml similarity index 100% rename from Utils/Spin.ml rename to common/lib/spin.ml diff --git a/Utils/Spin.mli b/common/lib/spin.mli similarity index 100% rename from Utils/Spin.mli rename to common/lib/spin.mli diff --git a/Utils/Util.ml b/common/lib/util.ml similarity index 64% rename from Utils/Util.ml rename to common/lib/util.ml index 4309fe1..a225d1b 100644 --- a/Utils/Util.ml +++ b/common/lib/util.ml @@ -3,7 +3,6 @@ (** {1 Functions from libm} *) open Constants -open Lacaml.D @@ -67,6 +66,8 @@ let factmax = 150 sha, Tokyo, 1991) p.227 [in Japanese] *) let incomplete_gamma ~alpha x = + assert (alpha >= 0.); + assert (x >= 0.); let a = alpha in let a_inv = 1./. a in let gf = gamma_float alpha in @@ -197,6 +198,7 @@ let chop f g = {% $F_m(t) = \frac{ 2t\, F_{m+1}(t) + e^{-t} }{2m+1}$ %} *) let boys_function ~maxm t = + assert (t >= 0.); match maxm with | 0 -> begin @@ -206,6 +208,7 @@ let boys_function ~maxm t = end | _ -> begin + assert (maxm > 0); let result = Array.init (maxm+1) (fun m -> 1. /. float_of_int (2*m+1)) in @@ -217,7 +220,7 @@ let boys_function ~maxm t = let dm = 0.5 +. n in let f = (pow t_inv power_t_inv ) in match classify_float f with - | FP_normal -> (incomplete_gamma dm t) *. 0.5 *. f + | FP_normal -> (incomplete_gamma ~alpha:dm t) *. 0.5 *. f | FP_zero | FP_subnormal -> 0. | _ -> raise Exit @@ -313,95 +316,13 @@ let array_range first last = Array.init (last-first+1) (fun i -> i+first) -(** {2 Linear algebra} *) - - let array_sum a = Array.fold_left ( +. ) 0. a let array_product a = - Array.fold_left ( *. ) 0. a + Array.fold_left ( *. ) 1. a -let diagonalize_symm m_H = - let m_V = lacpy m_H in - let result = - syevd ~vectors:true m_V - in - m_V, result - -let xt_o_x ~o ~x = - gemm o x - |> gemm ~transa:`T x - -let x_o_xt ~o ~x = - gemm o x ~transb:`T - |> gemm x - -let remove_epsilons m = - let vecs = - Mat.to_col_vecs m - in - Array.map (fun v -> - let m = abs_float (2. *. amax v) in - Vec.map (fun x -> if abs_float x < m *. epsilon_float then 0. else x) v - ) vecs - |> Mat.of_col_vecs - -let canonical_ortho ?thresh:(thresh=1.e-6) ~overlap c = - let d, u, _ = gesvd (lacpy overlap) in - let d_sqrt = Vec.sqrt d in - let n = (* Number of non-negligible singular vectors *) - Vec.fold (fun accu x -> if x > thresh then accu + 1 else accu) 0 d - in - let d_inv_sq = (* D^{-1/2} *) - Vec.map (fun x -> - if x >= thresh then 1. /. x - else 0. ) ~y:d d_sqrt - in - if n < Vec.dim d_sqrt then - Printf.printf "Removed linear dependencies below %f\n" (1. /. d.{n}) - ; - Mat.scal_cols u d_inv_sq ; - gemm c u - - -let qr_ortho m = - (** Performed twice for precision *) - let result = lacpy m in - let tau = geqrf result in - orgqr ~tau result; - let tau = geqrf result in - orgqr ~tau result; - result - - -let normalize v = - let result = copy v in - scal (1. /. (nrm2 v)) result; - result - - -let normalize_mat m = - Mat.to_col_vecs m - |> Array.map (fun v -> normalize v) - |> Mat.of_col_vecs - - -(** {2 Bitstring functions} *) -let bit_permtutations m n = - - let rec aux k u rest = - if k=1 then - List.rev (u :: rest) - else - let t = Z.(logor u (u-one)) in - let t' = Z.(t+one) in - let t'' = Z.(shift_right ((logand (lognot t) t') - one)) (Z.trailing_zeros u + 1) in - (aux [@tailcall]) (k-1) (Z.logor t' t'') (u :: rest) - in - aux (binom n m) Z.(shift_left one m - one) [] - (** {2 Printers} *) @@ -425,26 +346,6 @@ let pp_float_2darray_size ppf a = Array.iter (fun f -> Format.fprintf ppf "@[%a@]@ " pp_float_array_size f) a; Format.fprintf ppf "]@]@]" -let pp_matrix ppf m = - let open Lacaml.Io in - let rows = Mat.dim1 m - and cols = Mat.dim2 m - in - let rec aux first last = - if (first <= last) then begin - Format.fprintf ppf "@[\n\n %a@]@ " (Lacaml.Io.pp_lfmat - ~row_labels: - (Array.init rows (fun i -> Printf.sprintf "%d " (i + 1))) - ~col_labels: - (Array.init (min 5 (cols-first+1)) (fun i -> Printf.sprintf "-- %d --" (i + first) )) - ~print_right:false - ~print_foot:false - () ) (lacpy ~ac:first ~n:(min 5 (cols-first+1)) m); - (aux [@tailcall]) (first+5) last - end - in - aux 1 cols - let pp_bitstring n ppf bs = String.init n (fun i -> if (Z.testbit bs i) then '+' else '-') @@ -453,71 +354,3 @@ let pp_bitstring n ppf bs = -let string_of_matrix m = - Format.asprintf "%a" pp_matrix m - -let debug_matrix name a = - Format.printf "@[%s =\n@[%a@]@]@." name pp_matrix a - - -let matrix_of_file filename = - let ic = Scanf.Scanning.open_in filename in - let rec read_line accu = - let result = - try - Some (Scanf.bscanf ic " %d %d %f" (fun i j v -> - (i,j,v) :: accu)) - with End_of_file -> None - in - match result with - | Some accu -> (read_line [@tailcall]) accu - | None -> List.rev accu - in - let data = read_line [] in - Scanf.Scanning.close_in ic; - let isize, jsize = - List.fold_left (fun (accu_i,accu_j) (i,j,v) -> - (max i accu_i, max j accu_j)) (0,0) data - in - let result = - Lacaml.D.Mat.of_array - (Array.make_matrix isize jsize 0.) - in - List.iter (fun (i,j,v) -> result.{i,j} <- v) data; - result - - -let sym_matrix_of_file filename = - let result = - matrix_of_file filename - in - for j=1 to Mat.dim1 result do - for i=1 to j do - result.{j,i} <- result.{i,j} - done; - done; - result - - - -let test_case () = - - let test_external () = - Alcotest.(check (float 1.e-15)) "erf" 0.842700792949715 (erf_float 1.0); - Alcotest.(check (float 1.e-15)) "erf" 0.112462916018285 (erf_float 0.1); - Alcotest.(check (float 1.e-15)) "erf" (-0.112462916018285) (erf_float (-0.1)); - Alcotest.(check (float 1.e-15)) "erfc" 0.157299207050285 (erfc_float 1.0); - Alcotest.(check (float 1.e-15)) "erfc" 0.887537083981715 (erfc_float 0.1); - Alcotest.(check (float 1.e-15)) "erfc" (1.112462916018285) (erfc_float (-0.1)); - Alcotest.(check (float 1.e-14)) "gamma" (1.77245385090552) (gamma_float 0.5); - Alcotest.(check (float 1.e-14)) "gamma" (9.51350769866873) (gamma_float (0.1)); - Alcotest.(check (float 1.e-14)) "gamma" (-3.54490770181103) (gamma_float (-0.5)); - Alcotest.(check int) "popcnt" 6 (popcnt @@ Int64.of_int 63); - Alcotest.(check int) "popcnt" 8 (popcnt @@ Int64.of_int 299605); - Alcotest.(check int) "popcnt" 1 (popcnt @@ Int64.of_int 65536); - Alcotest.(check int) "popcnt" 0 (popcnt @@ Int64.of_int 0); - in - [ - "External", `Quick, test_external; - ] - diff --git a/Utils/Util.mli b/common/lib/util.mli similarity index 73% rename from Utils/Util.mli rename to common/lib/util.mli index c76599a..89cbb75 100644 --- a/Utils/Util.mli +++ b/common/lib/util.mli @@ -1,5 +1,3 @@ -open Lacaml.D - (** All utilities which should be included in all source files are defined here *) (** {2 Functions from libm} *) @@ -121,54 +119,6 @@ val stream_fold : ('a -> 'b -> 'a) -> 'a -> 'b Stream.t -> 'a (** Apply a fold to the elements of the stream. *) -(** {2 Linear algebra } *) - -val normalize : Vec.t -> Vec.t -(** Returns a the vector normalized *) - -val normalize_mat : Mat.t -> Mat.t -(** Returns the matrix with all the column vectors normalized *) - -val diagonalize_symm : Mat.t -> Mat.t * Vec.t -(** Diagonalize a symmetric matrix. Returns the eigenvectors and the eigenvalues. *) - -val xt_o_x : o:Mat.t -> x:Mat.t -> Mat.t -(** Computes {% $\mathbf{X^\dag\, O\, X}$ %} *) - -val x_o_xt : o:Mat.t -> x:Mat.t -> Mat.t -(** Computes {% $\mathbf{X\, O\, X^\dag}$ %} *) - -val remove_epsilons : Mat.t -> Mat.t -(** Remove values below machine precision *) - -val qr_ortho : Mat.t -> Mat.t -(** QR orthogonalization of the input matrix *) - -val canonical_ortho: ?thresh:float -> overlap:Mat.t -> Mat.t -> Mat.t -(** Canonical orthogonalization. [overlap] is the overlap matrix {% $\mathbf{S}$ %}, - and the last argument contains the vectors {% $\mathbf{C}$ %} to orthogonalize. - -{% -$$ -\mathbf{C_\bot} = \mathbf{C\, U\, D^{-1/2}}, \; -\mathbf{U\, D\, V^\dag} = \mathbf{S} -$$ -%} - - *) - -val debug_matrix: string -> Mat.t -> unit -(** Prints a matrix in stdout for debug *) - -val matrix_of_file : string -> Mat.t -(** Reads a matrix from a file with format "%d %d %f" corresponding to - [i, j, A.{i,j}]. *) - -val sym_matrix_of_file : string -> Mat.t -(** Reads a symmetric matrix from a file with format "%d %d %f" corresponding to - [i, j, A.{i,j}]. *) - - (** {2 Printers} *) val pp_float_array_size : Format.formatter -> float array -> unit (** Example: @@ -206,10 +156,4 @@ val pp_float_2darray : Format.formatter -> float array array -> unit val pp_bitstring : int -> Format.formatter -> Z.t -> unit (** Example: [ pp_bitstring 14 ppf z -> +++++------+-- ] *) -val pp_matrix : Format.formatter -> Mat.t -> unit - - -(** {1 Unit tests} *) - -val test_case : unit -> (string * [> `Quick ] * (unit -> unit)) list diff --git a/Utils/Zkey.ml b/common/lib/zkey.ml similarity index 97% rename from Utils/Zkey.ml rename to common/lib/zkey.ml index 76a0820..c044192 100644 --- a/Utils/Zkey.ml +++ b/common/lib/zkey.ml @@ -41,21 +41,21 @@ let of_powers_three { x=a ; y=b ; z=c ; _ } = let alpha = a lor b lor c in alpha >= 0 && alpha < (1 lsl 15) ); - make 3 a <+ b <+ c + make ~kind:3 a <+ b <+ c let of_int_four i j k l = assert ( let alpha = i lor j lor k lor l in alpha >= 0 && alpha < (1 lsl 15) ); - make 4 i <+ j <+ k <+ l + make ~kind:4 i <+ j <+ k <+ l let of_powers_six { x=a ; y=b ; z=c ; _ } { x=d ; y=e ; z=f ; _ } = assert ( let alpha = a lor b lor c lor d lor e lor f in alpha >= 0 && alpha < (1 lsl 10) ); - make 6 a << b << c << d << e << f + make ~kind:6 a << b << c << d << e << f let of_powers_nine { x=a ; y=b ; z=c ; _ } { x=d ; y=e ; z=f ; _ } { x=g ; y=h ; z=i ; _ } = @@ -63,7 +63,7 @@ let of_powers_nine { x=a ; y=b ; z=c ; _ } { x=d ; y=e ; z=f ; _ } let alpha = a lor b lor c lor d lor e lor f lor g lor h lor i in alpha >= 0 && alpha < (1 lsl 10) ); - make 9 a << b << c << d << e << f + make ~kind:9 a << b << c << d << e << f <| g << h << i let of_powers_twelve { x=a ; y=b ; z=c ; _ } { x=d ; y=e ; z=f ; _ } @@ -74,7 +74,7 @@ let of_powers_twelve { x=a ; y=b ; z=c ; _ } { x=d ; y=e ; z=f ; _ } in alpha >= 0 && alpha < (1 lsl 10) ); - make 12 a << b << c << d << e << f + make ~kind:12 a << b << c << d << e << f <| g << h << i << j << k << l diff --git a/Utils/Zkey.mli b/common/lib/zkey.mli similarity index 100% rename from Utils/Zkey.mli rename to common/lib/zkey.mli diff --git a/Utils/Zmap.ml b/common/lib/zmap.ml similarity index 100% rename from Utils/Zmap.ml rename to common/lib/zmap.ml diff --git a/Utils/Zmap.mli b/common/lib/zmap.mli similarity index 100% rename from Utils/Zmap.mli rename to common/lib/zmap.mli diff --git a/common/test/bitstring.ml b/common/test/bitstring.ml new file mode 100644 index 0000000..2ef6896 --- /dev/null +++ b/common/test/bitstring.ml @@ -0,0 +1,49 @@ +open Qcaml_common.Bitstring + +let check msg x = Alcotest.(check bool) msg true x + +let test_one () = + let x = 8745687 in + let one_x = One x in + Alcotest.(check bool) "of_x" true (one_x = (of_int x)); + Alcotest.(check bool) "shift_left1" true (One (x lsl 3) = shift_left one_x 3); + Alcotest.(check bool) "shift_right1" true (One (x lsr 3) = shift_right one_x 3); + Alcotest.(check bool) "shift_left_one1" true (One (1 lsl 3) = shift_left_one 4 3); + Alcotest.(check bool) "testbit1" true (testbit (One 8) 3); + Alcotest.(check bool) "testbit2" false (testbit (One 8) 2); + Alcotest.(check bool) "testbit3" false (testbit (One 8) 4); + Alcotest.(check bool) "logor1" true (One (1 lor 2) = logor (One 1) (One 2)); + Alcotest.(check bool) "logxor1" true (One (1 lxor 2) = logxor (One 1) (One 2)); + Alcotest.(check bool) "logand1" true (One (1 land 2) = logand (One 1) (One 2)); + Alcotest.(check bool) "to_list" true ([ 1 ; 3 ; 4 ; 6 ] = (to_list (One 45))) + + +let test_many () = + let x = 8745687 in + let z = Z.of_int x in + let one_x = One x in + let many_x = Many z in + Alcotest.(check bool) "of_z" true (one_x = (of_z z)); + Alcotest.(check bool) "shift_left2" true (Many (Z.shift_left z 3) = shift_left many_x 3); + Alcotest.(check bool) "shift_left3" true (Many (Z.shift_left z 100) = shift_left many_x 100); + Alcotest.(check bool) "shift_right2" true (Many (Z.shift_right z 3) = shift_right many_x 3); + Alcotest.(check bool) "shift_left_one2" true (Many (Z.shift_left Z.one 200) = shift_left_one 300 200); + Alcotest.(check bool) "testbit4" true (testbit (Many (Z.of_int 8)) 3); + Alcotest.(check bool) "testbit5" false (testbit (Many (Z.of_int 8)) 2); + Alcotest.(check bool) "testbit6" false (testbit (Many (Z.of_int 8)) 4); + Alcotest.(check bool) "logor2" true (Many (Z.of_int (1 lor 2)) = logor (Many Z.one) (Many (Z.of_int 2))); + Alcotest.(check bool) "logxor2" true (Many (Z.of_int (1 lxor 2)) = logxor (Many Z.one) (Many (Z.of_int 2))); + Alcotest.(check bool) "logand2" true (Many (Z.of_int (1 land 2)) = logand (Many Z.one) (Many (Z.of_int 2))) + + +let test_permutations () = + check "permutations" + (permtutations 2 4 = List.map of_int + [ 3 ; 5 ; 6 ; 9 ; 10 ; 12 ]) + +let tests = [ + "One", `Quick, test_one; + "Many", `Quick, test_many; + "permutations", `Quick, test_permutations; + ] + diff --git a/common/test/dune b/common/test/dune new file mode 100644 index 0000000..3d152f1 --- /dev/null +++ b/common/test/dune @@ -0,0 +1,7 @@ +(library + (name test_common) + (libraries + alcotest + qcaml.common + ) + (synopsis "Tests for common library")) diff --git a/common/test/math_functions.ml b/common/test/math_functions.ml new file mode 100644 index 0000000..5894dcb --- /dev/null +++ b/common/test/math_functions.ml @@ -0,0 +1,74 @@ +open Qcaml_common.Util +open Alcotest + +let test_external () = + check (float 1.e-15) "erf" 0.842700792949715 (erf_float 1.0); + check (float 1.e-15) "erf" 0.112462916018285 (erf_float 0.1); + check (float 1.e-15) "erf" (-0.112462916018285) (erf_float (-0.1)); + check (float 1.e-15) "erfc" 0.157299207050285 (erfc_float 1.0); + check (float 1.e-15) "erfc" 0.887537083981715 (erfc_float 0.1); + check (float 1.e-15) "erfc" (1.112462916018285) (erfc_float (-0.1)); + check (float 1.e-14) "gamma" (1.77245385090552) (gamma_float 0.5); + check (float 1.e-14) "gamma" (9.51350769866873) (gamma_float (0.1)); + check (float 1.e-14) "gamma" (-3.54490770181103) (gamma_float (-0.5)); + check int "popcnt" 6 (popcnt @@ Int64.of_int 63); + check int "popcnt" 8 (popcnt @@ Int64.of_int 299605); + check int "popcnt" 1 (popcnt @@ Int64.of_int 65536); + check int "popcnt" 0 (popcnt @@ Int64.of_int 0); + check int "trailz" 3 (trailz @@ Int64.of_int 8); + check int "trailz" 2 (trailz @@ Int64.of_int 12); + check int "trailz" 0 (trailz @@ Int64.of_int 1); + check int "trailz" 64 (trailz @@ Int64.of_int 0); + check int "leadz" 60 (leadz @@ Int64.of_int 8); + check int "leadz" 60 (leadz @@ Int64.of_int 12); + check int "leadz" 63 (leadz @@ Int64.of_int 1); + check int "leadz" 64 (leadz @@ Int64.of_int 0); + () + +let test_general () = + check int "of_some_of_int_fast" 1 (of_some (Some 1)) ; + check int "binom" 35 (binom 7 4); + check (float 1.e-15) "fact" 5040. (fact 7); + check (float 1.e-15) "binom_float" 35.0 (binom_float 7 4); + check (float 1.e-15) "pow" 729.0 (pow 3.0 6); + check (float 1.e-15) "float_of_int_fast" 10.0 (float_of_int_fast 10); + () + +let test_boys () = + check (float 1.e-15) "incomplete_gamma" 0.0 (incomplete_gamma ~alpha:0.5 0.); + check (float 1.e-15) "incomplete_gamma" 1.114707979049507 (incomplete_gamma ~alpha:0.5 0.4); + check (float 1.e-15) "incomplete_gamma" 1.4936482656248544 (incomplete_gamma ~alpha:0.5 1.); + check (float 1.e-15) "incomplete_gamma" 1.7724401246392805 (incomplete_gamma ~alpha:0.5 10.); + check (float 1.e-15) "incomplete_gamma" 1.7724538509055159 (incomplete_gamma ~alpha:0.5 100.); + + check (float 1.e-15) "boys" 1.0 (boys_function ~maxm:0 0.).(0); + check (float 1.e-15) "boys" 0.2 (boys_function ~maxm:2 0.).(2); + check (float 1.e-15) "boys" (1./.3.) (boys_function ~maxm:2 0.).(1); + check (float 1.e-15) "boys" 0.8556243918921488 (boys_function ~maxm:0 0.5).(0); + check (float 1.e-15) "boys" 0.14075053682591263 (boys_function ~maxm:2 0.5).(2); + check (float 1.e-15) "boys" 0.00012711171070276764 (boys_function ~maxm:3 15.).(3); + () + +let test_array () = + check bool "array_range" true ([| 2; 3; 4 |] = array_range 2 4); + check (float 1.e-15) "array_sum" 9. (array_sum [| 2.; 3.; 4. |]); + check (float 1.e-15) "array_product" 24. (array_product [| 2.; 3.; 4. |]); + () + +let test_list () = + check bool "list_range" true ([ 2; 3; 4 ] = list_range 2 4); + check bool "list_some" true ([ 2; 3; 4 ] = + list_some ([ None ; Some 2 ; None ; Some 3 ; None ; None ; Some 4]) ); + check bool "list_pack" true (list_pack 3 (list_range 1 20) = + [[1; 2; 3]; [4; 5; 6]; [7; 8; 9]; [10; 11; 12]; [13; 14; 15]; + [16; 17; 18]; [19; 20]]); + () + + +let tests = [ + "External", `Quick, test_external; + "General", `Quick, test_general; + "Array", `Quick, test_array; + "List", `Quick, test_list; + "Boys", `Quick, test_boys; +] diff --git a/configure b/configure deleted file mode 100755 index bdbac95..0000000 --- a/configure +++ /dev/null @@ -1,119 +0,0 @@ -#!/bin/sh - -# -------------------------------- -# Defaults - -package_name="QCaml" -prefix='/usr/local' -bin='$(prefix)/bin' -lib='$(prefix)/lib' -doc='$(prefix)/doc' -share='$(prefix)/share' -man='$(prefix)/man' -etc='$(prefix)/etc' -ocamlcflags='"-g -warn-error A -cc gcc -ccopt -Ofast -ccopt -march=native -ccopt=-fPIC "' -ocamllflags='"-g -warn-error A"' -ocamloptflags='"opt -O3 -nodynlink -remove-unused-arguments -rounds 16 -inline 100 -inline-max-unroll 100 -cc gcc -ccopt -Ofast -ccopt -march=native -ccopt=-fPIC "' -ocamldocflags='-docflags "-g ltxhtml.cma -sort -css-style $(PWD)/style.css -colorize-code"' -mpi='' -ocamloptflags_profile='"opt -p -cc gcc -ccopt -Ofast -ccopt -march=native -ccopt -no-pie "' - -# -------------------------------- - - -LC_ALL=C -export LC_ALL - -if [ x.$OPAM_PACKAGE_NAME != x. ] ; then - package_name=$OPAM_PACKAGE_NAME -fi - - -help() -{ - cat < Makefile -package_name=$package_name -prefix=$prefix -bin=$bin -lib=$lib -doc=$doc -share=$share -man=$man -etc=$etc -mpi=$mpi - -ocamlcflags=$ocamlcflags -ocamllflags=$ocamllflags -ocamloptflags=$ocamloptflags -ocamldocflags=$ocamldocflags - - -include Makefile.include -EOF - diff --git a/data/chamo.png b/data/chamo.png deleted file mode 100644 index 843695c..0000000 Binary files a/data/chamo.png and /dev/null differ diff --git a/data/chamo.svg b/data/chamo.svg deleted file mode 100644 index 3332240..0000000 --- a/data/chamo.svg +++ /dev/null @@ -1,283 +0,0 @@ - - - - - - image/svg+xml - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/data/chamo_bg.png b/data/chamo_bg.png deleted file mode 100644 index 2bf987d..0000000 Binary files a/data/chamo_bg.png and /dev/null differ diff --git a/data/chamo_head.png b/data/chamo_head.png deleted file mode 100644 index 1711ff2..0000000 Binary files a/data/chamo_head.png and /dev/null differ diff --git a/data/chamo_head.svg b/data/chamo_head.svg deleted file mode 100644 index ac751e8..0000000 --- a/data/chamo_head.svg +++ /dev/null @@ -1,283 +0,0 @@ - - - - - - image/svg+xml - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/dune-project b/dune-project new file mode 100644 index 0000000..74b9906 --- /dev/null +++ b/dune-project @@ -0,0 +1,36 @@ +(lang dune 1.10) +(name qcaml) + +(generate_opam_files true) + +(source (uri "git+https://gitlab.com/scemama/qcaml.git")) +(bug_reports "https://gitlab.com/scemama/qcaml/issues") +(homepage "https://gitlab.com/scemama/qcaml") +(documentation "https://gitlab.com/scemama/qcaml") + +(license "LGPL-2.1+ with OCaml linking exception") + +(maintainers + "Anthony Scemama " +) + +(authors + "Anthony Scemama " +) + +(package + (name qcaml) + (synopsis "QCaml - Quantum chemistry with OCaml") + (description "\ +QCaml provides a programming framewrok work wave function methods +in quantum chemistry.") + (depends + (ocaml (>= 4.10)) + (dune (>= 1.10)) + lacaml + getopt + zarith + alcotest + ) +) + diff --git a/Basis/AtomicShell.ml b/gaussian_basis/lib/atomic_shell.ml similarity index 91% rename from Basis/AtomicShell.ml rename to gaussian_basis/lib/atomic_shell.ml index 68c005f..523eabe 100644 --- a/Basis/AtomicShell.ml +++ b/gaussian_basis/lib/atomic_shell.ml @@ -1,20 +1,19 @@ -open Util -open Constants +open Qcaml_common type t = { expo : float array array; coef : float array array; norm_coef : float array array; norm_coef_scale : float array; - contr : ContractedShell.t array; + contr : Contracted_shell.t array; index : int; center : Coordinate.t; - ang_mom : AngularMomentum.t; + ang_mom : Angular_momentum.t; } -module Am = AngularMomentum +module Am = Angular_momentum module Co = Coordinate -module Cs = ContractedShell +module Cs = Contracted_shell let make ?(index=0) contr = @@ -38,7 +37,7 @@ let make ?(index=0) contr = | i -> if Cs.ang_mom contr.(i) = ang_mom then (unique_angmom [@tailcall]) (i-1) else false in if not (unique_angmom (Array.length contr - 1)) then - invalid_arg "ContractedShell.make: AngularMomentum.t differ"; + invalid_arg "Contracted_shell.make: Angular_momentum.t differ"; let norm_coef = Array.map Cs.normalizations contr @@ -78,6 +77,7 @@ let contracted_shells x = x.contr open Format +(* let pp_debug ppf x = fprintf ppf "@[<2>{@ "; fprintf ppf "@[<2>expo =@ %a ;@]@ " pp_float_2darray_size x.expo; @@ -88,6 +88,7 @@ let pp_debug ppf x = fprintf ppf "@[<2>norm_coef_scale =@ %a ;@]@ " pp_float_array_size x.norm_coef_scale; fprintf ppf "@[<2>index =@ %d ;@]@ " x.index; fprintf ppf "}@,@]" +*) let pp ppf s = fprintf ppf "@[%3d-%-3d@]" (s.index+1) (s.index+ (size_of_shell s)*(size s)); diff --git a/Basis/AtomicShell.mli b/gaussian_basis/lib/atomic_shell.mli similarity index 85% rename from Basis/AtomicShell.mli rename to gaussian_basis/lib/atomic_shell.mli index 0610906..bf0ce0d 100644 --- a/Basis/AtomicShell.mli +++ b/gaussian_basis/lib/atomic_shell.mli @@ -1,5 +1,5 @@ (** Set of contracted Gaussians differing only by the powers of x, y and z, with a - constant {!AngularMomentum.t}, all centered on the same center. + constant {!Angular_momentum.t}, all centered on the same center. In other words, it is the set of all contracted shells sharing the same center. @@ -12,16 +12,16 @@ where: -- {% $g_{ij\,n_x,n_y,n_z}(r)$ %} is the i-th {!PrimitiveShell.t} of the j-th {!ContractedShell.t} +- {% $g_{ij\,n_x,n_y,n_z}(r)$ %} is the i-th {!PrimitiveShell.t} of the j-th {!Contracted_shell.t} - {% $n_x + n_y + n_z = l$ %}, the total angular momentum -- {% $\alpha_{ij}$ %} are the exponents (tabulated) of the j-th {!ContractedShell.t} +- {% $\alpha_{ij}$ %} are the exponents (tabulated) of the j-th {!Contracted_shell.t} -- {% $d_{ij}$ %} are the contraction coefficients of the j-th {!ContractedShell.t} +- {% $d_{ij}$ %} are the contraction coefficients of the j-th {!Contracted_shell.t} - {% $\mathcal{N}_{ij}$ %} is the normalization coefficient of the i-th primitive shell - ({!PrimitiveShell.norm_coef}) of the j-th {!ContractedShell.t} + ({!PrimitiveShell.norm_coef}) of the j-th {!Contracted_shell.t} - {% $f(n_x,n_y,n_z)$ %} is a scaling factor adjusting the normalization coefficient for the particular powers of {% $x,y,z$ %} ({!PrimitiveShell.norm_coef_scale}) @@ -30,7 +30,9 @@ where: type t -val make : ?index:int -> ContractedShell.t array -> t +open Qcaml_common + +val make : ?index:int -> Contracted_shell.t array -> t (** Creates a contracted shell from a list of coefficients and primitives. *) val with_index : t -> int -> t @@ -42,13 +44,13 @@ val index : t -> int val center : t -> Coordinate.t (** Coordinate of the center {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %}. *) -val ang_mom : t -> AngularMomentum.t +val ang_mom : t -> Angular_momentum.t (** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *) val size : t -> int (** Number of contracted functions, {% $n$ %} in the definition. *) -val contracted_shells: t -> ContractedShell.t array +val contracted_shells: t -> Contracted_shell.t array (** Array of contracted gaussians *) val exponents : t -> float array array @@ -68,7 +70,7 @@ val normalizations : t -> float array array val norm_scales : t -> float array (** Scaling factors {% $f(n_x,n_y,n_z)$ %}, given in the same order as - [AngularMomentum.zkey_array ang_mom]. *) + [Angular_momentum.zkey_array ang_mom]. *) val size_of_shell : t -> int (** Number of contracted functions in the shell: length of {!norm_coef_scale}. *) diff --git a/Basis/AtomicShellPair.ml b/gaussian_basis/lib/atomic_shell_pair.ml similarity index 80% rename from Basis/AtomicShellPair.ml rename to gaussian_basis/lib/atomic_shell_pair.ml index 40a67ef..05fa850 100644 --- a/Basis/AtomicShellPair.ml +++ b/gaussian_basis/lib/atomic_shell_pair.ml @@ -1,21 +1,18 @@ -open Util -open Constants - -exception Null_contribution +open Qcaml_common type t = { - contracted_shell_pairs : ContractedShellPair.t list; - atomic_shell_a : AtomicShell.t; - atomic_shell_b : AtomicShell.t; + contracted_shell_pairs : Contracted_shell_pair.t list; + atomic_shell_a : Atomic_shell.t; + atomic_shell_b : Atomic_shell.t; } -module Am = AngularMomentum -module As = AtomicShell +module Am = Angular_momentum +module As = Atomic_shell module Co = Coordinate -module Cs = ContractedShell -module Csp = ContractedShellPair +module Cs = Contracted_shell +module Csp = Contracted_shell_pair (** Creates an atomic shell pair : an array of pairs of contracted shells. *) @@ -34,7 +31,7 @@ let make ?(cutoff=Constants.epsilon) atomic_shell_a atomic_shell_b = None ) l_b ) l_a - |> list_some + |> Util.list_some in match contracted_shell_pairs with | [] -> None @@ -60,7 +57,7 @@ let norm_scales x = Csp.norm_scales @@ List.hd x.contracted_shell_pairs *) let of_atomic_shell_array ?(cutoff=Constants.epsilon) basis = Array.mapi (fun i shell_a -> - Array.mapi (fun j shell_b -> + Array.map (fun shell_b -> make ~cutoff shell_a shell_b) (Array.sub basis 0 (i+1)) ) basis diff --git a/Basis/AtomicShellPair.mli b/gaussian_basis/lib/atomic_shell_pair.mli similarity index 66% rename from Basis/AtomicShellPair.mli rename to gaussian_basis/lib/atomic_shell_pair.mli index 674cca3..9c564c8 100644 --- a/Basis/AtomicShellPair.mli +++ b/gaussian_basis/lib/atomic_shell_pair.mli @@ -3,8 +3,10 @@ type t +open Qcaml_common -val make : ?cutoff:float -> AtomicShell.t -> AtomicShell.t -> t option + +val make : ?cutoff:float -> Atomic_shell.t -> Atomic_shell.t -> t option (** Creates an atomic shell pair from two atomic shells. The contracted shell pairs contains the only pairs of primitives for which @@ -14,22 +16,22 @@ val make : ?cutoff:float -> AtomicShell.t -> AtomicShell.t -> t option [None]. *) -val of_atomic_shell_array : ?cutoff:float -> AtomicShell.t array -> t option array array +val of_atomic_shell_array : ?cutoff:float -> Atomic_shell.t array -> t option array array (** Creates all possible atomic shell pairs from an array of atomic shells. If an atomic shell pair is not significant, sets the value to [None]. *) -val atomic_shell_a : t -> AtomicShell.t -(** Returns the first {!AtomicShell.t} which was used to build the atomic +val atomic_shell_a : t -> Atomic_shell.t +(** Returns the first {!Atomic_shell.t} which was used to build the atomic shell pair. *) -val atomic_shell_b : t -> AtomicShell.t -(** Returns the second {!AtomicShell.t} which was used to build the atomic +val atomic_shell_b : t -> Atomic_shell.t +(** Returns the second {!Atomic_shell.t} which was used to build the atomic shell pair. *) -val contracted_shell_pairs : t -> ContractedShellPair.t list +val contracted_shell_pairs : t -> Contracted_shell_pair.t list (** Returns an array of {!ContractedShellPair.t}, containing all the pairs of contracted functions used to build the atomic shell pair. *) @@ -43,7 +45,7 @@ val a_minus_b_sq : t -> float val norm_scales : t -> float array (* norm_coef.(i) / norm_coef.(0) *) -val ang_mom : t -> AngularMomentum.t +val ang_mom : t -> Angular_momentum.t (* Total angular Momentum *) val monocentric : t -> bool diff --git a/Basis/AtomicShellPairCouple.ml b/gaussian_basis/lib/atomic_shell_pair_couple.ml similarity index 76% rename from Basis/AtomicShellPairCouple.ml rename to gaussian_basis/lib/atomic_shell_pair_couple.ml index 8636401..703a07d 100644 --- a/Basis/AtomicShellPairCouple.ml +++ b/gaussian_basis/lib/atomic_shell_pair_couple.ml @@ -1,22 +1,22 @@ -open Util +open Qcaml_common type t = { - contracted_shell_pair_couples : ContractedShellPairCouple.t list ; - atomic_shell_pair_p: AtomicShellPair.t ; - atomic_shell_pair_q: AtomicShellPair.t ; - atomic_shell_a : AtomicShell.t ; - atomic_shell_b : AtomicShell.t ; - atomic_shell_c : AtomicShell.t ; - atomic_shell_d : AtomicShell.t ; - ang_mom : AngularMomentum.t ; + contracted_shell_pair_couples : Contracted_shell_pair_couple.t list ; + atomic_shell_pair_p: Atomic_shell_pair.t ; + atomic_shell_pair_q: Atomic_shell_pair.t ; + atomic_shell_a : Atomic_shell.t ; + atomic_shell_b : Atomic_shell.t ; + atomic_shell_c : Atomic_shell.t ; + atomic_shell_d : Atomic_shell.t ; + ang_mom : Angular_momentum.t ; } -module Am = AngularMomentum +module Am = Angular_momentum module Co = Coordinate -module As = AtomicShell -module Asp = AtomicShellPair -module Cspc = ContractedShellPairCouple +module As = Atomic_shell +module Asp = Atomic_shell_pair +module Cspc = Contracted_shell_pair_couple let make ?(cutoff=Constants.epsilon) atomic_shell_pair_p atomic_shell_pair_q = let ang_mom = @@ -30,10 +30,10 @@ let make ?(cutoff=Constants.epsilon) atomic_shell_pair_p atomic_shell_pair_q = let contracted_shell_pair_couples = List.concat_map (fun ap_ab -> List.map (fun ap_cd -> - ContractedShellPairCouple.make ~cutoff ap_ab ap_cd + Cspc.make ~cutoff ap_ab ap_cd ) (Asp.contracted_shell_pairs atomic_shell_pair_q) ) (Asp.contracted_shell_pairs atomic_shell_pair_p) - |> list_some + |> Util.list_some in match contracted_shell_pair_couples with | [] -> None diff --git a/Basis/AtomicShellPairCouple.mli b/gaussian_basis/lib/atomic_shell_pair_couple.mli similarity index 76% rename from Basis/AtomicShellPairCouple.mli rename to gaussian_basis/lib/atomic_shell_pair_couple.mli index 84ec73c..94f167a 100644 --- a/Basis/AtomicShellPairCouple.mli +++ b/gaussian_basis/lib/atomic_shell_pair_couple.mli @@ -13,39 +13,40 @@ acting on different electrons, since they will be coupled by a two-electron oper type t +open Qcaml_common -val make : ?cutoff:float -> AtomicShellPair.t -> AtomicShellPair.t -> t option +val make : ?cutoff:float -> Atomic_shell_pair.t -> Atomic_shell_pair.t -> t option (** Creates an atomic shell pair couple using two atomic shell pairs. *) -val ang_mom : t -> AngularMomentum.t +val ang_mom : t -> Angular_momentum.t (** Total angular momentum of the shell pair couple: sum of the angular momenta of all the shells. *) -val atomic_shell_a : t -> AtomicShell.t +val atomic_shell_a : t -> Atomic_shell.t (** Returns the first atomic shell of the first shell pair. *) -val atomic_shell_b : t -> AtomicShell.t +val atomic_shell_b : t -> Atomic_shell.t (** Returns the second atomic shell of the first shell pair. *) -val atomic_shell_c : t -> AtomicShell.t +val atomic_shell_c : t -> Atomic_shell.t (** Returns the first atomic shell of the second shell pair. *) -val atomic_shell_d : t -> AtomicShell.t +val atomic_shell_d : t -> Atomic_shell.t (** Returns the second atomic shell of the second shell pair. *) -val atomic_shell_pair_p : t -> AtomicShellPair.t +val atomic_shell_pair_p : t -> Atomic_shell_pair.t (** Returns the first atomic shell pair that was used to build the shell pair. *) -val atomic_shell_pair_q : t -> AtomicShellPair.t +val atomic_shell_pair_q : t -> Atomic_shell_pair.t (** Returns the second atomic shell pair that was used to build the shell pair. *) val monocentric : t -> bool (** True if all four atomic shells have the same center. *) -val contracted_shell_pair_couples : t -> ContractedShellPairCouple.t list +val contracted_shell_pair_couples : t -> Contracted_shell_pair_couple.t list (** Returns the list of significant contracted shell pair couples. *) val zkey_array : t -> Zkey.t array diff --git a/Basis/Basis.ml b/gaussian_basis/lib/basis.ml similarity index 67% rename from Basis/Basis.ml rename to gaussian_basis/lib/basis.ml index 3f417b6..6667248 100644 --- a/Basis/Basis.ml +++ b/gaussian_basis/lib/basis.ml @@ -1,22 +1,20 @@ type t = { size : int; - contracted_shells : ContractedShell.t array ; - atomic_shells : AtomicShell.t array lazy_t; - general_basis : GeneralBasis.t ; - range_separation : float option ; - f12 : F12factor.t option ; + contracted_shells : Contracted_shell.t array ; + atomic_shells : Atomic_shell.t array lazy_t; + general_basis : General_basis.t ; } -module As = AtomicShell -module Cs = ContractedShell -module Gb = GeneralBasis -module Ps = PrimitiveShell +module As = Atomic_shell +module Cs = Contracted_shell +module Gb = General_basis +module Ps = Primitive_shell let general_basis t = t.general_basis (** Returns an array of the basis set per atom *) -let of_nuclei_and_general_basis ?f12 ?range_separation nucl bas = +let of_nuclei_and_general_basis nucl bas = let index_ = ref 0 in let contracted_shells = Array.map (fun (e, center) -> @@ -54,7 +52,7 @@ let of_nuclei_and_general_basis ?f12 ?range_separation nucl bas = |> Array.of_list ) in { contracted_shells ; atomic_shells ; size = !index_; - general_basis = bas ; f12 ; range_separation } + general_basis = bas } let size t = t.size @@ -63,11 +61,6 @@ let atomic_shells t = Lazy.force t.atomic_shells let contracted_shells t = t.contracted_shells -let range_separation t = t.range_separation - -let f12 t = t.f12 - - let to_string b = let b = atomic_shells b in let line =" @@ -92,24 +85,24 @@ let to_string b = -let of_nuclei_and_basis_filename ?f12 ?range_separation ~nuclei filename = +let of_nuclei_and_basis_filename ~nuclei filename = let general_basis = - GeneralBasis.read filename + General_basis.read filename in - of_nuclei_and_general_basis ?f12 ?range_separation nuclei general_basis + of_nuclei_and_general_basis nuclei general_basis -let of_nuclei_and_basis_string ?f12 ?range_separation ~nuclei str = +let of_nuclei_and_basis_string ~nuclei str = let general_basis = - GeneralBasis.of_string str + General_basis.of_string str in - of_nuclei_and_general_basis ?f12 ?range_separation nuclei general_basis + of_nuclei_and_general_basis nuclei general_basis -let of_nuclei_and_basis_filenames ?f12 ?range_separation ~nuclei filenames = +let of_nuclei_and_basis_filenames ~nuclei filenames = let general_basis = - GeneralBasis.read_many filenames + General_basis.read_many filenames in - of_nuclei_and_general_basis ?f12 ?range_separation nuclei general_basis + of_nuclei_and_general_basis nuclei general_basis let pp ppf t = diff --git a/Basis/Basis.mli b/gaussian_basis/lib/basis.mli similarity index 56% rename from Basis/Basis.mli rename to gaussian_basis/lib/basis.mli index f9cac65..da5f8c7 100644 --- a/Basis/Basis.mli +++ b/gaussian_basis/lib/basis.mli @@ -2,9 +2,9 @@ type t +open Qcaml_particles -val of_nuclei_and_general_basis : ?f12:F12factor.t -> ?range_separation:float -> - Nuclei.t -> GeneralBasis.t -> t +val of_nuclei_and_general_basis : Nuclei.t -> General_basis.t -> t (** Takes an array of {!Nuclei.t}, and a {!GeneralBasis.t} (such as cc-pVDZ for instance) and creates the corresponding atomic basis set. All the {!Element.t}'s of the array of {!Nuclei.t} are searched in @@ -14,20 +14,17 @@ val of_nuclei_and_general_basis : ?f12:F12factor.t -> ?range_separation:float -> *) -val of_nuclei_and_basis_filename : ?f12:F12factor.t -> ?range_separation:float -> - nuclei:Nuclei.t -> string -> t +val of_nuclei_and_basis_filename : nuclei:Nuclei.t -> string -> t (** Same as {!of_nuclei_and_general_basis}, but taking the {!GeneralBasis.t} from a file. *) -val of_nuclei_and_basis_string : ?f12:F12factor.t -> ?range_separation:float -> - nuclei:Nuclei.t -> string -> t +val of_nuclei_and_basis_string : nuclei:Nuclei.t -> string -> t (** Same as {!of_nuclei_and_general_basis}, but taking the {!GeneralBasis.t} from a string. *) -val of_nuclei_and_basis_filenames : ?f12:F12factor.t -> ?range_separation:float -> - nuclei:Nuclei.t -> string list -> t +val of_nuclei_and_basis_filenames : nuclei:Nuclei.t -> string list -> t (** Same as {!of_nuclei_and_general_basis}, but taking the {!GeneralBasis.t} from multiple files. *) @@ -36,21 +33,15 @@ val of_nuclei_and_basis_filenames : ?f12:F12factor.t -> ?range_separation:float val size : t -> int (** Number of contracted basis functions. *) -val atomic_shells : t -> AtomicShell.t array +val atomic_shells : t -> Atomic_shell.t array (** Returns the contracted basis functions per atom. *) -val contracted_shells : t -> ContractedShell.t array +val contracted_shells : t -> Contracted_shell.t array (** Returns all the contracted basis functions. *) -val general_basis : t -> GeneralBasis.t +val general_basis : t -> General_basis.t (** Returns the [!GeneralBasis] that was used to build the current basis. *) -val f12 : t -> F12factor.t option -(** Returns the explicit correlation factor if present. *) - -val range_separation : t -> float option -(** Returns the electron-electrons interaction range-separation value if present. *) - (** {2 Printers} *) val to_string : t -> string diff --git a/Basis/ContractedShell.ml b/gaussian_basis/lib/contracted_shell.ml similarity index 95% rename from Basis/ContractedShell.ml rename to gaussian_basis/lib/contracted_shell.ml index bf94dd8..f558ee6 100644 --- a/Basis/ContractedShell.ml +++ b/gaussian_basis/lib/contracted_shell.ml @@ -1,20 +1,19 @@ -open Util -open Constants +open Qcaml_common type t = { expo : float array; coef : float array; norm_coef : float array; norm_coef_scale : float array; - prim : PrimitiveShell.t array; + prim : Primitive_shell.t array; center : Coordinate.t; - ang_mom : AngularMomentum.t; + ang_mom : Angular_momentum.t; index : int; } -module Am = AngularMomentum +module Am = Angular_momentum module Co = Coordinate -module Ps = PrimitiveShell +module Ps = Primitive_shell let make ?(index=0) lc = @@ -117,6 +116,7 @@ let values t point = open Format +(* let pp_debug ppf x = fprintf ppf "@[<2>{@ "; fprintf ppf "@[<2>expo =@ %a ;@]@ " pp_float_array_size x.expo; @@ -127,6 +127,7 @@ let pp_debug ppf x = fprintf ppf "@[<2>norm_coef_scale =@ %a ;@]@ " pp_float_array_size x.norm_coef_scale; fprintf ppf "@[<2>index =@ %d ;@]@ " x.index; fprintf ppf "}@,@]" +*) let pp ppf s = (match s.ang_mom with diff --git a/Basis/ContractedShell.mli b/gaussian_basis/lib/contracted_shell.mli similarity index 81% rename from Basis/ContractedShell.mli rename to gaussian_basis/lib/contracted_shell.mli index 8026169..45ace7d 100644 --- a/Basis/ContractedShell.mli +++ b/gaussian_basis/lib/contracted_shell.mli @@ -1,5 +1,5 @@ (** Set of contracted Gaussians differing only by the powers of x, y and z, with a - constant {!AngularMomentum.t}. + constant {!Angular_momentum.t}. {% \begin{align*} @@ -10,7 +10,7 @@ where: -- {% $g_{i\,n_x,n_y,n_z}(r)$ %} is the i-th {!PrimitiveShell.t} +- {% $g_{i\,n_x,n_y,n_z}(r)$ %} is the i-th {!Primitive_shell.t} - {% $n_x + n_y + n_z = l$ %}, the total angular momentum @@ -19,16 +19,18 @@ where: - {% $d_i$ %} are the contraction coefficients - {% $\mathcal{N}_i$ %} is the normalization coefficient of the i-th primitive shell - ({!PrimitiveShell.norm_coef}) + ({!Primitive_shell.norm_coef}) - {% $f(n_x,n_y,n_z)$ %} is a scaling factor adjusting the normalization coefficient for the - particular powers of {% $x,y,z$ %} ({!PrimitiveShell.norm_coef_scale}) + particular powers of {% $x,y,z$ %} ({!Primitive_shell.norm_coef_scale}) *) type t -val make : ?index:int -> (float * PrimitiveShell.t) array -> t +open Qcaml_common + +val make : ?index:int -> (float * Primitive_shell.t) array -> t (** Creates a contracted shell from a list of coefficients and primitives. *) val with_index : t -> int -> t @@ -40,13 +42,13 @@ val index : t -> int val center : t -> Coordinate.t (** Coordinate of the center {% $\mathbf{A} = (X_A,Y_A,Z_A)$ %}. *) -val ang_mom : t -> AngularMomentum.t +val ang_mom : t -> Angular_momentum.t (** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *) val size : t -> int (** Number of primitive functions, {% $m$ %} in the definition. *) -val primitives : t -> PrimitiveShell.t array +val primitives : t -> Primitive_shell.t array (** Array of primitive gaussians *) val exponents : t -> float array @@ -60,7 +62,7 @@ val normalizations : t -> float array val norm_scales : t -> float array (** Scaling factors {% $f(n_x,n_y,n_z)$ %}, given in the same order as - [AngularMomentum.zkey_array ang_mom]. *) + [Angular_momentum.zkey_array ang_mom]. *) val size_of_shell : t -> int (** Number of contracted functions in the shell: length of {!norm_coef_scale}. *) @@ -72,7 +74,7 @@ val zkey_array : t -> Zkey.t array val values : t -> Coordinate.t -> float array (** Evaluates the all the functions of the [ContractedShell] at a given Cartesian coordinate. The order in which the functions are stored corresponds - [AngularMomentum.(zkey_array @@ Singlet t.ang_mom)] + [Angular_momentum.(zkey_array @@ Singlet t.ang_mom)] *) (** {2 Printers} *) diff --git a/Basis/ContractedShellPair.ml b/gaussian_basis/lib/contracted_shell_pair.ml similarity index 87% rename from Basis/ContractedShellPair.ml rename to gaussian_basis/lib/contracted_shell_pair.ml index b967313..1946cb1 100644 --- a/Basis/ContractedShellPair.ml +++ b/gaussian_basis/lib/contracted_shell_pair.ml @@ -1,23 +1,20 @@ -open Util -open Constants - -exception Null_contribution - +open Qcaml_common + type t = { - coefs_and_shell_pairs : (float * PrimitiveShellPair.t) list; - shell_a : ContractedShell.t; - shell_b : ContractedShell.t; + coefs_and_shell_pairs : (float * Primitive_shell_pair.t) list; + shell_a : Contracted_shell.t; + shell_b : Contracted_shell.t; } -module Am = AngularMomentum +module Am = Angular_momentum module Co = Coordinate -module Cs = ContractedShell -module Ps = PrimitiveShell -module Psp = PrimitiveShellPair +module Cs = Contracted_shell +module Ps = Primitive_shell +module Psp = Primitive_shell_pair -(** Creates an contracted shell pair : an array of pairs of primitive shells. +(** Creates an contracted shell pair : a list of pairs of primitive shells. A contracted shell with N functions combined with a contracted shell with M functions generates a NxM array of shell pairs. *) @@ -93,11 +90,13 @@ let monocentric x = (** Returns an integer characteristic of a contracted shell pair *) let hash a = - Array.map Hashtbl.hash a - + List.rev_map Hashtbl.hash a + |> Array.of_list (** Comparison function, used for sorting *) -let cmp a b = +let compare t t' = + let a = hash t.coefs_and_shell_pairs in + let b = hash t'.coefs_and_shell_pairs in if a = b then 0 else if (Array.length a < Array.length b) then -1 else if (Array.length a > Array.length b) then 1 @@ -129,9 +128,10 @@ let of_contracted_shell_array ?(cutoff=Constants.epsilon) basis = in loop [] (List.rev (Array.to_list basis)) |> List.concat - |> list_some + |> Util.list_some +(* let equivalent x y = (Array.length x = Array.length y) && @@ -162,6 +162,7 @@ let unique sp = (aux [@tailcall]) newaccu rest in aux [] sp +*) let zkey_array x = diff --git a/Basis/ContractedShellPair.mli b/gaussian_basis/lib/contracted_shell_pair.mli similarity index 71% rename from Basis/ContractedShellPair.mli rename to gaussian_basis/lib/contracted_shell_pair.mli index 30c0d91..0750ee4 100644 --- a/Basis/ContractedShellPair.mli +++ b/gaussian_basis/lib/contracted_shell_pair.mli @@ -1,6 +1,6 @@ (** A datastructure to represent pairs of contracted shells. -A contracted shell pair is a product of two {!ContractedShell.t}: +A contracted shell pair is a product of two {!Contracted_shell.t}: {% \begin{align*} \varphi_{ab}(r) & = \chi_a(r) \times \chi_b(r) \\ @@ -13,8 +13,9 @@ A contracted shell pair is a product of two {!ContractedShell.t}: type t +open Qcaml_common -val make : ?cutoff:float -> ContractedShell.t -> ContractedShell.t -> t option +val make : ?cutoff:float -> Contracted_shell.t -> Contracted_shell.t -> t option (** Creates an contracted shell pair {% $\varphi_{ab}$ %} from a contracted shell {% $\chi_a$ %} (first argument) and a contracted shell {% $\chi_b$ %} (second argument). @@ -29,28 +30,28 @@ val make : ?cutoff:float -> ContractedShell.t -> ContractedShell.t -> t option *) -val of_contracted_shell_array : ?cutoff:float -> ContractedShell.t array -> t list +val of_contracted_shell_array : ?cutoff:float -> Contracted_shell.t array -> t list (** Creates all possible contracted shell pairs from an array of contracted shells. Only significant shell pairs are kept. *) -val shell_a : t -> ContractedShell.t -(** Returns the first {!ContractedShell.t} {% $\chi_a$ %} which was used to +val shell_a : t -> Contracted_shell.t +(** Returns the first {!Contracted_shell.t} {% $\chi_a$ %} which was used to build the contracted shell pair. *) -val shell_b : t -> ContractedShell.t -(** Returns the second {!ContractedShell.t} {% $\chi_b$ %} which was used to +val shell_b : t -> Contracted_shell.t +(** Returns the second {!Contracted_shell.t} {% $\chi_b$ %} which was used to build the contracted shell pair. *) -val coefs_and_shell_pairs : t -> (float * PrimitiveShellPair.t) list -(** Returns an arra of coefficients and of {!PrimitiveShellPair.t}, containing all +val coefs_and_shell_pairs : t -> (float * Primitive_shell_pair.t) list +(** Returns an arra of coefficients and of {!Primitive_shell_pair.t}, containing all the pairs of primitive functions used to build the contracted shell pair. *) -val shell_pairs : t -> PrimitiveShellPair.t array -(** Returns an array of {!PrimitiveShellPair.t}, containing all the pairs of +val shell_pairs : t -> Primitive_shell_pair.t array +(** Returns an array of {!Primitive_shell_pair.t}, containing all the pairs of primitive functions used to build the contracted shell pair. *) @@ -68,7 +69,7 @@ val a_minus_b_sq : t -> float val norm_scales : t -> float array (* normalizations.(i) / normalizations.(0) *) -val ang_mom : t -> AngularMomentum.t +val ang_mom : t -> Angular_momentum.t (* Total angular Momentum *) val monocentric : t -> bool @@ -77,6 +78,8 @@ val monocentric : t -> bool val zkey_array : t -> Zkey.t array (** Returns the array of Zkeys associated with the contracted shell pair. *) +val compare : t -> t -> int +(** Comparison function for sorting *) (* val hash : t -> int array diff --git a/Basis/ContractedShellPairCouple.ml b/gaussian_basis/lib/contracted_shell_pair_couple.ml similarity index 76% rename from Basis/ContractedShellPairCouple.ml rename to gaussian_basis/lib/contracted_shell_pair_couple.ml index 88f3891..2df01fe 100644 --- a/Basis/ContractedShellPairCouple.ml +++ b/gaussian_basis/lib/contracted_shell_pair_couple.ml @@ -1,22 +1,22 @@ -open Util +open Qcaml_common type t = { - coefs_and_shell_pair_couples : (float * PrimitiveShellPairCouple.t) list ; - shell_pair_p: ContractedShellPair.t ; - shell_pair_q: ContractedShellPair.t ; - shell_a : ContractedShell.t ; - shell_b : ContractedShell.t ; - shell_c : ContractedShell.t ; - shell_d : ContractedShell.t ; - ang_mom : AngularMomentum.t ; + coefs_and_shell_pair_couples : (float * Primitive_shell_pair_couple.t) list ; + shell_pair_p: Contracted_shell_pair.t ; + shell_pair_q: Contracted_shell_pair.t ; + shell_a : Contracted_shell.t ; + shell_b : Contracted_shell.t ; + shell_c : Contracted_shell.t ; + shell_d : Contracted_shell.t ; + ang_mom : Angular_momentum.t ; } -module Am = AngularMomentum +module Am = Angular_momentum module Co = Coordinate -module Cs = ContractedShell -module Csp = ContractedShellPair -module Pspc = PrimitiveShellPairCouple +module Cs = Contracted_shell +module Csp = Contracted_shell_pair +module Pspc = Primitive_shell_pair_couple let make ?(cutoff=Constants.epsilon) shell_pair_p shell_pair_q = let ang_mom = @@ -36,7 +36,7 @@ let make ?(cutoff=Constants.epsilon) shell_pair_p shell_pair_q = else Some (coef_prod, Pspc.make sp_ab sp_cd) ) (Csp.coefs_and_shell_pairs shell_pair_q) ) (Csp.coefs_and_shell_pairs shell_pair_p) - |> list_some + |> Util.list_some in match coefs_and_shell_pair_couples with | [] -> None diff --git a/Basis/ContractedShellPairCouple.mli b/gaussian_basis/lib/contracted_shell_pair_couple.mli similarity index 76% rename from Basis/ContractedShellPairCouple.mli rename to gaussian_basis/lib/contracted_shell_pair_couple.mli index 4de4016..7680bfb 100644 --- a/Basis/ContractedShellPairCouple.mli +++ b/gaussian_basis/lib/contracted_shell_pair_couple.mli @@ -13,39 +13,40 @@ acting on different electrons, since they will be coupled by a two-electron oper type t +open Qcaml_common -val make : ?cutoff:float -> ContractedShellPair.t -> ContractedShellPair.t -> t option +val make : ?cutoff:float -> Contracted_shell_pair.t -> Contracted_shell_pair.t -> t option (** Creates a contracted shell pair couple using two contracted shell pairs. *) -val ang_mom : t -> AngularMomentum.t +val ang_mom : t -> Angular_momentum.t (** Total angular momentum of the shell pair couple: sum of the angular momenta of all the shells. *) -val shell_a : t -> ContractedShell.t +val shell_a : t -> Contracted_shell.t (** Returns the first contracted shell of the first shell pair. *) -val shell_b : t -> ContractedShell.t +val shell_b : t -> Contracted_shell.t (** Returns the second contracted shell of the first shell pair. *) -val shell_c : t -> ContractedShell.t +val shell_c : t -> Contracted_shell.t (** Returns the first contracted shell of the second shell pair. *) -val shell_d : t -> ContractedShell.t +val shell_d : t -> Contracted_shell.t (** Returns the second contracted shell of the second shell pair. *) -val shell_pair_p : t -> ContractedShellPair.t +val shell_pair_p : t -> Contracted_shell_pair.t (** Returns the first contracted shell pair that was used to build the shell pair. *) -val shell_pair_q : t -> ContractedShellPair.t +val shell_pair_q : t -> Contracted_shell_pair.t (** Returns the second contracted shell pair that was used to build the shell pair. *) val monocentric : t -> bool (** True if all four contracted shells have the same center. *) -val coefs_and_shell_pair_couples : t -> (float * PrimitiveShellPairCouple.t) list +val coefs_and_shell_pair_couples : t -> (float * Primitive_shell_pair_couple.t) list (** Returns the list of significant shell pair couples. *) val zkey_array : t -> Zkey.t array diff --git a/gaussian_basis/lib/dune b/gaussian_basis/lib/dune new file mode 100644 index 0000000..bc8f66e --- /dev/null +++ b/gaussian_basis/lib/dune @@ -0,0 +1,11 @@ +; name = name of the supermodule that will wrap all source files as submodules +; public_name = name of the library for ocamlfind and opam +(library + (name qcaml_gaussian_basis) + (public_name qcaml.gaussian_basis) + (libraries + str + qcaml.common + qcaml.particles + ) + (synopsis "Gaussian basis sets.")) diff --git a/Basis/GeneralBasis.ml b/gaussian_basis/lib/general_basis.ml similarity index 93% rename from Basis/GeneralBasis.ml rename to gaussian_basis/lib/general_basis.ml index 3f05319..23ec71b 100644 --- a/Basis/GeneralBasis.ml +++ b/gaussian_basis/lib/general_basis.ml @@ -1,12 +1,15 @@ (** General basis set read from a file *) +open Qcaml_common +open Qcaml_particles + type primitive = { exponent : float ; coefficient: float ; } -type general_contracted_shell = AngularMomentum.t * (primitive array) +type general_contracted_shell = Angular_momentum.t * (primitive array) type element_basis = Element.t * (general_contracted_shell array) @@ -43,7 +46,7 @@ let read_shell line_stream = in contraction :: loop (pred i) in - Some (AngularMomentum.of_char shell, Array.of_list (loop n)) + Some (Angular_momentum.of_char shell, Array.of_list (loop n)) with | No_shell -> None @@ -119,7 +122,7 @@ let string_of_contracted_shell (angular_momentum, prim_array) = Array.length prim_array in Printf.sprintf "%s %d\n%s" - (AngularMomentum.to_string angular_momentum) n + (Angular_momentum.to_string angular_momentum) n (Array.init n (fun i -> string_of_primitive ~id:(i+1) prim_array.(i)) |> Array.to_list |> String.concat "\n") diff --git a/Basis/GeneralBasis.mli b/gaussian_basis/lib/general_basis.mli similarity index 91% rename from Basis/GeneralBasis.mli rename to gaussian_basis/lib/general_basis.mli index 2e0d540..04a4e1d 100644 --- a/Basis/GeneralBasis.mli +++ b/gaussian_basis/lib/general_basis.mli @@ -28,13 +28,16 @@ are created by picking the data from the general basis set. This data structure simplifies the creation of the atomic basis set. *) +open Qcaml_common +open Qcaml_particles + type primitive = private { exponent : float ; coefficient: float ; } -type general_contracted_shell = AngularMomentum.t * (primitive array) +type general_contracted_shell = Angular_momentum.t * (primitive array) type element_basis = Element.t * (general_contracted_shell array) @@ -85,12 +88,12 @@ returns {[ Some (Element.H, - [(AngularMomentum.S, + [(Angular_momentum.S, [{exponent = 13.01; coefficient = 0.019685}; {exponent = 1.962; coefficient = 0.137977}; {exponent = 0.4446; coefficient = 0.478148}]); - (AngularMomentum.S, [{exponent = 0.122; coefficient = 1.}]); - (AngularMomentum.P, [{exponent = 0.727; coefficient = 1.}])]) + (Angular_momentum.S, [{exponent = 0.122; coefficient = 1.}]); + (Angular_momentum.P, [{exponent = 0.727; coefficient = 1.}])]) ]} @raise Malformed_shell if the input is not well formed. @@ -110,7 +113,7 @@ S 3 returns {[ Some - (AngularMomentum.S, + (Angular_momentum.S, [{exponent = 13.01 ; coefficient = 0.019685}; {exponent = 1.962 ; coefficient = 0.137977}; {exponent = 0.4446; coefficient = 0.478148}]) diff --git a/Basis/PrimitiveShell.ml b/gaussian_basis/lib/primitive_shell.ml similarity index 95% rename from Basis/PrimitiveShell.ml rename to gaussian_basis/lib/primitive_shell.ml index b560679..794142c 100644 --- a/Basis/PrimitiveShell.ml +++ b/gaussian_basis/lib/primitive_shell.ml @@ -1,16 +1,16 @@ +open Qcaml_common open Util open Constants -open Coordinate type t = { norm_scales : float array lazy_t; exponent : float; normalization : float; center : Coordinate.t; - ang_mom : AngularMomentum.t; + ang_mom : Angular_momentum.t; } -module Am = AngularMomentum +module Am = Angular_momentum let compute_norm_coef alpha ang_mom = @@ -58,6 +58,7 @@ let make ang_mom center exponent = let to_string s = let coord = s.center in + let open Coordinate in Printf.sprintf "%1s %8.3f %8.3f %8.3f %16.8e" (Am.to_string s.ang_mom) (get X coord) (get Y coord) (get Z coord) s.exponent diff --git a/Basis/PrimitiveShell.mli b/gaussian_basis/lib/primitive_shell.mli similarity index 89% rename from Basis/PrimitiveShell.mli rename to gaussian_basis/lib/primitive_shell.mli index c0437a7..8647b62 100644 --- a/Basis/PrimitiveShell.mli +++ b/gaussian_basis/lib/primitive_shell.mli @@ -1,5 +1,5 @@ (** Set of Gaussians differing only by the powers of x, y and z, with a - constant {!AngularMomentum.t}. + constant {!Angular_momentum.t}. {% \\[ g_{n_x,n_y,n_z}(\mathbf{r}) = (x-X_A)^{n_x} (y-Y_A)^{n_y} (z-Z_A)^{n_z} @@ -20,10 +20,12 @@ where: type t +open Qcaml_common + val to_string : t -> string (** Pretty-printing of the primitive shell in a string. *) -val make : AngularMomentum.t -> Coordinate.t -> float -> t +val make : Angular_momentum.t -> Coordinate.t -> float -> t (** Creates a primitive shell from the total angular momentum, the coordinates of the center and the exponent. *) @@ -33,7 +35,7 @@ val exponent : t -> float val center : t -> Coordinate.t (** Coordinate {% $\mathbf{A}$ %}.of the center. *) -val ang_mom : t -> AngularMomentum.t +val ang_mom : t -> Angular_momentum.t (** Total angular momentum : {% $l = n_x + n_y + n_z$ %}. *) val norm : t -> float @@ -54,7 +56,7 @@ val norm_scales : t -> float array (** Scaling factors {% $f(n_x,n_y,n_z)$ %} adjusting the normalization coefficient for the powers of {% $x,y,z$ %}. The normalization coefficients of the functions of the shell are given by {% $\mathcal{N}\times f$ %}. They are - given in the same order as [AngularMomentum.zkey_array ang_mom]: + given in the same order as [Angular_momentum.zkey_array ang_mom]: {% \\[ f(n_x,n_y,n_z) = \frac{|| g_{l,0,0}(\mathbf{r}) ||}{|| g_{n_x,n_y,n_z}(\mathbf{r}) ||} \\] %} *) diff --git a/Basis/PrimitiveShellPair.ml b/gaussian_basis/lib/primitive_shell_pair.ml similarity index 93% rename from Basis/PrimitiveShellPair.ml rename to gaussian_basis/lib/primitive_shell_pair.ml index 1084705..b64df39 100644 --- a/Basis/PrimitiveShellPair.ml +++ b/gaussian_basis/lib/primitive_shell_pair.ml @@ -1,4 +1,4 @@ -open Util +open Qcaml_common open Constants @@ -12,16 +12,14 @@ type t = { center : Coordinate.t; (* {% $P = (\alpha A + \beta B)/(\alpha+\beta)$ %} *) center_minus_a : Coordinate.t; (* {% $P - A$ %} *) a_minus_b : Coordinate.t; (* {% $A - B$ %} *) - ang_mom : AngularMomentum.t; - shell_a : PrimitiveShell.t; - shell_b : PrimitiveShell.t; + ang_mom : Angular_momentum.t; + shell_a : Primitive_shell.t; + shell_b : Primitive_shell.t; } -exception Null_contribution - -module Am = AngularMomentum +module Am = Angular_momentum module Co = Coordinate -module Ps = PrimitiveShell +module Ps = Primitive_shell let hash a = diff --git a/Basis/PrimitiveShellPair.mli b/gaussian_basis/lib/primitive_shell_pair.mli similarity index 86% rename from Basis/PrimitiveShellPair.mli rename to gaussian_basis/lib/primitive_shell_pair.mli index e3cfb40..be2ec7e 100644 --- a/Basis/PrimitiveShellPair.mli +++ b/gaussian_basis/lib/primitive_shell_pair.mli @@ -37,13 +37,14 @@ References: type t +open Qcaml_common -val make : PrimitiveShell.t -> PrimitiveShell.t -> t +val make : Primitive_shell.t -> Primitive_shell.t -> t (** Creates a primitive shell pair using two primitive shells. *) -val create_make_of : PrimitiveShell.t -> PrimitiveShell.t -> - (PrimitiveShell.t -> PrimitiveShell.t -> float -> t option) -(** Creates a make function [PrimitiveShell.t -> PrimitiveShell.t -> float -> t] in which +val create_make_of : Primitive_shell.t -> Primitive_shell.t -> + (Primitive_shell.t -> Primitive_shell.t -> float -> t option) +(** Creates a make function [Primitive_shell.t -> Primitive_shell.t -> float -> t] in which all the quantities common to the shell and independent of the exponent are pre-computed. @@ -51,7 +52,7 @@ val create_make_of : PrimitiveShell.t -> PrimitiveShell.t -> function is below the cutoff given as a last argument. *) -val ang_mom : t -> AngularMomentum.t +val ang_mom : t -> Angular_momentum.t (** Total angular momentum of the shell pair: sum of the angular momenta of the shells. *) @@ -62,10 +63,10 @@ val monocentric : t -> bool (** True if both shells of the pair have the same center. *) -val shell_a : t -> PrimitiveShell.t +val shell_a : t -> Primitive_shell.t (** Returns the first primitive shell that was used to build the shell pair. *) -val shell_b : t -> PrimitiveShell.t +val shell_b : t -> Primitive_shell.t (** Returns the second primitive shell that was used to build the shell pair. *) val normalization : t -> float @@ -74,7 +75,7 @@ val normalization : t -> float val norm_scales : t -> float array (** Normalization factor, characteristic of the powers of x, y and z of both shells of the pair. It is the outer product of the 2 - {!PrimitiveShell.norm_coef_scale} arrays of the shells consituting the + {!Primitive_shell.norm_coef_scale} arrays of the shells consituting the pair. *) diff --git a/Basis/PrimitiveShellPairCouple.ml b/gaussian_basis/lib/primitive_shell_pair_couple.ml similarity index 78% rename from Basis/PrimitiveShellPairCouple.ml rename to gaussian_basis/lib/primitive_shell_pair_couple.ml index fc8c21e..2b51122 100644 --- a/Basis/PrimitiveShellPairCouple.ml +++ b/gaussian_basis/lib/primitive_shell_pair_couple.ml @@ -1,21 +1,21 @@ -exception NullContribution - +open Qcaml_common + type t = { zkey_array : Zkey.t array lazy_t; - shell_pair_p: PrimitiveShellPair.t ; - shell_pair_q: PrimitiveShellPair.t ; - shell_a : PrimitiveShell.t ; - shell_b : PrimitiveShell.t ; - shell_c : PrimitiveShell.t ; - shell_d : PrimitiveShell.t ; - ang_mom : AngularMomentum.t ; + shell_pair_p: Primitive_shell_pair.t ; + shell_pair_q: Primitive_shell_pair.t ; + shell_a : Primitive_shell.t ; + shell_b : Primitive_shell.t ; + shell_c : Primitive_shell.t ; + shell_d : Primitive_shell.t ; + ang_mom : Angular_momentum.t ; } -module Am = AngularMomentum +module Am = Angular_momentum module Co = Coordinate -module Ps = PrimitiveShell -module Psp = PrimitiveShellPair +module Ps = Primitive_shell +module Psp = Primitive_shell_pair let make shell_pair_p shell_pair_q = let ang_mom = diff --git a/Basis/PrimitiveShellPairCouple.mli b/gaussian_basis/lib/primitive_shell_pair_couple.mli similarity index 81% rename from Basis/PrimitiveShellPairCouple.mli rename to gaussian_basis/lib/primitive_shell_pair_couple.mli index cce84f3..b721603 100644 --- a/Basis/PrimitiveShellPairCouple.mli +++ b/gaussian_basis/lib/primitive_shell_pair_couple.mli @@ -13,33 +13,34 @@ acting on different electrons, since they will be coupled by a two-electron oper type t +open Qcaml_common -val make : PrimitiveShellPair.t -> PrimitiveShellPair.t -> t +val make : Primitive_shell_pair.t -> Primitive_shell_pair.t -> t (** Creates a primitive shell pair couple using two primitive shell pairs. *) -val ang_mom : t -> AngularMomentum.t +val ang_mom : t -> Angular_momentum.t (** Total angular momentum of the shell pair couple: sum of the angular momenta of all the shells. *) -val shell_a : t -> PrimitiveShell.t +val shell_a : t -> Primitive_shell.t (** Returns the first primitive shell of the first shell pair. *) -val shell_b : t -> PrimitiveShell.t +val shell_b : t -> Primitive_shell.t (** Returns the second primitive shell of the first shell pair. *) -val shell_c : t -> PrimitiveShell.t +val shell_c : t -> Primitive_shell.t (** Returns the first primitive shell of the second shell pair. *) -val shell_d : t -> PrimitiveShell.t +val shell_d : t -> Primitive_shell.t (** Returns the second primitive shell of the second shell pair. *) -val shell_pair_p : t -> PrimitiveShellPair.t +val shell_pair_p : t -> Primitive_shell_pair.t (** Returns the first primitive shell pair that was used to build the shell pair. *) -val shell_pair_q : t -> PrimitiveShellPair.t +val shell_pair_q : t -> Primitive_shell_pair.t (** Returns the second primitive shell pair that was used to build the shell pair. *) val p_minus_q : t -> Coordinate.t diff --git a/gaussian_basis/test/dune b/gaussian_basis/test/dune new file mode 100644 index 0000000..f6a55c6 --- /dev/null +++ b/gaussian_basis/test/dune @@ -0,0 +1,8 @@ +(library + (name test_gaussian_basis) + (libraries + alcotest + qcaml.particles + qcaml.gaussian_basis + ) + (synopsis "Tests for Gaussian basis sets")) diff --git a/gaussian_basis/test/general_basis.ml b/gaussian_basis/test/general_basis.ml new file mode 100644 index 0000000..faf4dc8 --- /dev/null +++ b/gaussian_basis/test/general_basis.ml @@ -0,0 +1,52 @@ +open Qcaml_common +open Qcaml_particles +open Qcaml_gaussian_basis +open Alcotest + +let wd = Qcaml.root ^ Filename.dir_sep ^ "test" + +let test_read () = + let oxygen = Element.of_string "O" in + let basis = General_basis.read (wd ^ Filename.dir_sep ^ "cc-pvdz") in + let contractions = List.assoc oxygen basis in + let n_prim = [| ('S',9) ; ('S',9) ; ('S',1) ; ('P',4) ; ('P',1) ; ('D',1) |] in + check int "number of contractions" (Array.length n_prim) (Array.length contractions); + Array.iteri (fun i (l,n) -> + let l', primitives = contractions.(i) in + check char "Angular momentum" l (Angular_momentum.to_char l'); + check int "Number of primitives" n (Array.length primitives)) n_prim; + () + +let test_read_many () = + let helium = Element.of_string "He" in + let basis = General_basis.read (wd ^ Filename.dir_sep ^ "cc-pvdz") in + let basis_f12 = General_basis.read_many (List.map (fun x -> wd ^ Filename.dir_sep ^x) + ["cc-pvdz"; "cc-pvdz-f12-ri"]) in + let contractions = List.assoc helium basis in + let contractions_f12 = List.assoc helium basis_f12 in + let n_prim = [| ('S',4) ; ('S',1) ; ('P',1) |] in + let n_prim_f12 = + [| ('S',4) ; ('S',1) ; ('P',1) ; ('S',1) ; ('S',1) ; ('S',1) ; ('P',1) ; ('P',1) |] + in + check int "number of contractions" (Array.length n_prim) (Array.length contractions); + check int "number of f12 contractions" (Array.length n_prim_f12) (Array.length contractions_f12); + Printf.printf "%s\n\n" (General_basis.to_string ("He", contractions)); + Printf.printf "%s\n" (General_basis.to_string ("He", contractions_f12)); + Array.iteri (fun i (l,n) -> + let l', primitives = contractions.(i) in + let _ , primitives_f12 = contractions_f12.(i) in + check char "Angular momentum" l (Angular_momentum.to_char l'); + check int "Number of primitives" n (Array.length primitives); + check bool "Same primitives as f12" true (primitives = primitives_f12) + ) n_prim; + Array.iteri (fun i (l,n) -> + let l', primitives = contractions_f12.(i) in + check char "Angular momentum f12" l (Angular_momentum.to_char l'); + check int "Number of primitives f12" n (Array.length primitives) + ) n_prim_f12; + () + +let tests = [ + "read", `Quick, test_read; + "read_many", `Quick, test_read_many; +] diff --git a/gaussian_integrals/lib/dependencies.ml b/gaussian_integrals/lib/dependencies.ml new file mode 100644 index 0000000..2b3c528 --- /dev/null +++ b/gaussian_integrals/lib/dependencies.ml @@ -0,0 +1,4 @@ +include Qcaml_common +include Qcaml_particles +include Qcaml_linear_algebra +include Qcaml_gaussian_basis diff --git a/gaussian_integrals/lib/dune b/gaussian_integrals/lib/dune new file mode 100644 index 0000000..a467a86 --- /dev/null +++ b/gaussian_integrals/lib/dune @@ -0,0 +1,13 @@ +; name = name of the supermodule that will wrap all source files as submodules +; public_name = name of the library for ocamlfind and opam +(library + (name qcaml_gaussian_integrals) + (public_name qcaml.gaussian_integrals) + (libraries + str + qcaml.common + qcaml.linear_algebra + qcaml.gaussian_basis + ) + (modules_without_implementation matrix_on_basis) + (synopsis "Integrals on the Gaussian basis sets.")) diff --git a/Basis/NucInt.ml b/gaussian_integrals/lib/electron_nucleus.ml similarity index 74% rename from Basis/NucInt.ml rename to gaussian_integrals/lib/electron_nucleus.ml index 2001d18..fef1db9 100644 --- a/Basis/NucInt.ml +++ b/gaussian_integrals/lib/electron_nucleus.ml @@ -1,16 +1,19 @@ (** Electron-nucleus repulsion integrals *) +include Qcaml_common +include Qcaml_particles +include Qcaml_linear_algebra +include Qcaml_gaussian_basis open Util open Constants -open Lacaml.D -type t = Mat.t -external matrix : t -> Mat.t = "%identity" -external of_matrix : Mat.t -> t = "%identity" +type t = Matrix.t +external matrix : t -> Matrix.t = "%identity" +external of_matrix : Matrix.t -> t = "%identity" -module Am = AngularMomentum +module Am = Angular_momentum module Bs = Basis -module Cs = ContractedShell +module Cs = Contracted_shell (** (0|0)^m : Fundamental electron-nucleus repulsion integral $ \int \phi_p(r1) 1/r_{C} dr_1 $ @@ -34,13 +37,7 @@ let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq = (** Compute all the integrals of a contracted class *) let contracted_class_shell_pair shell_p geometry: float Zmap.t = - OneElectronRR.contracted_class_shell_pair ~zero_m shell_p geometry - - -let cutoff = integrals_cutoff - -let cutoff2 = cutoff *. cutoff -exception NullIntegral + One_electron_rr.contracted_class_shell_pair ~zero_m shell_p geometry let of_basis_nuclei ~basis nuclei = @@ -55,12 +52,13 @@ let of_basis_nuclei ~basis nuclei = and shell = Bs.contracted_shells basis in - let eni_array = Mat.create n n in + let eni_array = Matrix.create n n in + let eni_array_x = Matrix.to_bigarray_inplace eni_array in (* Pre-compute all shell pairs *) let shell_pairs = Array.mapi (fun i shell_a -> Array.map (fun shell_b -> - ContractedShellPair.make shell_a shell_b) (Array.sub shell 0 (i+1)) ) shell + Contracted_shell_pair.make shell_a shell_b) (Array.sub shell 0 (i+1)) ) shell in (* Compute Integrals *) @@ -87,23 +85,24 @@ let of_basis_nuclei ~basis nuclei = let value = Zmap.find cls key in - eni_array.{j_c,i_c} <- value; - eni_array.{i_c,j_c} <- value; + eni_array_x.{j_c,i_c} <- value; + eni_array_x.{i_c,j_c} <- value; ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(j)))) ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(i)))) done; done; - Mat.detri eni_array; + Matrix.detri_inplace eni_array; eni_array let to_file ~filename eni_array = - let n = Mat.dim1 eni_array in + let n = Matrix.dim1 eni_array in let oc = open_out filename in + let eni_array_x = Matrix.to_bigarray_inplace eni_array in for j=1 to n do for i=1 to j do - let value = eni_array.{i,j} in + let value = eni_array_x.{i,j} in if (value <> 0.) then Printf.fprintf oc " %5d %5d %20.15f\n" i j value; done; @@ -111,9 +110,9 @@ let to_file ~filename eni_array = close_out oc -let of_basis basis = +let of_basis _basis = invalid_arg "of_basis_nuclei should be called for NucInt" -let of_basis_pair basis = +let of_basis_pair _basis = failwith "Not implemented" diff --git a/Basis/NucInt.mli b/gaussian_integrals/lib/electron_nucleus.mli similarity index 80% rename from Basis/NucInt.mli rename to gaussian_integrals/lib/electron_nucleus.mli index 8ea1860..3d10e26 100644 --- a/Basis/NucInt.mli +++ b/gaussian_integrals/lib/electron_nucleus.mli @@ -6,7 +6,10 @@ $$ %} *) -include module type of MatrixOnBasis +open Qcaml_particles +open Qcaml_gaussian_basis + +include module type of Matrix_on_basis val of_basis_nuclei : basis:Basis.t -> Nuclei.t -> t (** Build from a {Basis.t} and the nuclei (coordinates and charges). *) diff --git a/Basis/KinInt.ml b/gaussian_integrals/lib/kinetic.ml similarity index 85% rename from Basis/KinInt.ml rename to gaussian_integrals/lib/kinetic.ml index 1f849c1..29c7ea9 100644 --- a/Basis/KinInt.ml +++ b/gaussian_integrals/lib/kinetic.ml @@ -1,19 +1,21 @@ +open Qcaml_common +open Qcaml_linear_algebra +open Qcaml_gaussian_basis open Util open Constants -open Lacaml.D -module Am = AngularMomentum +module Am = Angular_momentum module Bs = Basis module Co = Coordinate -module Cs = ContractedShell -module Csp = ContractedShellPair +module Cs = Contracted_shell +module Csp = Contracted_shell_pair module Po = Powers -module Ps = PrimitiveShell -module Psp = PrimitiveShellPair +module Ps = Primitive_shell +module Psp = Primitive_shell_pair -type t = Mat.t -external matrix : t -> Mat.t = "%identity" -external of_matrix : Mat.t -> t = "%identity" +type t = Matrix.t +external matrix : t -> Matrix.t = "%identity" +external of_matrix : Matrix.t -> t = "%identity" let cutoff = integrals_cutoff @@ -51,7 +53,7 @@ let contracted_class shell_a shell_b : float Zmap.t = let coef_prod = (Csp.coefficients shell_p).(ab) in - (** Screening on thr product of coefficients *) + (* Screening on thr product of coefficients *) if (abs_float coef_prod) > 1.e-4*.cutoff then begin let center_pa = @@ -131,7 +133,8 @@ let of_basis basis = and shell = Bs.contracted_shells basis in - let result = Mat.create n n in + let result = Matrix.create n n in + let result_x = Matrix.to_bigarray_inplace result in for j=0 to (Array.length shell) - 1 do for i=0 to j do (* Compute all the integrals of the class *) @@ -152,16 +155,16 @@ let of_basis basis = try Zmap.find cls key with Not_found -> 0. in - result.{i_c,j_c} <- value; - result.{j_c,i_c} <- value; + result_x.{i_c,j_c} <- value; + result_x.{j_c,i_c} <- value; ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(i)))) ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(j)))) done; done; - Mat.detri result; + Matrix.detri_inplace result; result -let of_basis_pair first_basis second_basis = +let of_basis_pair _first_basis _second_basis = failwith "Not implemented" (** Write all kinetic integrals to a file *) @@ -169,13 +172,14 @@ let to_file ~filename kinetic = let oc = open_out filename in let n = - Mat.dim1 kinetic + Matrix.dim1 kinetic in + let kinetic_x = Matrix.to_bigarray kinetic in for j=1 to n do for i=1 to j do - if (abs_float kinetic.{i,j} > cutoff) then - Printf.fprintf oc "%4d %4d %20.12e\n" i j kinetic.{i,j} + if (abs_float kinetic_x.{i,j} > cutoff) then + Printf.fprintf oc "%4d %4d %20.12e\n" i j kinetic_x.{i,j} done; done; close_out oc diff --git a/Basis/KinInt.mli b/gaussian_integrals/lib/kinetic.mli similarity index 82% rename from Basis/KinInt.mli rename to gaussian_integrals/lib/kinetic.mli index 30432e6..db09544 100644 --- a/Basis/KinInt.mli +++ b/gaussian_integrals/lib/kinetic.mli @@ -7,6 +7,6 @@ $$ %} *) -include module type of MatrixOnBasis +include module type of Matrix_on_basis diff --git a/Basis/MatrixOnBasis.mli b/gaussian_integrals/lib/matrix_on_basis.mli similarity index 74% rename from Basis/MatrixOnBasis.mli rename to gaussian_integrals/lib/matrix_on_basis.mli index 99a8f53..16f4edd 100644 --- a/Basis/MatrixOnBasis.mli +++ b/gaussian_integrals/lib/matrix_on_basis.mli @@ -1,8 +1,9 @@ (** Signature for matrices built on the {!Basis.t} *) -open Lacaml.D +open Qcaml_gaussian_basis +open Qcaml_linear_algebra -type t +type t = Matrix.t val of_basis : Basis.t -> t (** Build from a {!Basis.t}. *) @@ -13,8 +14,8 @@ val of_basis_pair : Basis.t -> Basis.t -> t val to_file : filename:string -> t -> unit (** Write the integrals in a file. *) -val matrix : t -> Mat.t +val matrix : t -> Matrix.t (** Returns the matrix suitable for Lacaml. *) -val of_matrix : Mat.t -> t +val of_matrix : Matrix.t -> t (** Build from a Lacaml matrix. *) diff --git a/Basis/Multipole.ml b/gaussian_integrals/lib/multipole.ml similarity index 75% rename from Basis/Multipole.ml rename to gaussian_integrals/lib/multipole.ml index 67df599..5cb99ef 100644 --- a/Basis/Multipole.ml +++ b/gaussian_integrals/lib/multipole.ml @@ -1,19 +1,20 @@ -open Util +open Qcaml_common +open Qcaml_linear_algebra +open Qcaml_gaussian_basis open Constants -open Lacaml.D -type t = Mat.t array +type t = Matrix.t array (* [| "x"; "y"; "z"; "x2"; "y2"; "z2" |] *) -module Am = AngularMomentum +module Am = Angular_momentum module Bs = Basis module Co = Coordinate -module Cs = ContractedShell -module Csp = ContractedShellPair +module Cs = Contracted_shell +module Csp = Contracted_shell_pair module Po = Powers -module Psp = PrimitiveShellPair +module Psp = Primitive_shell_pair let matrix_x t = t.(0) let matrix_y t = t.(1) @@ -22,8 +23,8 @@ let matrix_x2 t = t.(3) let matrix_y2 t = t.(4) let matrix_z2 t = t.(5) let matrix_xy t = t.(6) +let matrix_xz t = t.(8) let matrix_yz t = t.(7) -let matrix_zx t = t.(8) let matrix_x3 t = t.(9) let matrix_y3 t = t.(10) let matrix_z3 t = t.(11) @@ -31,13 +32,6 @@ let matrix_x4 t = t.(12) let matrix_y4 t = t.(13) let matrix_z4 t = t.(14) -let add3 a1 a2 a3 = - let result = Mat.add a1 a2 in - Mat.add a3 result ~c:result - -let matrix_r2 t = - add3 t.(3) t.(4) t.(5) - @@ -81,7 +75,7 @@ let contracted_class shell_a shell_b : float Zmap.t array = in List.iter (fun (coef_prod, psp) -> - (** Screening on the product of coefficients *) + (* Screening on the product of coefficients *) if (abs_float coef_prod) > 1.e-6*.cutoff then begin let expo_inv = Psp.exponent_inv psp @@ -140,25 +134,25 @@ let contracted_class shell_a shell_b : float Zmap.t array = let x2 = h0 +. xa *. (2. *. x -. xa *. f0) in let y2 = h1 +. ya *. (2. *. y -. ya *. f1) in let z2 = h2 +. za *. (2. *. z -. za *. f2) in - let x3 = j0 +. xa *. f0 *. (3. *. x2 +. xa *. ( -. 3. *. x +. xa)) in - let y3 = j1 +. ya *. f1 *. (3. *. y2 +. ya *. ( -. 3. *. y +. ya)) in - let z3 = j2 +. za *. f2 *. (3. *. z2 +. za *. ( -. 3. *. z +. za)) in - let x4 = l0 +. xa *. f0 *. (4. *. x3 +. xa *. ( -. 6. *. x2 +. xa *. (4. *. x -. xa))) in - let y4 = l1 +. ya *. f1 *. (4. *. y3 +. ya *. ( -. 6. *. y2 +. ya *. (4. *. y -. ya))) in - let z4 = l2 +. za *. f2 *. (4. *. z3 +. za *. ( -. 6. *. z2 +. za *. (4. *. z -. za))) in + let x3 = j0 +. xa *. f0 *. (3. *. x2 -. 3. *. x *. xa +. xa *. xa) in + let y3 = j1 +. ya *. f1 *. (3. *. y2 -. 3. *. y *. ya +. ya *. ya) in + let z3 = j2 +. za *. f2 *. (3. *. z2 -. 3. *. z *. za +. za *. za) in + let x4 = l0 +. xa *. f0 *. ( 4. *. x3 -. 6. *. x2 *. xa +. 4. *. x *. xa *. xa -. xa *. xa *. xa) in + let y4 = l1 +. ya *. f1 *. ( 4. *. y3 -. 6. *. y2 *. ya +. 4. *. y *. ya *. ya -. ya *. ya *. ya) in + let z4 = l2 +. za *. f2 *. ( 4. *. z3 -. 6. *. z2 *. za +. 4. *. z *. za *. za -. za *. za *. za) in let c = contracted_class in let d = coef_prod *. norm in - c.( 0).(i) <- c.( 0).(i) +. d *. x *. f1 *. f2; - c.( 1).(i) <- c.( 1).(i) +. d *. f0 *. y *. f2; - c.( 2).(i) <- c.( 2).(i) +. d *. f0 *. f1 *. z; - c.( 3).(i) <- c.( 3).(i) +. d *. x2 *. f1 *. f2; - c.( 4).(i) <- c.( 4).(i) +. d *. f0 *. y2 *. f2; - c.( 5).(i) <- c.( 5).(i) +. d *. f0 *. f1 *. z2; - c.( 6).(i) <- c.( 6).(i) +. d *. x *. y *. f2; - c.( 7).(i) <- c.( 7).(i) +. d *. f0 *. y *. z; - c.( 8).(i) <- c.( 8).(i) +. d *. x *. f1 *. z; - c.( 9).(i) <- c.( 9).(i) +. d *. x3 *. f1 *. f2; + c.(0).(i) <- c.(0).(i) +. d *. x *. f1 *. f2; + c.(1).(i) <- c.(1).(i) +. d *. f0 *. y *. f2; + c.(2).(i) <- c.(2).(i) +. d *. f0 *. f1 *. z; + c.(3).(i) <- c.(3).(i) +. d *. x2 *. f1 *. f2; + c.(4).(i) <- c.(4).(i) +. d *. f0 *. y2 *. f2; + c.(5).(i) <- c.(5).(i) +. d *. f0 *. f1 *. z2; + c.(6).(i) <- c.(6).(i) +. d *. x *. y *. f2; + c.(7).(i) <- c.(7).(i) +. d *. f0 *. y *. z; + c.(8).(i) <- c.(8).(i) +. d *. x *. f1 *. z; + c.(9).(i) <- c.(9).(i) +. d *. x3 *. f1 *. f2; c.(10).(i) <- c.(10).(i) +. d *. f0 *. y3 *. f2; c.(11).(i) <- c.(11).(i) +. d *. f0 *. f1 *. z3; c.(12).(i) <- c.(12).(i) +. d *. x4 *. f1 *. f2; @@ -193,7 +187,7 @@ let of_basis basis = and shell = Bs.contracted_shells basis in - let result = Array.init 15 (fun _ -> Mat.create n n) in + let result = Array.init 15 (fun _ -> Matrix.create n n |> Matrix.to_bigarray_inplace) in for j=0 to (Array.length shell) - 1 do for i=0 to j do (* Compute all the integrals of the class *) @@ -222,23 +216,9 @@ let of_basis basis = done; done; done; - for k=0 to Array.length result - 1 do - Mat.detri result.(k) - done; + let result = + Array.map Matrix.of_bigarray_inplace result + in + Array.iter Matrix.detri_inplace result; result - -let to_file ~filename eni_array = - let n = Mat.dim1 eni_array in - let oc = open_out filename in - - for j=1 to n do - for i=1 to j do - let value = eni_array.{i,j} in - if (value <> 0.) then - Printf.fprintf oc " %5d %5d %20.15f\n" i j value; - done; - done; - close_out oc - - diff --git a/Basis/Multipole.mli b/gaussian_integrals/lib/multipole.mli similarity index 61% rename from Basis/Multipole.mli rename to gaussian_integrals/lib/multipole.mli index c377045..8e576b4 100644 --- a/Basis/Multipole.mli +++ b/gaussian_integrals/lib/multipole.mli @@ -9,54 +9,54 @@ *) -open Lacaml.D +open Qcaml_linear_algebra +open Qcaml_gaussian_basis type t -val matrix_x : t -> Mat.t +val matrix_x : t -> Matrix.t (** {% $$ \langle \chi_i | x | \chi_j \rangle $$ %} *) -val matrix_y : t -> Mat.t +val matrix_y : t -> Matrix.t (** {% $$ \langle \chi_i | y | \chi_j \rangle $$ %} *) -val matrix_z : t -> Mat.t +val matrix_z : t -> Matrix.t (** {% $$ \langle \chi_i | z | \chi_j \rangle $$ %} *) -val matrix_x2 : t -> Mat.t +val matrix_x2 : t -> Matrix.t (** {% $$ \langle \chi_i | x^2 | \chi_j \rangle $$ %} *) -val matrix_y2 : t -> Mat.t +val matrix_xy : t -> Matrix.t +(** {% $$ \langle \chi_i | xy | \chi_j \rangle $$ %} *) + +val matrix_yz : t -> Matrix.t +(** {% $$ \langle \chi_i | yz | \chi_j \rangle $$ %} *) + +val matrix_xz : t -> Matrix.t +(** {% $$ \langle \chi_i | xz | \chi_j \rangle $$ %} *) + +val matrix_y2 : t -> Matrix.t (** {% $$ \langle \chi_i | y^2 | \chi_j \rangle $$ %} *) -val matrix_z2 : t -> Mat.t +val matrix_z2 : t -> Matrix.t (** {% $$ \langle \chi_i | z^2 | \chi_j \rangle $$ %} *) -val matrix_x3 : t -> Mat.t +val matrix_x3 : t -> Matrix.t (** {% $$ \langle \chi_i | x^3 | \chi_j \rangle $$ %} *) -val matrix_y3 : t -> Mat.t +val matrix_y3 : t -> Matrix.t (** {% $$ \langle \chi_i | y^3 | \chi_j \rangle $$ %} *) -val matrix_z3 : t -> Mat.t +val matrix_z3 : t -> Matrix.t (** {% $$ \langle \chi_i | z^3 | \chi_j \rangle $$ %} *) -val matrix_x4 : t -> Mat.t +val matrix_x4 : t -> Matrix.t (** {% $$ \langle \chi_i | x^4 | \chi_j \rangle $$ %} *) -val matrix_y4 : t -> Mat.t +val matrix_y4 : t -> Matrix.t (** {% $$ \langle \chi_i | y^4 | \chi_j \rangle $$ %} *) -val matrix_z4 : t -> Mat.t +val matrix_z4 : t -> Matrix.t (** {% $$ \langle \chi_i | z^4 | \chi_j \rangle $$ %} *) - -val matrix_r2 : t -> Mat.t -(** {% $$ \langle \chi_i | r^2 | \chi_j \rangle $$ %} *) - - val of_basis : Basis.t -> t - - -val to_file : filename:string -> Mat.t -> unit -(** Write a matrix to a file *) - diff --git a/Basis/OneElectronRR.ml b/gaussian_integrals/lib/one_electron_rr.ml similarity index 91% rename from Basis/OneElectronRR.ml rename to gaussian_integrals/lib/one_electron_rr.ml index 8b850dd..5425b30 100644 --- a/Basis/OneElectronRR.ml +++ b/gaussian_integrals/lib/one_electron_rr.ml @@ -1,21 +1,24 @@ +open Qcaml_common +open Qcaml_particles open Util open Constants +open Qcaml_gaussian_basis exception NullPair -module Am = AngularMomentum +module Am = Angular_momentum module Co = Coordinate -module Cs = ContractedShell -module Csp = ContractedShellPair +module Cs = Contracted_shell +module Csp = Contracted_shell_pair module Po = Powers -module Ps = PrimitiveShell -module Psp = PrimitiveShellPair +module Ps = Primitive_shell +module Psp = Primitive_shell_pair (** Horizontal and Vertical Recurrence Relations (HVRR) *) let hvrr_one_e angMom_a angMom_b - zero_m_array expo_b expo_inv_p + zero_m_array expo_inv_p center_ab center_pa center_pc map = @@ -30,9 +33,9 @@ let hvrr_one_e angMom_a angMom_b in - (** Vertical recurrence relations *) + (* Vertical recurrence relations *) let rec vrr angMom_a = - let { Po.x=ax ; y=ay ; z=az } = angMom_a in + let { Po.x=ax ; y=ay ; z=az ; _ } = angMom_a in if ax < 0 || ay < 0 || az < 0 then raise Exit else match angMom_a.Po.tot with @@ -67,7 +70,7 @@ let hvrr_one_e angMom_a angMom_b result - (** Horizontal recurrence relations *) + (* Horizontal recurrence relations *) and hrr angMom_a angMom_b = match angMom_b.Po.tot with @@ -119,12 +122,11 @@ let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t = List.iter (fun (coef_prod, psp) -> try begin - (** Screening on the product of coefficients *) + (* Screening on the product of coefficients *) if abs_float coef_prod < 1.e-3 *. integrals_cutoff then raise NullPair; let expo_pq_inv = Psp.exponent_inv psp - and expo_b = Ps.exponent (Psp.shell_b psp) and center_p = Psp.center psp and center_pa = Psp.center_minus_a psp in @@ -162,7 +164,6 @@ let contracted_class_shell_pair ~zero_m shell_p geometry : float Zmap.t = hvrr_one_e angMomA angMomB zero_m_array - expo_b expo_pq_inv center_ab center_pa center_pc map diff --git a/gaussian_integrals/lib/orthonormalization.ml b/gaussian_integrals/lib/orthonormalization.ml new file mode 100644 index 0000000..0396ca3 --- /dev/null +++ b/gaussian_integrals/lib/orthonormalization.ml @@ -0,0 +1,72 @@ +open Qcaml_common +open Qcaml_linear_algebra +open Qcaml_gaussian_basis + +type t = Matrix.t + +module Am = Angular_momentum +module Bs = Basis +module Cs = Contracted_shell +module Ov = Overlap + + + +let make_canonical ~thresh ~basis ~cartesian ~overlap = + + let overlap_matrix = Ov.matrix overlap in + + let make_canonical_spherical basis = + let ao_num = Bs.size basis in + let cart_sphe = Matrix.make ao_num ao_num 0. + and i = ref 0 + and n = ref 0 in + Array.iter (fun shell -> + let submatrix = + Spherical_to_cartesian.matrix (Cs.ang_mom shell) + in + Matrix.copy_inplace ~b:cart_sphe ~br:(!i+1) ~bc:(!n+1) submatrix; + i := !i + Matrix.dim1 submatrix; + n := !n + Matrix.dim2 submatrix; + ) (Bs.contracted_shells basis); + let s = Matrix.gemm ~transa:`T ~m:!n cart_sphe overlap_matrix in + let overlap_matrix = Matrix.gemm s ~n:!n cart_sphe in + let s = Orthonormalization.canonical_ortho ~thresh ~overlap:overlap_matrix (Matrix.identity !n) in + Matrix.gemm cart_sphe ~k:!n s + in + + if cartesian then + Orthonormalization.canonical_ortho ~thresh ~overlap:overlap_matrix (Matrix.identity @@ Matrix.dim1 overlap_matrix) + else + match basis with + | None -> invalid_arg + "Basis.t is required when cartesian=false in make_canonical" + | Some basis -> make_canonical_spherical basis + + + +let make_lowdin ~thresh ~overlap = + + let overlap_matrix = Ov.matrix overlap in + let u_vec, u_val = + Matrix.diagonalize_symm overlap_matrix + in + let u_vec_x = Matrix.to_bigarray_inplace u_vec in + + Vector.iter (fun x -> if x < thresh then + invalid_arg (__FILE__^": make_lowdin") ) u_val; + + let u_val = Vector.reci (Vector.sqrt u_val) in + + let u_vec' = + Matrix.init_cols (Matrix.dim1 u_vec) (Matrix.dim2 u_vec) (fun i j -> u_vec_x.{i,j} *. u_val.{j}) + in + Matrix.gemm u_vec' ~transb:`T u_vec + + + +let make ?(thresh=1.e-12) ?basis ~cartesian overlap = + (* + make_lowdin ~thresh ~overlap + *) + make_canonical ~thresh ~basis ~cartesian ~overlap + diff --git a/Basis/Orthonormalization.mli b/gaussian_integrals/lib/orthonormalization.mli similarity index 73% rename from Basis/Orthonormalization.mli rename to gaussian_integrals/lib/orthonormalization.mli index f6adc77..98f4caa 100644 --- a/Basis/Orthonormalization.mli +++ b/gaussian_integrals/lib/orthonormalization.mli @@ -1,8 +1,9 @@ (** Orthonormalization of the basis. *) -open Lacaml.D +open Qcaml_gaussian_basis +open Qcaml_linear_algebra -type t = Mat.t +type t = Matrix.t val make: ?thresh:float -> ?basis:Basis.t -> cartesian:bool -> Overlap.t -> t (** Returns a matrix or orthonormal vectors in the basis. The vectors are @@ -12,3 +13,5 @@ val make: ?thresh:float -> ?basis:Basis.t -> cartesian:bool -> Overlap.t -> t coordinates (5d,7f,...). *) +val make_lowdin: thresh:float -> overlap:Overlap.t -> t +(** Lowdin orthonormalization *) diff --git a/Basis/Overlap.ml b/gaussian_integrals/lib/overlap.ml similarity index 83% rename from Basis/Overlap.ml rename to gaussian_integrals/lib/overlap.ml index 0eb858c..181bc93 100644 --- a/Basis/Overlap.ml +++ b/gaussian_integrals/lib/overlap.ml @@ -1,19 +1,21 @@ +open Qcaml_common +open Qcaml_linear_algebra +open Qcaml_gaussian_basis open Util open Constants -open Lacaml.D -type t = Mat.t -external matrix : t -> Mat.t = "%identity" -external of_matrix : Mat.t -> t = "%identity" +type t = Matrix.t +external matrix : t -> Matrix.t = "%identity" +external of_matrix : Matrix.t -> t = "%identity" -module Am = AngularMomentum +module Am = Angular_momentum module Bs = Basis module Co = Coordinate -module Cs = ContractedShell -module Csp = ContractedShellPair +module Cs = Contracted_shell +module Csp = Contracted_shell_pair module Po = Powers -module Psp = PrimitiveShellPair +module Psp = Primitive_shell_pair let cutoff = integrals_cutoff @@ -56,7 +58,7 @@ let contracted_class shell_a shell_b : float Zmap.t = in List.iter (fun (coef_prod, psp) -> - (** Screening on the product of coefficients *) + (* Screening on the product of coefficients *) if (abs_float coef_prod) > 1.e-6*.cutoff then begin let expo_inv = Psp.exponent_inv psp @@ -99,7 +101,8 @@ let of_basis basis = and shell = Bs.contracted_shells basis in - let result = Mat.create n n in + let result = Matrix.create n n in + let result_x = Matrix.to_bigarray_inplace result in for j=0 to (Array.length shell) - 1 do for i=0 to j do (* Compute all the integrals of the class *) @@ -120,13 +123,13 @@ let of_basis basis = try Zmap.find cls key with Not_found -> 0. in - result.{i_c,j_c} <- value; - result.{j_c,i_c} <- value; + result_x.{i_c,j_c} <- value; + result_x.{j_c,i_c} <- value; ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(i)))) ) (Am.zkey_array (Singlet (Cs.ang_mom shell.(j)))) done; done; - Mat.detri result; + Matrix.detri_inplace result; result @@ -145,7 +148,8 @@ let of_basis_pair first_basis second_basis = and second = Bs.contracted_shells second_basis in - let result = Mat.create n m in + let result = Matrix.create n m in + let result_x = Matrix.to_bigarray_inplace result in for j=0 to (Array.length second) - 1 do for i=0 to (Array.length first) - 1 do (* Compute all the integrals of the class *) @@ -166,7 +170,7 @@ let of_basis_pair first_basis second_basis = try Zmap.find cls key with Not_found -> 0. in - result.{i_c,j_c} <- value; + result_x.{i_c,j_c} <- value; ) (Am.zkey_array (Singlet (Cs.ang_mom first.(i)))) ) (Am.zkey_array (Singlet (Cs.ang_mom second.(j)))) done; @@ -180,13 +184,14 @@ let to_file ~filename overlap = let oc = open_out filename in let n = - Mat.dim1 overlap + Matrix.dim1 overlap in + let overlap_x = Matrix.to_bigarray_inplace overlap in for j=1 to n do for i=1 to j do - if (abs_float overlap.{i,j} > cutoff) then - Printf.fprintf oc "%4d %4d %20.12e\n" i j overlap.{i,j} + if (abs_float overlap_x.{i,j} > cutoff) then + Printf.fprintf oc "%4d %4d %20.12e\n" i j overlap_x.{i,j} done; done; close_out oc diff --git a/Basis/Overlap.mli b/gaussian_integrals/lib/overlap.mli similarity index 70% rename from Basis/Overlap.mli rename to gaussian_integrals/lib/overlap.mli index 57be445..004437a 100644 --- a/Basis/Overlap.mli +++ b/gaussian_integrals/lib/overlap.mli @@ -3,4 +3,4 @@ {% $$ \langle \chi_i | \chi_j \rangle $$ %} *) -include module type of MatrixOnBasis +include module type of Matrix_on_basis diff --git a/Basis/Overlap_primitives.ml b/gaussian_integrals/lib/overlap_primitives.ml similarity index 79% rename from Basis/Overlap_primitives.ml rename to gaussian_integrals/lib/overlap_primitives.ml index 93c4065..902b2b0 100644 --- a/Basis/Overlap_primitives.ml +++ b/gaussian_integrals/lib/overlap_primitives.ml @@ -1,11 +1,12 @@ +open Qcaml_common open Util -(** Horizontal and Vertical Recurrence Relations (HVRR) *) +(* Horizontal and Vertical Recurrence Relations (HVRR) *) let hvrr (angMom_a, angMom_b) (expo_inv_p) (center_ab, center_pa) = - (** Vertical recurrence relations *) + (* Vertical recurrence relations *) let rec vrr angMom_a = if angMom_a > 0 then @@ -16,7 +17,7 @@ let hvrr (angMom_a, angMom_b) (expo_inv_p) (center_ab, center_pa) else 0. - (** Horizontal recurrence relations *) + (* Horizontal recurrence relations *) and hrr angMom_a angMom_b = if angMom_b > 0 then diff --git a/gaussian_integrals/test/dune b/gaussian_integrals/test/dune new file mode 100644 index 0000000..ef168dd --- /dev/null +++ b/gaussian_integrals/test/dune @@ -0,0 +1,8 @@ +(library + (name test_gaussian_integrals) + (libraries + alcotest + qcaml.particles + qcaml.gaussian_integrals + ) + (synopsis "Tests for integrals on the Gaussian basis sets")) diff --git a/gaussian_integrals/test/general_basis.ml b/gaussian_integrals/test/general_basis.ml new file mode 100644 index 0000000..faf4dc8 --- /dev/null +++ b/gaussian_integrals/test/general_basis.ml @@ -0,0 +1,52 @@ +open Qcaml_common +open Qcaml_particles +open Qcaml_gaussian_basis +open Alcotest + +let wd = Qcaml.root ^ Filename.dir_sep ^ "test" + +let test_read () = + let oxygen = Element.of_string "O" in + let basis = General_basis.read (wd ^ Filename.dir_sep ^ "cc-pvdz") in + let contractions = List.assoc oxygen basis in + let n_prim = [| ('S',9) ; ('S',9) ; ('S',1) ; ('P',4) ; ('P',1) ; ('D',1) |] in + check int "number of contractions" (Array.length n_prim) (Array.length contractions); + Array.iteri (fun i (l,n) -> + let l', primitives = contractions.(i) in + check char "Angular momentum" l (Angular_momentum.to_char l'); + check int "Number of primitives" n (Array.length primitives)) n_prim; + () + +let test_read_many () = + let helium = Element.of_string "He" in + let basis = General_basis.read (wd ^ Filename.dir_sep ^ "cc-pvdz") in + let basis_f12 = General_basis.read_many (List.map (fun x -> wd ^ Filename.dir_sep ^x) + ["cc-pvdz"; "cc-pvdz-f12-ri"]) in + let contractions = List.assoc helium basis in + let contractions_f12 = List.assoc helium basis_f12 in + let n_prim = [| ('S',4) ; ('S',1) ; ('P',1) |] in + let n_prim_f12 = + [| ('S',4) ; ('S',1) ; ('P',1) ; ('S',1) ; ('S',1) ; ('S',1) ; ('P',1) ; ('P',1) |] + in + check int "number of contractions" (Array.length n_prim) (Array.length contractions); + check int "number of f12 contractions" (Array.length n_prim_f12) (Array.length contractions_f12); + Printf.printf "%s\n\n" (General_basis.to_string ("He", contractions)); + Printf.printf "%s\n" (General_basis.to_string ("He", contractions_f12)); + Array.iteri (fun i (l,n) -> + let l', primitives = contractions.(i) in + let _ , primitives_f12 = contractions_f12.(i) in + check char "Angular momentum" l (Angular_momentum.to_char l'); + check int "Number of primitives" n (Array.length primitives); + check bool "Same primitives as f12" true (primitives = primitives_f12) + ) n_prim; + Array.iteri (fun i (l,n) -> + let l', primitives = contractions_f12.(i) in + check char "Angular momentum f12" l (Angular_momentum.to_char l'); + check int "Number of primitives f12" n (Array.length primitives) + ) n_prim_f12; + () + +let tests = [ + "read", `Quick, test_read; + "read_many", `Quick, test_read_many; +] diff --git a/Utils/DIIS.ml b/linear_algebra/lib/diis.ml similarity index 51% rename from Utils/DIIS.ml rename to linear_algebra/lib/diis.ml index bc9afc2..63aebed 100644 --- a/Utils/DIIS.ml +++ b/linear_algebra/lib/diis.ml @@ -1,10 +1,7 @@ -open Lacaml.D -open Util - type t = { - p : Vec.t list; - e : Vec.t list; + p : Vector.t list; + e : Vector.t list; m : int; mmax : int; } @@ -36,26 +33,28 @@ let append ~p ~e diis = let next diis = - let e = Mat.of_col_vecs_list diis.e - and p = Mat.of_col_vecs_list diis.p + let e = Matrix.of_col_vecs_list diis.e + and p = Matrix.of_col_vecs_list diis.p in let a = let rec aux m = - let a = Mat.make (m+1) (m+1) 1. in - a.{m+1,m+1} <- 0.; - ignore @@ lacpy ~b:a (gemm ~transa:`T ~m ~n:m e e); - if m > 1 && sycon (lacpy a) > 1.e-14 then + let a = Matrix.make (m+1) (m+1) 1. in + let ax = Matrix.to_bigarray_inplace a in + ax.{m+1,m+1} <- 0.; + Matrix.gemm_inplace ~c:a ~transa:`T ~m ~n:m e e; + if m > 1 && Matrix.sycon a > 1.e-14 then (aux [@tailcall]) (m-1) else a in aux diis.m in - let m = Mat.dim1 a - 1 in - let c = Mat.make0 (m+1) 1 in - c.{m+1,1} <- 1.; - sysv a c; - gemm p c ~k:m - |> Mat.as_vec + let m = Matrix.dim1 a - 1 in + let c = Matrix.make0 (m+1) 1 in + let cx = Matrix.to_bigarray_inplace c in + cx.{m+1,1} <- 1.; + Matrix.sysv_inplace ~b:c a; + Matrix.gemm p c ~k:m + |> Matrix.as_vec_inplace diff --git a/Utils/DIIS.mli b/linear_algebra/lib/diis.mli similarity index 95% rename from Utils/DIIS.mli rename to linear_algebra/lib/diis.mli index e658508..929c7e5 100644 --- a/Utils/DIIS.mli +++ b/linear_algebra/lib/diis.mli @@ -53,10 +53,10 @@ type t val make : ?mmax:int -> unit -> t (** Initialize DIIS with a maximum size.*) -val append : p:Lacaml.D.Vec.t -> e:Lacaml.D.Vec.t -> t -> t +val append : p:Vector.t -> e:Vector.t -> t -> t (** Append a parameter vector [p] and the corresponding error vector [e]. *) -val next : t -> Lacaml.D.Vec.t +val next : t -> Vector.t (** Returns a new parameter vector. *) diff --git a/linear_algebra/lib/dune b/linear_algebra/lib/dune new file mode 100644 index 0000000..1423256 --- /dev/null +++ b/linear_algebra/lib/dune @@ -0,0 +1,10 @@ +; name = name of the supermodule that will wrap all source files as submodules +; public_name = name of the library for ocamlfind and opam +(library + (name qcaml_linear_algebra) + (public_name qcaml.linear_algebra) + (libraries + qcaml.common + lacaml + ) + (synopsis "Linear algebra utilities of QCaml libraries.")) diff --git a/linear_algebra/lib/four_idx_storage.ml b/linear_algebra/lib/four_idx_storage.ml new file mode 100644 index 0000000..3d3f517 --- /dev/null +++ b/linear_algebra/lib/four_idx_storage.ml @@ -0,0 +1,496 @@ +open Qcaml_common + +let max_index = 1 lsl 14 + +type index_pair = { first : int ; second : int } + +type storage_t = + | Dense of Matrix.t + | Sparse of (int, float) Hashtbl.t + +type t = + { + size : int ; + two_index : Matrix.t; + two_index_anti : Matrix.t; + three_index : Matrix.t; + three_index_anti : Matrix.t; + four_index : storage_t ; + } + +let key_of_indices ~r1 ~r2 = + let { first=i ; second=k } = r1 and { first=j ; second=l } = r2 in + let f i k = + let p, r = + if i <= k then i, k else k, i + in p + (r*(r-1))/2 + in + let p = f i k and q = f j l in + f p q + + +let check_bounds r1 r2 t = + let { first=i ; second=k } = r1 and { first=j ; second=l } = r2 in + let size = t.size in + assert ( (i lor j lor k lor l) > 0 ); + assert ( i <= size && j <= size && k <= size && l <= size ) + + +let dense_index i j size = + (j-1)*size + i + + +let sym_index i j = + if i < j then + (j*(j-1))/2 + i + else + (i*(i-1))/2 + j + + +let unsafe_get_four_index ~r1 ~r2 t = + + let get a = + Matrix.to_bigarray a + |> Bigarray.Array2.unsafe_get + in + let { first=i ; second=k } = r1 and { first=j ; second=l } = r2 in + + if i=k then + if j=l then + get t.two_index i j + else + get t.three_index (dense_index j l t.size) i + else if j=l then + get t.three_index (dense_index i k t.size) j + + else if i=l then + if k=j then + get t.two_index_anti i j + else + get t.three_index_anti (dense_index j k t.size) i + + else if j=k then + get t.three_index_anti (dense_index i l t.size) j + + else if i=j then + if k=l then + get t.two_index_anti i k + else + get t.three_index_anti (dense_index k l t.size) i + + else if k=l then + (* *) + get t.three_index_anti (dense_index i j t.size) k + + else + match t.four_index with + | Dense a -> get a (dense_index i k t.size) (sym_index j l) + | Sparse a -> let key = key_of_indices ~r1 ~r2 in + try Hashtbl.find a key + with Not_found -> 0. + + +let get_four_index ~r1 ~r2 t = + check_bounds r1 r2 t; + unsafe_get_four_index ~r1 ~r2 t + + +let unsafe_set_four_index ~r1 ~r2 ~value t = + + + let unsafe_set a = + Matrix.to_bigarray a + |> Bigarray.Array2.unsafe_set + in + + let { first=i ; second=k } = r1 and { first=j ; second=l } = r2 in + + let () = + + if i=k then + begin + if j=l then + begin + unsafe_set t.two_index i j value; + unsafe_set t.two_index j i value; + unsafe_set t.three_index (dense_index i i t.size) j value; + end; + unsafe_set t.three_index (dense_index j l t.size) i value; + unsafe_set t.three_index (dense_index l j t.size) i value; + end + else if j=l then + begin + unsafe_set t.three_index (dense_index i k t.size) j value; + unsafe_set t.three_index (dense_index k i t.size) j value; + end + + else if i=l then + begin + if j=k then + begin + unsafe_set t.two_index_anti i j value; + unsafe_set t.two_index_anti j i value; + unsafe_set t.three_index_anti (dense_index i i t.size) j value; + end; + unsafe_set t.three_index_anti (dense_index j k t.size) i value; + unsafe_set t.three_index_anti (dense_index k j t.size) i value; + end + else if j=k then + begin + unsafe_set t.three_index_anti (dense_index i l t.size) j value; + unsafe_set t.three_index_anti (dense_index l i t.size) j value; + end + + else if i=j then + begin + if k=l then + begin + unsafe_set t.two_index_anti i k value; + unsafe_set t.two_index_anti k i value; + unsafe_set t.three_index_anti (dense_index i i t.size) k value; + end; + unsafe_set t.three_index_anti (dense_index k l t.size) i value; + unsafe_set t.three_index_anti (dense_index l k t.size) i value; + end + + else if k=l then + (* *) + begin + unsafe_set t.three_index_anti (dense_index i j t.size) k value; + unsafe_set t.three_index_anti (dense_index j i t.size) k value; + end + in + + match t.four_index with + | Dense a -> let ik = (dense_index i k t.size) + and jl = (dense_index j l t.size) + and ki = (dense_index k i t.size) + and lj = (dense_index l j t.size) + and ik_s = (sym_index i k) + and jl_s = (sym_index j l) + in + begin + unsafe_set a ik jl_s value; + unsafe_set a ki jl_s value; + unsafe_set a jl ik_s value; + unsafe_set a lj ik_s value; + end + | Sparse a -> let key = key_of_indices ~r1 ~r2 in + Hashtbl.replace a key value + + +let set_four_index ~r1 ~r2 ~value t = + check_bounds r1 r2 t; + unsafe_set_four_index ~r1 ~r2 ~value t + + +let unsafe_increment_four_index ~r1 ~r2 ~value t = + let updated_value = + value +. unsafe_get_four_index ~r1 ~r2 t + in + unsafe_set_four_index ~r1 ~r2 ~value:updated_value t + + +let increment_four_index ~r1 ~r2 ~value t = + check_bounds r1 r2 t; + unsafe_increment_four_index ~r1 ~r2 ~value t + + +let get ~r1 ~r2 a = + get_four_index ~r1 ~r2 a + +let set ~r1 ~r2 ~value = + match classify_float value with + | FP_normal -> set_four_index ~r1 ~r2 ~value + | FP_zero + | FP_subnormal -> fun _ -> () + | FP_infinite + | FP_nan -> + let msg = + Printf.sprintf "FourIdxStorage.ml : set : r1 = (%d,%d) ; r2 = (%d,%d)" + r1.first r1.second r2.first r2.second + in + raise (Invalid_argument msg) + + +let increment ~r1 ~r2 = + increment_four_index ~r1 ~r2 + +let create ~size sparsity = + assert (size < max_index); + let two_index = Matrix.make0 size size in + let two_index_anti = Matrix.make0 size size in + let three_index = Matrix.make0 (size*size) size in + let three_index_anti = Matrix.make0 (size*size) size in + let four_index = + match sparsity with + | `Dense -> Dense ( Matrix.make0 (size*size) ((size*(size+1))/2) ) + | `Sparse -> Sparse ( Hashtbl.create (size*size+13) ) + in + { size ; two_index ; two_index_anti ; three_index ; three_index_anti ; four_index } + + +let size t = t.size + +let get_chem t i j k l = get ~r1:{ first=i ; second=j } ~r2:{ first=k ; second=l } t +let get_phys t i j k l = get ~r1:{ first=i ; second=k } ~r2:{ first=j ; second=l } t + +let set_chem t i j k l value = set ~r1:{ first=i ; second=j } ~r2:{ first=k ; second=l } ~value t +let set_phys t i j k l value = set ~r1:{ first=i ; second=k } ~r2:{ first=j ; second=l } ~value t + +let increment_chem t i j k l value = increment ~r1:{ first=i ; second=j } ~r2:{ first=k ; second=l } ~value t +let increment_phys t i j k l value = increment ~r1:{ first=i ; second=k } ~r2:{ first=j ; second=l } ~value t + + + +(** Element for the stream *) +type element = +{ + i_r1: int ; + j_r2: int ; + k_r1: int ; + l_r2: int ; + value: float +} + + +let get_phys_all_i d ~j ~k ~l = + Vector.init d.size (fun i -> get_phys d i j k l) + + +let get_chem_all_i d ~j ~k ~l = + Vector.init d.size (fun i -> get_chem d i j k l) + + +let get_phys_all_ij d ~k ~l = + Matrix.init_cols d.size d.size (fun i j -> get_phys d i j k l) + + +let get_chem_all_ij d ~k ~l = + + if k = l then + + let result = + Matrix.col d.three_index k + |> Vector.to_bigarray + |> Bigarray.genarray_of_array1 + in + Bigarray.reshape_2 result d.size d.size + |> Matrix.of_bigarray + + else + + match d.four_index with + | Dense a -> + let kl = sym_index k l in + let result = + Matrix.col a kl + |> Vector.to_bigarray + |> Bigarray.genarray_of_array1 + in + Bigarray.reshape_2 result d.size d.size + |> Matrix.of_bigarray + | Sparse _ -> + Matrix.init_cols d.size d.size (fun i j -> get_chem d i j k l) + + + +let to_stream d = + + let i = ref 0 + and j = ref 1 + and k = ref 1 + and l = ref 1 + in + let f_dense _ = + incr i; + if !i > !k then begin + i := 1; + incr j; + if !j > !l then begin + j := 1; + incr k; + if !k > !l then begin + k := 1; + incr l; + end; + end; + end; + if !l <= d.size then + Some { i_r1 = !i ; j_r2 = !j ; + k_r1 = !k ; l_r2 = !l ; + value = get_phys d !i !j !k !l + } + else + None + in + Stream.from f_dense + + +(** Write all integrals to a file with the convention *) +let to_file ?(cutoff=Constants.integrals_cutoff) ~filename data = + let oc = open_out filename in + to_stream data + |> Stream.iter (fun {i_r1 ; j_r2 ; k_r1 ; l_r2 ; value} -> + if (abs_float value > cutoff) then + Printf.fprintf oc " %5d %5d %5d %5d%20.15f\n" i_r1 j_r2 k_r1 l_r2 value); + close_out oc + + + +let of_file ~size ~sparsity filename = + let result = create ~size sparsity in + let ic = Scanf.Scanning.open_in filename in + let rec read_line () = + let result = + try + Some (Scanf.bscanf ic " %d %d %d %d %f" (fun i j k l v -> + set_phys result i j k l v)) + with End_of_file -> None + in + match result with + | Some () -> (read_line [@tailcall]) () + | None -> () + in + read_line (); + Scanf.Scanning.close_in ic; + result + + +let to_list data = + let s = + to_stream data + in + let rec append accu = + let d = + try Some (Stream.next s) with + | Stream.Failure -> None + in + match d with + | None -> List.rev accu + | Some d -> (append [@tailcall]) (d :: accu) + in + append [] + + + + + +let four_index_transform_dense_sparse ds coef source = + + let mo_num = Matrix.dim2 coef in + let ao_num = Matrix.dim1 coef in + let mo_num_2 = mo_num * mo_num in + let ao_num_2 = ao_num * ao_num in + let ao_mo_num = ao_num * mo_num in + let range_ao = Util.array_range 1 ao_num in + let coefx = Matrix.to_bigarray coef in + + Printf.eprintf "4-idx transformation \n%!"; + + let n = ref 0 in + let task delta = + let u = Matrix.create mo_num_2 mo_num + and o = Matrix.create ao_num ao_num_2 + and p = Matrix.create ao_num_2 mo_num + and q = Matrix.create ao_mo_num mo_num + in + + Matrix.fill_inplace u 0.; + + Array.iter (fun l -> + if abs_float coefx.{l,delta} > Constants.epsilon then + begin + + (* o_i_jk *) + let jk = ref 1 in + Array.iter (fun k -> + get_chem_all_ij source ~k ~l + |> Matrix.copy_inplace ~b:o ~bc:!jk + |> ignore; + jk := !jk + ao_num; + ) range_ao; + + (* p_jk_alpha = \sum_i o_i_jk c_i_alpha *) + Matrix.gemm_inplace ~transa:`T ~c:p o coef; + + (* p_j_kalpha *) + let p' = Matrix.reshape p ao_num ao_mo_num in + + (* q_kalpha_beta = \sum_j p_j_kalpha c_j_beta *) + Matrix.gemm_inplace ~transa:`T ~c:q p' coef; + + (* q_k_alphabeta = \sum_j p_j_kalpha c_j_beta *) + let q' = Matrix.reshape q ao_num mo_num_2 in + + (* u_alphabeta_gamma = \sum_k q_k_alphabeta c_k_gamma *) + Matrix.gemm_inplace ~transa:`T ~beta:1. ~alpha:coefx.{l,delta} ~c:u q' coef ; + + end + ) range_ao; + let u = + let b = + Matrix.to_bigarray u + |> Bigarray.genarray_of_array2 + in + Bigarray.reshape b [| mo_num ; mo_num ; mo_num |] + |> Bigarray.array3_of_genarray + in + let rec aux accu alpha beta gamma = + if alpha > beta then + aux accu 1 (beta+1) gamma + else if beta > mo_num then + aux accu 1 1 (gamma+1) + else if gamma > delta then + accu + else + let x = u.{alpha,beta,gamma} in + let new_accu = + if abs_float x > Constants.integrals_cutoff then + (alpha, beta, gamma, delta, x) :: accu + else + accu + in + aux new_accu (alpha+1) beta gamma + in + aux [] 1 1 1 + |> Array.of_list +(* + let result = ref [] in + for gamma = 1 to delta do + for beta = 1 to mo_num do + for alpha = 1 to beta do + let x = u.{alpha,beta,gamma} in + if abs_float x > Constants.integrals_cutoff then + result := (alpha, beta, gamma, delta, x) :: !result; + done + done + done; + Array.of_list !result + *) + in + + let destination = create ~size:mo_num ds in + + Util.list_range 1 mo_num +(* + |> Stream.of_list + |> Parallel.stream_map task +*) + |> List.map task + |> Stream.of_list + + |> Stream.iter (fun l -> + (incr n ; Printf.eprintf "\r%d / %d%!" !n mo_num); + Array.iter (fun (alpha, beta, gamma, delta, x) -> + set_chem destination alpha beta gamma delta x) l); + + Printf.eprintf "\n%!"; + destination + + +let four_index_transform coef source = + match source.four_index with + | Sparse _ -> four_index_transform_dense_sparse `Sparse coef source + | Dense _ -> four_index_transform_dense_sparse `Dense coef source + diff --git a/Utils/FourIdxStorage.mli b/linear_algebra/lib/four_idx_storage.mli similarity index 81% rename from Utils/FourIdxStorage.mli rename to linear_algebra/lib/four_idx_storage.mli index f2ef7b5..f8651bd 100644 --- a/Utils/FourIdxStorage.mli +++ b/linear_algebra/lib/four_idx_storage.mli @@ -7,11 +7,10 @@ There are two kinds of ordering of indices: *) -open Lacaml.D - type t -type element = (** Element for the stream *) +(** Element for the stream *) +type element = { i_r1: int ; j_r2: int ; @@ -20,13 +19,16 @@ type element = (** Element for the stream *) value: float } -val create : size:int -> ?temp_dir:string -> [< `Dense | `Sparse ] -> t +val create : size:int -> [< `Dense | `Sparse ] -> t (** If [`Dense] is chosen, internally the data is stored as a 4-dimensional [Bigarray]. Else, it is stored as a hash table. *) (** {2 Accessors} *) +val size : t -> int +(** Number of stored elements *) + val get_chem : t -> int -> int -> int -> int -> float (** Get an integral using the Chemist's convention {% $(ij|kl)$ %}. *) @@ -45,16 +47,16 @@ val increment_chem : t -> int -> int -> int -> int -> float -> unit val increment_phys : t -> int -> int -> int -> int -> float -> unit (** Increments an integral using the Physicist's convention {% $\langle ij|kl \rangle$ %}. *) -val get_chem_all_i : t -> j:int -> k:int -> l:int -> Vec.t +val get_chem_all_i : t -> j:int -> k:int -> l:int -> Vector.t (** Get all integrals in an array [a.{i} =] {% $(\cdot j|kl)$ %} . *) -val get_phys_all_i : t -> j:int -> k:int -> l:int -> Vec.t +val get_phys_all_i : t -> j:int -> k:int -> l:int -> Vector.t (** Get all integrals in an array [a.{i} =] {% $\langle \cdot j|kl \rangle$ %} . *) -val get_chem_all_ij : t -> k:int -> l:int -> Mat.t +val get_chem_all_ij : t -> k:int -> l:int -> Matrix.t (** Get all integrals in an array [a.{i,j} =] {% $(\cdot \cdot|kl)$ %} . *) -val get_phys_all_ij : t -> k:int -> l:int -> Mat.t +val get_phys_all_ij : t -> k:int -> l:int -> Matrix.t (** Get all integrals in an array [a.{i,j} =] {% $\langle \cdot \cdot|kl \rangle$ %} . *) val to_stream : t -> element Stream.t @@ -63,7 +65,7 @@ val to_stream : t -> element Stream.t val to_list : t -> element list (** Retrun the data structure as a list. *) -val four_index_transform : Mat.t -> t -> t +val four_index_transform : Matrix.t -> t -> t (** Perform a four-index transformation *) (** {2 I/O} *) @@ -75,5 +77,3 @@ val of_file : size:int -> sparsity:[< `Dense | `Sparse ] -> Scanf.Scanning.file_name -> t (** Read from a text file with format ["%d %d %d %d %f"]. *) -val broadcast : t -> t -(** Broadcast the data to the distributed processes. *) diff --git a/linear_algebra/lib/matrix.ml b/linear_algebra/lib/matrix.ml new file mode 100644 index 0000000..4fe515a --- /dev/null +++ b/linear_algebra/lib/matrix.ml @@ -0,0 +1,250 @@ +open Lacaml.D + +type t = Mat.t + +let dim1 t = Mat.dim1 t +let dim2 t = Mat.dim2 t + +let out_of_place f t = + let result = lacpy t in + f result; + result + +let make m n x = Mat.make m n x +let make0 m n = Mat.make0 m n +let create m n = Mat.create m n +let identity m = Mat.identity m + +let fill_inplace t x = Mat.fill t x + +let add a b = Mat.add a b +let sub a b = Mat.sub a b +let mul a b = Mat.mul a b +let div a b = Mat.div a b + +let add_inplace ~c a b = ignore @@ Mat.add ~c a b +let sub_inplace ~c a b = ignore @@ Mat.sub ~c a b +let mul_inplace ~c a b = ignore @@ Mat.mul ~c a b +let div_inplace ~c a b = ignore @@ Mat.div ~c a b + +let add_const_diag_inplace x a = + Mat.add_const_diag x a + +let add_const_diag x a = + out_of_place (fun t -> add_const_diag_inplace x t) a + +let add_const_inplace x a = + ignore @@ Mat.add_const x ~b:a a + +let add_const x a = + Mat.add_const x a + +let at t i j = t.{i,j} + +external to_bigarray_inplace : t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t = "%identity" + +external of_bigarray_inplace : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t -> t = "%identity" + +let to_bigarray t = lacpy t +let of_bigarray t = lacpy t + +let reshape a m n = + assert ( (dim1 a) * (dim2 a) = m*n); + let b = + to_bigarray a + |> Bigarray.genarray_of_array2 + in + Bigarray.reshape_2 b m n + +let col t j = + Mat.col t j + |> Vector.of_bigarray + +let to_col_vecs t = + Mat.to_col_vecs t + |> Array.map Vector.of_bigarray + +let to_col_vecs_list t = + Mat.to_col_vecs_list t + |> List.rev_map Vector.of_bigarray + |> List.rev + +let detri_inplace t = + Mat.detri t + +let detri t = + out_of_place detri_inplace t + +let as_vec_inplace t = + Mat.as_vec t + +let as_vec t = + Mat.as_vec t + |> Vector.copy + +let random ?rnd_state ?(from= -. 1.0) ?(range=2.0) m n = + Mat.random ?rnd_state ~from ~range m n + +let map_inplace f ~b a = + ignore @@ Mat.map f ~b a + +let map f a = + Mat.map f a + +let scale_inplace x t = + Mat.scal x t + +let scale x t = + out_of_place (fun t -> scale_inplace x t) t + +let gemm_inplace ?m ?n ?k ?(beta=0.) ~c ?(transa=`N) ?(alpha=1.0) a ?(transb=`N) b = + ignore @@ gemm ?m ?n ?k ~beta ~c ~transa ~alpha a ~transb b + +let gemm ?m ?n ?k ?beta ?c ?(transa=`N) ?(alpha=1.0) a ?(transb=`N) b = + let c = + match c with + | Some x -> Some (lacpy x) + | None -> None + in + gemm ?m ?n ?k ?beta ?c ~transa ~alpha a ~transb b + +let init_cols = Mat.init_cols + +let of_col_vecs a = + Array.map Vector.to_bigarray_inplace a + |> Mat.of_col_vecs + +let of_col_vecs_list a = + List.rev_map Vector.to_bigarray_inplace a + |> List.rev + |> Mat.of_col_vecs_list + +let normalize_mat_inplace t = + let norm = Mat.as_vec t |> nrm2 in + Mat.scal norm t + +let normalize_mat t = + out_of_place normalize_mat_inplace t + +let diagonalize_symm m_H = + let m_V = lacpy m_H in + let result = + syevd ~vectors:true m_V + in + m_V, result + +let sycon t = + lacpy t + |> sycon + +let xt_o_x ~o ~x = + gemm o x + |> gemm ~transa:`T x + +let x_o_xt ~o ~x = + gemm o x ~transb:`T + |> gemm x + +let pp ppf m = + let rows = Mat.dim1 m + and cols = Mat.dim2 m + in + let rec aux first last = + if (first <= last) then begin + Format.fprintf ppf "@[\n\n %a@]@ " (Lacaml.Io.pp_lfmat + ~row_labels: + (Array.init rows (fun i -> Printf.sprintf "%d " (i + 1))) + ~col_labels: + (Array.init (min 5 (cols-first+1)) (fun i -> Printf.sprintf "-- %d --" (i + first) )) + ~print_right:false + ~print_foot:false + () ) (lacpy ~ac:first ~n:(min 5 (cols-first+1)) m); + (aux [@tailcall]) (first+5) last + end + in + aux 1 cols + +let sysv_inplace ~b a = + sysv a b + +let sysv ~b a = + out_of_place (fun b -> sysv_inplace ~b a) b + +let debug_matrix name a = + Format.printf "@[%s =\n@[%a@]@]@." name pp a + + +let matrix_of_file filename = + let ic = Scanf.Scanning.open_in filename in + let rec read_line accu = + let result = + try + Some (Scanf.bscanf ic " %d %d %f" (fun i j v -> + (i,j,v) :: accu)) + with End_of_file -> None + in + match result with + | Some accu -> (read_line [@tailcall]) accu + | None -> List.rev accu + in + let data = read_line [] in + Scanf.Scanning.close_in ic; + let isize, jsize = + List.fold_left (fun (accu_i,accu_j) (i,j,_) -> + (max i accu_i, max j accu_j)) (0,0) data + in + let result = + Lacaml.D.Mat.of_array + (Array.make_matrix isize jsize 0.) + in + List.iter (fun (i,j,v) -> result.{i,j} <- v) data; + result + + +let sym_matrix_of_file filename = + let result = + matrix_of_file filename + in + for j=1 to Mat.dim1 result do + for i=1 to j do + result.{j,i} <- result.{i,j} + done; + done; + result + + +let copy ?m ?n ?br ?bc ?ar ?ac a = + lacpy a ?m ?n ?br ?bc ?ar ?ac + +let copy_inplace ?m ?n ?br ?bc ~b ?ar ?ac a = + ignore @@ lacpy ?m ?n ?br ?bc ~b ?ar ?ac a + +let scale_cols_inplace a v = + Mat.scal_cols a v + +let scale_cols a v = + out_of_place (fun a -> Mat.scal_cols a v) a + + +let svd a = + let d, u, vt = + gesvd (lacpy a) + in + u, (Vector.of_bigarray d), vt + + +let qr a = + let result = lacpy a in + let tau = geqrf result in + let r = + let r = to_bigarray result in + for j=1 to Mat.dim2 r do + for i=j+1 to Mat.dim2 r do + r.{i,j} <- 0. + done + done; + of_bigarray r + in + orgqr ~tau result; + let q = result in + q, r diff --git a/linear_algebra/lib/matrix.mli b/linear_algebra/lib/matrix.mli new file mode 100644 index 0000000..014d316 --- /dev/null +++ b/linear_algebra/lib/matrix.mli @@ -0,0 +1,194 @@ +type t + +val dim1: t -> int +(** First dimension of the matrix *) + +val dim2: t -> int +(** Second dimension of the matrix *) + +val make : int -> int -> float -> t +(** Creates a matrix initialized with the given value. *) + +val make0 : int -> int -> t +(** Creates a zero-initialized matrix. *) + +val create : int -> int -> t +(** Creates an uninitialized matrix. *) + +val reshape : t -> int -> int -> t +(** Changes the dimensions of the matrix *) + +val init_cols : int -> int -> (int -> int -> float) -> t +(** Creates an uninitialized matrix. *) + +val identity: int -> t +(** Creates an identity matrix. *) + +val fill_inplace: t -> float -> unit +(** Fills the matrix with the give value. *) + +val add_const_diag : float -> t -> t +(** Adds a constant to the diagonal *) + +val add_const_diag_inplace : float -> t -> unit +(** Adds a constant to the diagonal *) + +val add_const_inplace : float -> t -> unit +(** Adds a constant to the diagonal *) + +val add_const : float -> t -> t +(** Adds a constant to the diagonal *) + +val add : t -> t -> t +(** Adds two matrices *) + +val sub : t -> t -> t +(** Subtracts two matrices *) + +val mul : t -> t -> t +(** Multiplies two matrices element-wise *) + +val div : t -> t -> t +(** Divides two matrices element-wise *) + +val add_inplace : c:t -> t -> t -> unit +(** [add_inplace c a b] : performs [c = a+b] in-place. *) + +val sub_inplace : c:t -> t -> t -> unit +(** [sub_inplace c a b] : performs [c = a+b] in-place. *) + +val mul_inplace : c:t -> t -> t -> unit +(** [mul_inplace c a b] : performs [c = a*b] element-wise in-place. *) + +val div_inplace : c:t -> t -> t -> unit +(** [div_inplace c a b] : performs [c = a/b] element-wise in-place. *) + +val at : t -> int -> int -> float +(** [at i j] returns the element at i,j. *) + +val to_bigarray : t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t +(** Converts the matrix into a Bigarray in Fortran layout *) + +val to_bigarray_inplace : + t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t +(** Converts the matrix into a Bigarray in Fortran layout in place*) + +val to_col_vecs : t -> Vector.t array +(** Converts the matrix into an array of vectors *) + +val to_col_vecs_list : t -> Vector.t list +(** Converts the matrix into a list of vectors *) + +val of_col_vecs : Vector.t array -> t +(** Converts an array of vectors into a matrix *) + +val of_col_vecs_list : Vector.t list -> t +(** Converts a list of vectors into a matrix *) + +val of_bigarray : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t -> t +(** Converts a [Bigarray.Array2] in Fortran layout into a matrix *) + +val of_bigarray_inplace : + (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array2.t -> t +(** Converts a [Bigarray.Array2] in Fortran layout into a matrix in place*) + +val copy: ?m:int -> ?n:int -> ?br:int -> ?bc:int -> ?ar:int -> ?ac:int -> t -> t +(** Copies all or part of a two-dimensional matrix A to a new matrix B *) + +val copy_inplace: ?m:int -> ?n:int -> ?br:int -> ?bc:int -> b:t -> ?ar:int -> ?ac:int -> t -> unit +(** Copies all or part of a two-dimensional matrix A to an existing matrix B *) + +val col: t -> int -> Vector.t +(** Returns a column of the matrix as a vector *) + +val detri: t -> t +(** Takes an upper-triangular matrix, and makes it a symmetric matrix +by mirroring the defined triangle along the diagonal. *) + +val detri_inplace: t -> unit +(** Takes an upper-triangular matrix, and makes it a symmetric matrix +by mirroring the defined triangle along the diagonal. *) + +val as_vec_inplace: t -> Vector.t +(** Interpret the matrix as a vector (reshape). *) + +val as_vec: t -> Vector.t +(** Return a copy of the reshaped matrix into a vector *) + +val random: ?rnd_state:Random.State.t -> ?from:float -> ?range:float -> int -> int -> t +(** Creates a random matrix, similarly to [Vector.random] *) + +val map: (float -> float) -> t -> t +(** Apply the function to all elements of the matrix *) + +val map_inplace: (float -> float) -> b:t -> t -> unit +(** [map_inplace f b a] : Apply the function to all elements of the + matrix [a] and store the results in [b] *) + +val scale: float -> t -> t +(** Multiplies the matrix by a constant *) + +val scale_inplace: float -> t -> unit +(** Multiplies the matrix by a constant *) + +val scale_cols: t -> Vector.t -> t +(** Multiplies the matrix by a constant *) + +val scale_cols_inplace: t -> Vector.t -> unit +(** Multiplies the matrix by a constant *) + +val sycon: t -> float +(** Returns the condition number of a matrix *) + +val gemm_inplace : ?m:int -> ?n:int -> ?k:int -> ?beta:float -> c:t -> ?transa:[`N | `T] -> ?alpha:float -> + t -> ?transb:[`N | `T] -> t -> unit +(** Performs the Lapack DGEMM operation. Default values: +[beta=0.] [transa=`N] [alpha=1.0] [transb=`N]. +[gemm ~beta c ~alpha a b]: %{ $C = \beta C + \alpha A B$ *) + +val gemm: ?m:int -> ?n:int -> ?k:int -> ?beta:float -> ?c:t -> ?transa:[`N | `T] -> ?alpha:float -> + t -> ?transb:[`N | `T] -> t -> t +(** Performs the Lapack DGEMM operation. Default values: +[beta=0.] [transa=`N] [alpha=1.0] [transb=`N] +[gemm ~beta ~alpha a b]: %{ $C = \beta C + \alpha A B$ *) + +val svd: t -> t * Vector.t * t +(** Singular value decomposition. *) + +val qr: t -> t * t +(** QR factorization *) + +val normalize_mat : t -> t +(** Returns the matrix with all the column vectors normalized *) + +val normalize_mat_inplace : t -> unit +(** Returns the matrix with all the column vectors normalized *) + +val diagonalize_symm : t -> t * Vector.t +(** Diagonalize a symmetric matrix. Returns the eigenvectors and the eigenvalues. *) + +val xt_o_x : o:t -> x:t -> t +(** Computes {% $\mathbf{X^\dag\, O\, X}$ %} *) + +val x_o_xt : o:t -> x:t -> t +(** Computes {% $\mathbf{X\, O\, X^\dag}$ %} *) + +val debug_matrix: string -> t -> unit +(** Prints a matrix in stdout for debug *) + +val matrix_of_file : string -> t +(** Reads a matrix from a file with format "%d %d %f" corresponding to + [i, j, A.{i,j}]. *) + +val sym_matrix_of_file : string -> t +(** Reads a symmetric matrix from a file with format "%d %d %f" corresponding to + [i, j, A.{i,j}]. *) + +val sysv_inplace : b:t -> t -> unit +(** Solves %{ $AX=B$ %} when A is symmetric, and stores the result in B. *) + +val sysv : b:t -> t -> t +(** Solves %{ $AX=B$ %} when A is symmetric *) + +val pp : Format.formatter -> t -> unit + diff --git a/linear_algebra/lib/orthonormalization.ml b/linear_algebra/lib/orthonormalization.ml new file mode 100644 index 0000000..905806b --- /dev/null +++ b/linear_algebra/lib/orthonormalization.ml @@ -0,0 +1,27 @@ +let canonical_ortho ?thresh:(thresh=1.e-6) ~overlap c = + let u, d, _ = Matrix.svd overlap in + let d_sqrt = Vector.sqrt d in + let n = (* Number of non-negligible singular vectors *) + Vector.fold (fun accu x -> if x > thresh then accu + 1 else accu) 0 d + in + let d_inv_sq = (* D^{-1/2} *) + Vector.map (fun x -> + if x >= thresh then 1. /. x + else 0. ) d_sqrt + in + if n < Vector.dim d_sqrt then + Printf.printf "Removed linear dependencies below %f\n" (1. /. d.{n}) + ; + Matrix.scale_cols_inplace u d_inv_sq ; + Matrix.gemm c u + + +let qr_ortho m = + (* Performed twice for precision *) + let q, _ = Matrix.qr m in + let q, _ = Matrix.qr q in + q + + + + diff --git a/linear_algebra/lib/orthonormalization.mli b/linear_algebra/lib/orthonormalization.mli new file mode 100644 index 0000000..1a3e253 --- /dev/null +++ b/linear_algebra/lib/orthonormalization.mli @@ -0,0 +1,18 @@ +val canonical_ortho: ?thresh:float -> overlap:Matrix.t -> Matrix.t -> Matrix.t +(** Canonical orthogonalization. [overlap] is the overlap matrix {% $\mathbf{S}$ %}, + and the last argument contains the vectors {% $\mathbf{C}$ %} to orthogonalize. + +{% +$$ +\mathbf{C_\bot} = \mathbf{C\, U\, D^{-1/2}}, \; +\mathbf{U\, D\, V^\dag} = \mathbf{S} +$$ +%} + + *) + + +val qr_ortho: Matrix.t -> Matrix.t +(** QR orthogonalization of the input matrix *) + + diff --git a/Utils/SphericalToCartesian.ml b/linear_algebra/lib/spherical_to_cartesian.ml similarity index 95% rename from Utils/SphericalToCartesian.ml rename to linear_algebra/lib/spherical_to_cartesian.ml index e13011e..aa7a52f 100644 --- a/Utils/SphericalToCartesian.ml +++ b/linear_algebra/lib/spherical_to_cartesian.ml @@ -1,21 +1,27 @@ -open Lacaml.D +open Qcaml_common -module Am = AngularMomentum +module Am = Angular_momentum let matrix = function - | Am.S -> Mat.make 1 1 1. + | Am.S -> Matrix.make 1 1 1. | Am.P -> begin - let result = Mat.make 3 3 0. in + let result = + Matrix.make0 3 3 + |> Matrix.to_bigarray_inplace + in result.{ 3, 1} <- 1.0; result.{ 1, 2} <- 1.0; result.{ 2, 3} <- 1.0; - result + Matrix.of_bigarray_inplace result end | Am.D -> begin - let result = Mat.make 6 5 0. in + let result = + Matrix.make0 6 5 + |> Matrix.to_bigarray_inplace + in result.{ 1, 1} <- -0.5; result.{ 4, 1} <- -0.5; result.{ 6, 1} <- 1.0; @@ -24,11 +30,14 @@ let matrix = function result.{ 1, 4} <- 0.86602540378443864676; result.{ 4, 4} <- -0.86602540378443864676; result.{ 2, 5} <- 1.0; - result + Matrix.of_bigarray_inplace result end | Am.F -> begin - let result = Mat.make 10 7 0. in + let result = + Matrix.make0 10 7 + |> Matrix.to_bigarray_inplace + in result.{ 3, 1} <- -0.67082039324993690892; result.{ 8, 1} <- -0.67082039324993690892; result.{10, 1} <- 1.0; @@ -45,11 +54,14 @@ let matrix = function result.{ 4, 6} <- -1.0606601717798212866; result.{ 2, 7} <- 1.0606601717798212866; result.{ 7, 7} <- -0.790569415042094833; - result + Matrix.of_bigarray_inplace result end | Am.G -> begin - let result = Mat.make 15 9 0. in + let result = + Matrix.make0 15 9 + |> Matrix.to_bigarray_inplace + in result.{ 1, 1} <- 0.375; result.{ 4, 1} <- 0.21957751641341996535; result.{ 6, 1} <- -0.87831006565367986142; @@ -78,11 +90,14 @@ let matrix = function result.{11, 8} <- 0.73950997288745200532; result.{ 2, 9} <- 1.1180339887498948482; result.{ 7, 9} <- -1.1180339887498948482; - result + Matrix.of_bigarray_inplace result end | Am.H -> begin - let result = Mat.make 21 11 0. in + let result = + Matrix.make0 21 11 + |> Matrix.to_bigarray_inplace + in result.{ 3, 1} <- 0.625; result.{ 8, 1} <- 0.36596252735569994226; result.{10, 1} <- -1.0910894511799619063; @@ -129,11 +144,14 @@ let matrix = function result.{ 2,11} <- 1.169267933366856683; result.{ 7,11} <- -1.5309310892394863114; result.{16,11} <- 0.7015607600201140098; - result + Matrix.of_bigarray_inplace result end |Am.I -> begin - let result = Mat.make 28 13 0. in + let result = + Matrix.make0 28 13 + |> Matrix.to_bigarray_inplace + in result.{ 1, 1} <- -0.3125; result.{ 4, 1} <- -0.16319780245846672329; result.{ 6, 1} <- 0.97918681475080033975; @@ -204,11 +222,14 @@ let matrix = function result.{ 2,13} <- 1.2151388809514737933; result.{ 7,13} <- -1.9764235376052370825; result.{16,13} <- 1.2151388809514737933; - result + Matrix.of_bigarray_inplace result end |Am.J -> begin - let result = Mat.make 36 15 0. in + let result = + Matrix.make0 36 15 + |> Matrix.to_bigarray_inplace + in result.{ 3, 1} <- -0.60670333962134435221; result.{ 8, 1} <- -0.31684048566533184861; result.{10, 1} <- 1.4169537279434593918; @@ -311,11 +332,14 @@ let matrix = function result.{ 7,15} <- -2.4456993503903949804; result.{16,15} <- 1.96875; result.{29,15} <- -0.64725984928774934788; - result + Matrix.of_bigarray_inplace result end |Am.K -> begin - let result = Mat.make 45 17 0. in + let result = + Matrix.make0 45 17 + |> Matrix.to_bigarray_inplace + in result.{ 1, 1} <- 0.2734375; result.{ 4, 1} <- 0.13566299095694674896; result.{ 6, 1} <- -1.0853039276555739917; @@ -457,11 +481,14 @@ let matrix = function result.{ 7,17} <- -2.9348392204684739765; result.{16,17} <- 2.9348392204684739765; result.{29,17} <- -1.2945196985754986958; - result + Matrix.of_bigarray_inplace result end |Am.L -> begin - let result = Mat.make 55 19 0. in + let result = + Matrix.make0 55 19 + |> Matrix.to_bigarray_inplace + in result.{ 3, 1} <- 0.59686501473785067702; result.{ 8, 1} <- 0.29612797475437320937; result.{10, 1} <- -1.7657660842403202261; @@ -649,7 +676,7 @@ let matrix = function result.{16,19} <- 4.1179360680974030877; result.{29,19} <- -2.3781845426185916576; result.{46,19} <- 0.60904939217552380708; - result + Matrix.of_bigarray_inplace result end | _ -> invalid_arg "Not implemented" diff --git a/Utils/SphericalToCartesian.mli b/linear_algebra/lib/spherical_to_cartesian.mli similarity index 84% rename from Utils/SphericalToCartesian.mli rename to linear_algebra/lib/spherical_to_cartesian.mli index 0f0e99e..504dc07 100644 --- a/Utils/SphericalToCartesian.mli +++ b/linear_algebra/lib/spherical_to_cartesian.mli @@ -1,6 +1,8 @@ (** Conversion from spherical coordinate to cartesian corrdinates. *) -val matrix : AngularMomentum.t -> Lacaml.D.Mat.t +open Qcaml_common + +val matrix : Angular_momentum.t -> Matrix.t (** Returns a transformation matrix to rotate between the basis of atom-centered spherical coordinates to x,y,z coordinates. @@ -10,7 +12,7 @@ val matrix : AngularMomentum.t -> Lacaml.D.Mat.t Example: {[ - SphericalToCartesian.matrix AngularMomentum.D -> + SphericalToCartesian.matrix Angular_momentum.D -> ]} *) diff --git a/linear_algebra/lib/vector.ml b/linear_algebra/lib/vector.ml new file mode 100644 index 0000000..28d288b --- /dev/null +++ b/linear_algebra/lib/vector.ml @@ -0,0 +1,62 @@ +open Lacaml.D + +type t = Vec.t + +let copy ?n ?ofsy ?incy ?y ?ofsx ?incx t = copy ?n ?ofsy ?incy ?y ?ofsx ?incx t +let norm t = nrm2 t + +let dim t = Vec.dim t +let neg t = Vec.neg t +let sum t = Vec.sum t +let abs t = Vec.abs t +let sin t = Vec.sin t +let cos t = Vec.cos t +let tan t = Vec.tan t +let asin t = Vec.asin t +let acos t = Vec.acos t +let atan t = Vec.atan t +let reci t = Vec.reci t +let sqr t = Vec.sqr t +let sqrt t = Vec.sqrt t + +let init f t = Vec.init f t +let iter f t = Vec.iter f t +let map f t = Vec.map f t +let iteri f t = Vec.iteri f t + +let fold f a t = Vec.fold f a t + +let add t1 t2 = Vec.add t1 t2 +let sub t1 t2 = Vec.add t1 t2 +let mul t1 t2 = Vec.mul t1 t2 +let div t1 t2 = Vec.mul t1 t2 +let dot t1 t2 = dot t1 t2 + +let create n = Vec.create n +let make0 n = Vec.make0 n +let of_array a = Vec.of_array a +let of_list l = Vec.of_list l +let to_array t = Vec.to_array t +let to_list t = Vec.to_list t + +let make n x = Vec.make n x + +let of_bigarray_inplace t = t +let of_bigarray t = copy t +let to_bigarray t = copy t +let to_bigarray_inplace t = t + +let random ?rnd_state ?(from= -. 1.0) ?(range=2.0) n = + let state = + match rnd_state with + | None -> Random.get_state () + | Some state -> state + in + Vec.random ~rnd_state:state ~from ~range n + + +let normalize v = + let result = copy v in + scal (1. /. (nrm2 v)) result; + result + diff --git a/linear_algebra/lib/vector.mli b/linear_algebra/lib/vector.mli new file mode 100644 index 0000000..b0f9b5e --- /dev/null +++ b/linear_algebra/lib/vector.mli @@ -0,0 +1,128 @@ +(** Vector module + +This module encapsulates the [Vec] module of Lacaml, to facilitate the change of backend +in the future, or to easily implement distributed vectors. + +The indexing of vectors is 1-based. +*) + +open Lacaml.D + +type t = Vec.t + +val dim : t -> int +(** Returns the dimension of the vector *) + +val add : t -> t -> t +(** [c = add a b] : %{ $c = a + b$ %} *) + +val sub : t -> t -> t +(** [c = sub a b] : %{ $c = a - b$ %} *) + +val mul : t -> t -> t +(** [c = mul a b] : %{ $c_i = a_i \times b_i$ %} *) + +val div : t -> t -> t +(** [c = div a b] : %{ $c_i = a_i / b_i$ %} *) + +val dot : t -> t -> float +(** [dot v1 v2] : Dot product between v1 and v2 *) + +val norm : t -> float +(** Norm of the vector : %{ ||v|| = $\sqrt{v.v}$ %} *) + +val sqr : t -> t +(** [sqr t = map (fun x -> x *. x) t] *) + +val sqrt : t -> t +(** [sqrt t = map sqrt t] *) + +val neg : t -> t +(** [neg t = map (f x -> -. x) t *) + +val reci : t -> t +(** [reci t = map (f x -> 1./x) t *) + +val abs : t -> t +(** [abs t = map (f x -> abs_float x) t *) + +val cos : t -> t +(** [cos t = map (f x -> cos x) t *) + +val sin : t -> t +(** [sin t = map (f x -> sin x) t *) + +val tan : t -> t +(** [tan t = map (f x -> tan x) t *) + +val acos : t -> t +(** [acos t = map (f x -> acos x) t *) + +val asin : t -> t +(** [asin t = map (f x -> asin x) t *) + +val atan : t -> t +(** [atan t = map (f x -> atan x) t *) + +val normalize : t -> t +(** Returns the vector normalized *) + +val init : int -> (int -> float) -> t +(** Initialized the vector with a function taking the index as parameter.*) + +val sum : t -> float +(** Returns the sum of the elements of the vector *) + +val copy : ?n:int -> ?ofsy:int -> ?incy:int -> ?y:vec -> ?ofsx:int -> ?incx:int -> t -> t +(** Returns a copy of the vector X into Y. [ofs] controls the offset and [inc] + the increment. *) + +val map : (float -> float) -> t -> t +(** Equivalent to [Array.map] *) + +val iter : (float -> unit) -> t -> unit +(** Equivalent to [Array.iter] *) + +val iteri : (int -> float -> unit) -> t -> unit +(** Equivalent to [Array.iteri] *) + +val of_array : float array -> t +(** Converts an array of floats into a vector *) + +val of_list : float list -> t +(** Converts a list of floats into a vector *) + +val to_array : t -> float array +(** Converts to an array of floats *) + +val to_list : t -> float list +(** Converts to a list of floats *) + +val create : int -> t +(** Creates an uninitialized vector *) + +val make : int -> float -> t +(** Creates a vector initialized with the given [float].*) + +val make0 : int -> t +(** Creates a zero-initialized vector.*) + +val fold : ('a -> float -> 'a) -> 'a -> t -> 'a +(** Equivalent to [Array.fold] *) + +val random : ?rnd_state:Random.State.t -> ?from:float -> ?range:float -> int -> t +(** Returns a vector of uniform random numbers %{ $ f \le u \le f+r $ + %} where [f] is [from] and [r] is [range]. + Default values: [from:-1.0] [range:2.0] *) + +val of_bigarray : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t -> t +(** Builds by converting from a Fortran bigarray *) + +val to_bigarray : t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t +(** Converts the vector into a Fortran bigarray *) + +val of_bigarray_inplace : (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t -> t +(** Builds by converting from a Fortran bigarray *) + +val to_bigarray_inplace : t -> (float, Stdlib.Bigarray.float64_elt, Stdlib.Bigarray.fortran_layout) Stdlib.Bigarray.Array1.t +(** Converts the vector into a Fortran bigarray *) diff --git a/linear_algebra/test/b.ml b/linear_algebra/test/b.ml new file mode 100644 index 0000000..7dc33ba --- /dev/null +++ b/linear_algebra/test/b.ml @@ -0,0 +1,14 @@ +(* + Tests for Sub1.B +*) + +let test_string () = + Alcotest.(check (neg string)) "foo is not bar" "foo" "bar" + +let test_string_hasty () = + assert ("foo" <> "bar") + +let tests = [ + "string", `Quick, test_string; + "string, hasty", `Quick, test_string_hasty; +] diff --git a/linear_algebra/test/dune b/linear_algebra/test/dune new file mode 100644 index 0000000..b7bf554 --- /dev/null +++ b/linear_algebra/test/dune @@ -0,0 +1,7 @@ +(library + (name test_linear_algebra) + (libraries + alcotest + qcaml.linear_algebra + ) + (synopsis "Tests for linear algebra")) diff --git a/myocamlbuild.ml b/myocamlbuild.ml deleted file mode 100644 index 321f3e9..0000000 --- a/myocamlbuild.ml +++ /dev/null @@ -1,8 +0,0 @@ - -open Ocamlbuild_plugin;; - -dispatch (function - | After_rules -> - pdep ["link"] "linkdep" (fun param -> [param]) - | _ -> ()) - diff --git a/particles/lib/dune b/particles/lib/dune new file mode 100644 index 0000000..35d7d1d --- /dev/null +++ b/particles/lib/dune @@ -0,0 +1,17 @@ +; name = name of the supermodule that will wrap all source files as submodules +; public_name = name of the library for ocamlfind and opam +(library + (name qcaml_particles) + (public_name qcaml.particles) + (libraries + str + qcaml.common + ) + (modules_without_implementation xyz_ast) + (synopsis "Defines nuclei and electrons.")) +(ocamllex + (modules nuclei_lexer) +) +(ocamlyacc + (modules xyz_parser) +) diff --git a/Utils/Electrons.ml b/particles/lib/electrons.ml similarity index 74% rename from Utils/Electrons.ml rename to particles/lib/electrons.ml index e99c2d5..970845b 100644 --- a/Utils/Electrons.ml +++ b/particles/lib/electrons.ml @@ -1,13 +1,18 @@ (** Number of {% $\alpha$ %} and {% $\beta$ %} electrons *) +open Qcaml_common + type t = { n_alfa : int ; n_beta : int ; - multiplicity : int; } -let make ?multiplicity:(multiplicity=1) ?charge:(charge=0) nuclei = +let make n_alfa n_beta = + { n_alfa ; n_beta } + + +let of_atoms ?multiplicity:(multiplicity=1) ?charge:(charge=0) nuclei = let positive_charges = Array.fold_left (fun accu (e, _) -> accu + Charge.to_int (Element.to_charge e) ) 0 nuclei @@ -16,16 +21,18 @@ let make ?multiplicity:(multiplicity=1) ?charge:(charge=0) nuclei = let n_elec = - negative_charges in let n_beta = ((n_elec - multiplicity)+1)/2 in let n_alfa = n_elec - n_beta in - let result = { n_alfa ; n_beta ; multiplicity } in + let result = { n_alfa ; n_beta } in if multiplicity <> (n_alfa - n_beta)+1 then invalid_arg (__FILE__^": make"); result + let charge e = - (e.n_alfa + e.n_beta) |> Charge.of_int + let n_alfa t = t.n_alfa let n_beta t = t.n_beta let n_elec t = t.n_alfa + t.n_beta -let multiplicity t = t.multiplicity +let multiplicity t = t.n_alfa - t.n_beta + 1 diff --git a/Utils/Electrons.mli b/particles/lib/electrons.mli similarity index 82% rename from Utils/Electrons.mli rename to particles/lib/electrons.mli index d84244b..6775380 100644 --- a/Utils/Electrons.mli +++ b/particles/lib/electrons.mli @@ -1,8 +1,13 @@ (** Information related to electrons. *) +open Qcaml_common + type t -val make : ?multiplicity:int -> ?charge:int -> Nuclei.t -> t +val make : int -> int -> t +(** make [n_alfa] [n_beta] *) + +val of_atoms : ?multiplicity:int -> ?charge:int -> Nuclei.t -> t (** Creates the data relative to electrons for a molecular system described by {!Nuclei.t} for a given total charge and spin multiplicity. @param multiplicity default is 1 diff --git a/Nuclei/Element.ml b/particles/lib/element.ml similarity index 99% rename from Nuclei/Element.ml rename to particles/lib/element.ml index c0b8a43..ca5cd05 100644 --- a/Nuclei/Element.ml +++ b/particles/lib/element.ml @@ -1,3 +1,5 @@ +open Qcaml_common + exception ElementError of string type t = @@ -141,7 +143,7 @@ let covalent_radius x = | Te -> 1.38 | I -> 1.39 | Xe -> 1.40 | Pt -> 1.30 in Constants.a0 *. (result x) - |> NonNegativeFloat.of_float + |> Non_negative_float.of_float let vdw_radius x = @@ -162,7 +164,7 @@ let vdw_radius x = | Te -> 2.06 | I -> 1.98 | Xe -> 2.16 | Pt -> 1.75 in Constants.a0 *. (result x) - |> NonNegativeFloat.of_float + |> Non_negative_float.of_float let mass c = diff --git a/Nuclei/Element.mli b/particles/lib/element.mli similarity index 94% rename from Nuclei/Element.mli rename to particles/lib/element.mli index 9b025d8..eda983a 100644 --- a/Nuclei/Element.mli +++ b/particles/lib/element.mli @@ -1,5 +1,7 @@ (** Chemical elements. *) +open Qcaml_common + exception ElementError of string type t = @@ -54,10 +56,10 @@ val to_charge : t -> Charge.t val of_charge : Charge.t -> t (** Create from the atomic charge, with {!Charge.t} type. *) -val covalent_radius : t -> NonNegativeFloat.t +val covalent_radius : t -> Non_negative_float.t (** Covalent radii of the elements, in atomic units. *) -val vdw_radius : t -> NonNegativeFloat.t +val vdw_radius : t -> Non_negative_float.t (** Van der Waals radii of the elements, in atomic units. *) val mass : t -> Mass.t diff --git a/particles/lib/mass.ml b/particles/lib/mass.ml new file mode 100644 index 0000000..112464f --- /dev/null +++ b/particles/lib/mass.ml @@ -0,0 +1,3 @@ +(** Atomic mass. *) + +include Qcaml_common.Non_negative_float diff --git a/particles/lib/mass.mli b/particles/lib/mass.mli new file mode 100644 index 0000000..ff76a11 --- /dev/null +++ b/particles/lib/mass.mli @@ -0,0 +1,3 @@ +(** Atomic mass. *) + +include module type of Qcaml_common.Non_negative_float diff --git a/Nuclei/Nuclei.ml b/particles/lib/nuclei.ml similarity index 92% rename from Nuclei/Nuclei.ml rename to particles/lib/nuclei.ml index 33da7e4..ae028f7 100644 --- a/Nuclei/Nuclei.ml +++ b/particles/lib/nuclei.ml @@ -1,4 +1,4 @@ -open Util +open Qcaml_common open Xyz_ast type t = (Element.t * Coordinate.t) array @@ -20,14 +20,6 @@ let of_xyz_lexbuf lexbuf = |> Array.of_list -let of_xyz_string buffer = - Zmatrix.of_string buffer - |> Zmatrix.to_xyz - |> Array.map (fun (e,x,y,z) -> - (e, Coordinate.(angstrom_to_bohr @@ make_angstrom { x ; y ; z} )) - ) - - let of_xyz_string input_string = Lexing.from_string input_string |> of_xyz_lexbuf @@ -122,7 +114,7 @@ let charge nuclei = let to_xyz_string t = [ string_of_int (Array.length t) ; "" ] @ - ( Array.mapi (fun i (e, coord) -> + ( Array.map (fun (e, coord) -> let open Coordinate in let coord = bohr_to_angstrom coord @@ -140,7 +132,7 @@ let to_t2_string t = (Array.fold_left (+) 0 (Array.map (fun (e,_) -> Element.to_int e) t) ) (2 * Array.length t); "# Znuc x y z" ] - @ (Array.mapi (fun i (e, coord) -> + @ (Array.map (fun (e, coord) -> let open Coordinate in Printf.sprintf " %5f %12.6f %12.6f %12.6f" (Element.to_int e |> float_of_int) coord.x coord.y coord.z diff --git a/Nuclei/Nuclei.mli b/particles/lib/nuclei.mli similarity index 98% rename from Nuclei/Nuclei.mli rename to particles/lib/nuclei.mli index 9944784..6349d79 100644 --- a/Nuclei/Nuclei.mli +++ b/particles/lib/nuclei.mli @@ -2,6 +2,8 @@ of tuples ({!Element.t}, {!Coordinate.t}). *) +open Qcaml_common + type t = (Element.t * Coordinate.t) array diff --git a/Nuclei/Nuclei_lexer.mll b/particles/lib/nuclei_lexer.mll similarity index 100% rename from Nuclei/Nuclei_lexer.mll rename to particles/lib/nuclei_lexer.mll diff --git a/Nuclei/Xyz_ast.mli b/particles/lib/xyz_ast.mli similarity index 94% rename from Nuclei/Xyz_ast.mli rename to particles/lib/xyz_ast.mli index 393a60d..335f0ad 100644 --- a/Nuclei/Xyz_ast.mli +++ b/particles/lib/xyz_ast.mli @@ -1,6 +1,8 @@ (** When an [xyz] file is read by the [Xyz_parser.mly], it is converted into an {!xyz_file} data structure. *) +open Qcaml_common + type nucleus = { element: Element.t ; diff --git a/Nuclei/Xyz_parser.mly b/particles/lib/xyz_parser.mly similarity index 86% rename from Nuclei/Xyz_parser.mly rename to particles/lib/xyz_parser.mly index 50dd1dd..adc4bd0 100644 --- a/Nuclei/Xyz_parser.mly +++ b/particles/lib/xyz_parser.mly @@ -1,7 +1,8 @@ /* Parses nuclear coordinates in xyz format */ %{ -exception InputError of string +open Qcaml_common + let make_angstrom x y z = Coordinate.(make_angstrom { x ; y ; z @@ -9,7 +10,7 @@ let make_angstrom x y z = let output_of f x y z = let a = make_angstrom x y z in - fun e -> + fun e -> { Xyz_ast. element = f e; @@ -34,8 +35,8 @@ let output_of_int = output_of Element.of_int %% /* Grammar rules and actions follow */ input: - | integer title atoms_xyz { - { + | integer title atoms_xyz { + { number_of_atoms = $1; file_title = $2; nuclei = $3; @@ -76,12 +77,12 @@ atoms_list: | { [] } | atoms_list WORD SPACE FLOAT SPACE FLOAT SPACE FLOAT EOL { output_of_string $4 $6 $8 $2 :: $1 } | atoms_list WORD SPACE FLOAT SPACE FLOAT SPACE FLOAT SPACE EOL { output_of_string $4 $6 $8 $2 :: $1 } - | atoms_list INTEGER SPACE FLOAT SPACE FLOAT SPACE FLOAT EOL { output_of_int $4 $6 $8 $2 :: $1 } - | atoms_list INTEGER SPACE FLOAT SPACE FLOAT SPACE FLOAT SPACE EOL { output_of_int $4 $6 $8 $2 :: $1 } + | atoms_list INTEGER SPACE FLOAT SPACE FLOAT SPACE FLOAT EOL { output_of_int $4 $6 $8 $2 :: $1 } + | atoms_list INTEGER SPACE FLOAT SPACE FLOAT SPACE FLOAT SPACE EOL { output_of_int $4 $6 $8 $2 :: $1 } | atoms_list SPACE WORD SPACE FLOAT SPACE FLOAT SPACE FLOAT EOL { output_of_string $5 $7 $9 $3 :: $1 } | atoms_list SPACE WORD SPACE FLOAT SPACE FLOAT SPACE FLOAT SPACE EOL { output_of_string $5 $7 $9 $3 :: $1 } - | atoms_list SPACE INTEGER SPACE FLOAT SPACE FLOAT SPACE FLOAT EOL { output_of_int $5 $7 $9 $3 :: $1 } - | atoms_list SPACE INTEGER SPACE FLOAT SPACE FLOAT SPACE FLOAT SPACE EOL { output_of_int $5 $7 $9 $3 :: $1 } + | atoms_list SPACE INTEGER SPACE FLOAT SPACE FLOAT SPACE FLOAT EOL { output_of_int $5 $7 $9 $3 :: $1 } + | atoms_list SPACE INTEGER SPACE FLOAT SPACE FLOAT SPACE FLOAT SPACE EOL { output_of_int $5 $7 $9 $3 :: $1 } ; diff --git a/Nuclei/Zmatrix.ml b/particles/lib/zmatrix.ml similarity index 99% rename from Nuclei/Zmatrix.ml rename to particles/lib/zmatrix.ml index cba38d6..27431f3 100644 --- a/Nuclei/Zmatrix.ml +++ b/particles/lib/zmatrix.ml @@ -97,7 +97,7 @@ let line_of_string l = in match line_clean with | e :: [] -> First (Element.of_string e) - | e :: i :: r :: [] -> Second + | e :: _ :: r :: [] -> Second (Element.of_string e, distance_of_string r) | e :: i :: r :: j :: a :: [] -> Third diff --git a/particles/test/dune b/particles/test/dune new file mode 100644 index 0000000..f64979f --- /dev/null +++ b/particles/test/dune @@ -0,0 +1,7 @@ +(library + (name test_particles) + (libraries + alcotest + qcaml.particles + ) + (synopsis "Tests for particles")) diff --git a/particles/test/electrons.ml b/particles/test/electrons.ml new file mode 100644 index 0000000..d8aae87 --- /dev/null +++ b/particles/test/electrons.ml @@ -0,0 +1,34 @@ +open Qcaml_common +open Qcaml_particles +open Alcotest + + +let test_all () = + let nuclei = +"3 +Water +O 0. 0. 0. +H -0.756950272703377558 0. -0.585882234512562827 +H 0.756950272703377558 0. -0.585882234512562827 +" + |> Nuclei.of_xyz_string + in + let e = Electrons.of_atoms nuclei in + check int "of_atoms alfa" 5 (Electrons.n_alfa e); + check int "of_atoms beta" 5 (Electrons.n_beta e); + check int "charge " (-10) (Charge.to_int @@ Electrons.charge e); + check int "n_elec" 10 (Electrons.n_elec e); + check int "multiplicity" 1 (Electrons.multiplicity e); + check int "of_atoms alfa m3" 6 (Electrons.(of_atoms ~multiplicity:3 nuclei |> n_alfa)); + check int "of_atoms beta m3" 4 (Electrons.(of_atoms ~multiplicity:3 nuclei |> n_beta)); + check int "of_atoms n_elec m3" 10 (Electrons.(of_atoms ~multiplicity:3 nuclei |> n_elec)); + check int "of_atoms alfa m2 c1" 5 (Electrons.(of_atoms ~multiplicity:2 ~charge:1 nuclei |> n_alfa)); + check int "of_atoms beta m2 c1" 4 (Electrons.(of_atoms ~multiplicity:2 ~charge:1 nuclei |> n_beta)); + check int "of_atoms beta m2 c1" 9 (Electrons.(of_atoms ~multiplicity:2 ~charge:1 nuclei |> n_elec)); + check int "of_atoms mult m2 c1" 2 (Electrons.(of_atoms ~multiplicity:2 ~charge:1 nuclei |> multiplicity)); + check bool "make" true (Electrons.make 6 4 = Electrons.(of_atoms ~multiplicity:3 nuclei)); + () + +let tests = [ + "all", `Quick, test_all +] diff --git a/particles/test/nuclei.ml b/particles/test/nuclei.ml new file mode 100644 index 0000000..74a83ac --- /dev/null +++ b/particles/test/nuclei.ml @@ -0,0 +1,18 @@ +open Qcaml_common +open Qcaml_particles +open Alcotest + +let wd = Qcaml.root ^ Filename.dir_sep ^ "test" + +let test_xyz molecule length repulsion charge core = + let xyz = Nuclei.of_xyz_file (wd^Filename.dir_sep^molecule^".xyz") in + check int "length" length (Array.length xyz); + check (float 1.e-4) "repulsion" repulsion (Nuclei.repulsion xyz); + check int "charge" charge (Charge.to_int @@ Nuclei.charge xyz); + check int "small_core" core (Nuclei.small_core xyz); + () + +let tests = [ + "caffeine", `Quick, (fun () -> test_xyz "caffeine" 24 917.0684 102 28); + "water", `Quick, (fun () -> test_xyz "water" 3 9.19497 10 2); +] diff --git a/run_Localisation.ml b/run_Localisation.ml deleted file mode 100644 index e6679f7..0000000 --- a/run_Localisation.ml +++ /dev/null @@ -1,151 +0,0 @@ -(* ./run_Localisation.native -b basis -x xyz -c charge -o name.mos -i EZFIOdirectory > name.out *) -(* -#.mos contains the localised orbitales -#.out contains the localization convergence and the analysis of the spatial extent of the orbitales -*) - -open Lacaml.D - -let read_qp_mo dirname = - let ic = Unix.open_process_in ("zcat "^dirname^"/mo_basis/mo_coef.gz") in - let check = String.trim (input_line ic) in - assert (check = "2"); - let int_list = - input_line ic - |> String.split_on_char ' ' - |> List.filter (fun x -> x <> "") - |> List.map int_of_string - in - let n_ao, n_mo = - match int_list with - | [ x ; y ] -> x, y - | _ -> assert false - in - let result = - Mat.init_cols n_ao n_mo (fun i j -> - let s = input_line ic in - Scanf.sscanf s " %f " (fun x -> x) - ) - in - let exit_code = Unix.close_process_in ic in - assert (exit_code = Unix.WEXITED 0); - result - - - -let () = - let open Command_line in - begin - set_header_doc (Sys.argv.(0) ^ " - QCaml command"); - set_description_doc "Localizes MOs"; - set_specs - [ { short='b' ; long="basis" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the basis set"; } ; - - { short='x' ; long="xyz" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the nuclear coordinates in xyz format"; } ; - - { short='m' ; long="multiplicity" ; opt=Optional; - arg=With_arg ""; - doc="Spin multiplicity (2S+1). Default is singlet"; } ; - - { short='c' ; long="charge" ; opt=Optional; - arg=With_arg ""; - doc="Total charge of the molecule. Default is 0"; } ; - - { short='o' ; long="output" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the localized MOs"; } ; - - { short='i' ; long="import" ; opt=Optional; - arg=With_arg ""; - doc="Name of the EZFIO directory containing MOs"; } ; - - { short='s' ; long="separation" ; opt=Optional; - arg=With_arg ""; - doc="Type of separation: [ov: occ/vir | sp: sigma/pi | custom] "; } ; - - ] - end; - - - let basis_file = Util.of_some @@ Command_line.get "basis" in - - let nuclei_file = Util.of_some @@ Command_line.get "xyz" in - - let ezfio_file = Command_line.get "import" in - - let charge = - match Command_line.get "charge" with - | Some x -> int_of_string x - | None -> 0 - in - - let multiplicity = - match Command_line.get "multiplicity" with - | Some x -> int_of_string x - | None -> 1 - in - - let output_filename = Util.of_some @@ Command_line.get "output" in - - let separation = - match Command_line.get "separation" with - | None - | Some "ov" -> Localisation.Occ_vir - | Some "sp" -> Localisation.Sigma_pi - | Some "custom" -> - let list_of_lists = - print_endline "Enter ranges, one per line:"; - let rec loop accu = - try - let r = - input_line stdin - |> Range.of_string - |> Range.to_int_list - in - loop (r::accu) - with End_of_file -> List.rev accu - in loop [] - in - Localisation.Custom list_of_lists - | _ -> invalid_arg "separation" - in - - - (* II : Hartree-Fock *) - - (* 1. Def pour HF *) - - let simulation = - Simulation.of_filenames - ~charge ~multiplicity ~nuclei:nuclei_file basis_file - in - - (* 2. Calcul de Hartree-Fock*) - let mo_basis = - match ezfio_file with - | Some ezfio_file -> - let mo_coef = read_qp_mo ezfio_file in - let mo_type = MOBasis.Localized "Boys" in - let elec = Simulation.electrons simulation in - let n_mo = Mat.dim2 mo_coef in - let mo_occupation = Vec.init n_mo (fun i -> - if i <= Electrons.n_beta elec then 2. - else if i <= Electrons.n_alfa elec then 1. - else 0.) in - MOBasis.make ~simulation ~mo_type ~mo_occupation ~mo_coef () - | None -> HartreeFock.make simulation - |> MOBasis.of_hartree_fock - in - - let local_mos = Localisation.localize mo_basis separation in - - let oc = open_out output_filename in - Printf.fprintf oc "[\n"; - Mat.as_vec local_mos - |> Vec.iter (fun x -> Printf.fprintf oc "%20.15e,\n" x); - Printf.fprintf oc "]\n"; - close_out oc diff --git a/run_cas.ml b/run_cas.ml deleted file mode 100644 index 568214f..0000000 --- a/run_cas.ml +++ /dev/null @@ -1,119 +0,0 @@ -let () = - let open Command_line in - begin - set_header_doc (Sys.argv.(0) ^ " - QCaml command"); - set_description_doc "Runs a CAS-CI calculation"; - set_specs - [ { short='b' ; long="basis" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the basis set"; } ; - - { short='x' ; long="xyz" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the nuclear coordinates in xyz format"; } ; - - { short='m' ; long="multiplicity" ; opt=Optional; - arg=With_arg ""; - doc="Spin multiplicity (2S+1). Default is singlet"; } ; - - { short='c' ; long="charge" ; opt=Optional; - arg=With_arg ""; - doc="Total charge of the molecule. Default is 0"; } ; - - { short='f' ; long="frozen-core" ; opt=Optional; - arg=Without_arg ; - doc="Freeze core MOs. Default is false."; } ; - - { short='s' ; long="state" ; opt=Optional; - arg=With_arg ""; - doc="Requested state. Default is 1."; } ; - - { short='n' ; long="n_elec" ; opt=Mandatory; - arg=With_arg ""; - doc="Number of electrons in the active space."; } ; - - { short='o' ; long="n_orb" ; opt=Mandatory; - arg=With_arg ""; - doc="Number of MOs in the active space."; } ; - ] - end; - - (* Handle options *) - let basis_file = Util.of_some @@ Command_line.get "basis" in - - let nuclei_file = Util.of_some @@ Command_line.get "xyz" in - - let n = Util.of_some @@ Command_line.get "n_elec" |> int_of_string in - let m = Util.of_some @@ Command_line.get "n_orb" |> int_of_string in - - let charge = - match Command_line.get "charge" with - | Some x -> ( if x.[0] = 'm' then - ~- (int_of_string (String.sub x 1 (String.length x - 1))) - else - int_of_string x ) - | None -> 0 - in - - let state = - match Command_line.get "state" with - | Some x -> int_of_string x - | None -> 1 - in - - let multiplicity = - match Command_line.get "multiplicity" with - | Some x -> int_of_string x - | None -> 1 - in - - let ppf = - if Parallel.master then Format.std_formatter - else Printing.ppf_dev_null - in - - let s = - Simulation.of_filenames ~charge ~multiplicity ~nuclei:nuclei_file basis_file - in - - let hf = HartreeFock.make s in - if Parallel.master then - Format.fprintf ppf "@[%a@]@." HartreeFock.pp hf; - - let mo_basis = - MOBasis.of_hartree_fock hf - in - - let frozen_core = - Command_line.get_bool "frozen-core" - in - - let space = - DeterminantSpace.cas_of_mo_basis ~frozen_core mo_basis n m - in - let ci = CI.make space ~n_states:state in - if Parallel.master then - Format.fprintf ppf "CAS-CI energy : %20.16f@." ((CI.eigenvalues ci).{1} +. Simulation.nuclear_repulsion s); - - let pt2 = CI.pt2_mp ci in - Format.fprintf ppf "CAS-MP2 energy : %20.16f@." ((CI.eigenvalues ci).{1} +. Simulation.nuclear_repulsion s +. pt2); - - - let pt2 = CI.pt2_en ci in - Format.fprintf ppf "CAS-EN2 energy : %20.16f@." ((CI.eigenvalues ci).{1} +. Simulation.nuclear_repulsion s +. pt2); - - let pt2 = CI.pt2_en_reference ci in - Format.fprintf ppf "CAS-EN2 energy (reference) : %20.16f@." ((CI.eigenvalues ci).{1} +. Simulation.nuclear_repulsion s +. pt2); - -(* - let variance = CI.variance ci in - Format.fprintf ppf "CAS variance : %20.16f@." variance - *) - - (* - let s2 = Util.xt_o_x ~o:(CI.s2_matrix ci) ~x:(CI.eigenvectors ci) in - Util.list_range 1 (DeterminantSpace.size space) - |> List.iter (fun i -> Format.printf "@[%f@]@;" s2.{i,i}); - *) - - Format.fprintf ppf "@."; diff --git a/run_cis.ml b/run_cis.ml deleted file mode 100644 index d4bef7a..0000000 --- a/run_cis.ml +++ /dev/null @@ -1,53 +0,0 @@ -let out_file : string option ref = ref None -let basis_file : string option ref = ref None -let nuclei_file : string option ref = ref None -let charge : int ref = ref 0 -let multiplicity: int ref = ref 1 - - -let speclist = [ - ( "-b" , Arg.String (fun x -> basis_file := Some x), - "File containing the atomic basis set") ; - ( "-c" , Arg.String (fun x -> nuclei_file := Some x), - "File containing the nuclear coordinates") ; - ( "-o" , Arg.String (fun x -> out_file := Some x) , - "Output file") ; - ( "-charge" , Arg.Int (fun x -> charge := x), - "Charge of the system") ; - ( "-mult" , Arg.Int (fun x -> multiplicity := x), - "Spin multiplicity of the system") ; -] - -let run ~out = - (* - let gc = Gc.get () in - Gc.set { gc with minor_heap_size=(262144 / 16) }; - *) - let basis_file = - match !basis_file with - | None -> raise (Invalid_argument "Basis set file should be specified with -b") - | Some x -> x - and nuclei_file = - match !nuclei_file with - | None -> raise (Invalid_argument "Coordinate file should be specified with -c") - | Some x -> x - and charge = !charge - and multiplicity = !multiplicity - in - - let s = - Simulation.of_filenames ~charge ~multiplicity ~nuclei:nuclei_file basis_file - in - - let hf = HartreeFock.make s in - let mos = - MOBasis.of_hartree_fock hf - in - let ee_ints = MOBasis.ee_ints mos in - ERI.to_file ~filename:("mo.eri") ee_ints - -let () = - let usage_msg = "Available options:" in - Arg.parse speclist (fun _ -> ()) usage_msg; - run ~out:!out_file - diff --git a/run_fci.ml b/run_fci.ml deleted file mode 100644 index 72c4d38..0000000 --- a/run_fci.ml +++ /dev/null @@ -1,99 +0,0 @@ -open Lacaml.D - -let () = - let open Command_line in - begin - set_header_doc (Sys.argv.(0) ^ " - QCaml command"); - set_description_doc "Runs a Full CI calculation"; - set_specs - [ { short='b' ; long="basis" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the basis set"; } ; - - { short='x' ; long="xyz" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the nuclear coordinates in xyz format"; } ; - - { short='m' ; long="multiplicity" ; opt=Optional; - arg=With_arg ""; - doc="Spin multiplicity (2S+1). Default is singlet"; } ; - - { short='c' ; long="charge" ; opt=Optional; - arg=With_arg ""; - doc="Total charge of the molecule. Default is 0"; } ; - - { short='f' ; long="frozen-core" ; opt=Optional; - arg=Without_arg ; - doc="Freeze core MOs. Default is false."; } ; - - { short='s' ; long="state" ; opt=Optional; - arg=With_arg ""; - doc="Requested state. Default is 1."; } ; - ] - end; - - (* Handle options *) - let basis_file = Util.of_some @@ Command_line.get "basis" in - - let nuclei_file = Util.of_some @@ Command_line.get "xyz" in - - let charge = - match Command_line.get "charge" with - | Some x -> ( if x.[0] = 'm' then - ~- (int_of_string (String.sub x 1 (String.length x - 1))) - else - int_of_string x ) - | None -> 0 - in - - let state = - match Command_line.get "state" with - | Some x -> int_of_string x - | None -> 1 - in - - let multiplicity = - match Command_line.get "multiplicity" with - | Some x -> int_of_string x - | None -> 1 - in - - let ppf = - if Parallel.master then Format.std_formatter - else Printing.ppf_dev_null - in - - let simulation = - Simulation.of_filenames ~charge ~multiplicity ~nuclei:nuclei_file basis_file - in - - let hf = HartreeFock.make simulation in - if Parallel.master then - Format.fprintf ppf "@[%a@]@." HartreeFock.pp hf; - - let mo_basis = - MOBasis.of_hartree_fock hf - in - - let frozen_core = - Command_line.get_bool "frozen-core" - in - - let space = - DeterminantSpace.fci_of_mo_basis ~frozen_core mo_basis - in - - let ci = CI.make space ~n_states:state in - if Parallel.master then - Format.fprintf ppf "FCI energy : "; - Vec.iteri (fun i x -> if i <= state then - Format.fprintf ppf "%20.16f@; " (x +. Simulation.nuclear_repulsion simulation) ) - (CI.eigenvalues ci); - - (* - let s2 = Util.xt_o_x ~o:(CI.s2_matrix ci) ~x:(CI.eigenvectors ci) in - Util.list_range 1 (DeterminantSpace.size space) - |> List.iter (fun i -> Format.printf "@[%f@]@;" s2.{i,i}); - *) - - Format.fprintf ppf "@."; diff --git a/run_fci_f12.ml b/run_fci_f12.ml deleted file mode 100644 index 0088307..0000000 --- a/run_fci_f12.ml +++ /dev/null @@ -1,123 +0,0 @@ -open Lacaml.D - -let () = - let open Command_line in - begin - set_header_doc (Sys.argv.(0) ^ " - QCaml command"); - set_description_doc "Runs a F12-Full CI calculation"; - set_specs - [ { short='b' ; long="basis" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the basis set"; } ; - - { short='a' ; long="aux_basis" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the auxiliary basis set"; } ; - - { short='x' ; long="xyz" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the nuclear coordinates in xyz format"; } ; - - { short='m' ; long="multiplicity" ; opt=Optional; - arg=With_arg ""; - doc="Spin multiplicity (2S+1). Default is singlet"; } ; - - { short='c' ; long="charge" ; opt=Optional; - arg=With_arg ""; - doc="Total charge of the molecule. Default is 0"; } ; - - { short='f' ; long="frozen-core" ; opt=Optional; - arg=Without_arg ; - doc="Freeze core MOs. Default is false."; } ; - - { short='e' ; long="expo" ; opt=Optional; - arg=With_arg ""; - doc="Exponent of the Gaussian geminal"; } ; - - { short='s' ; long="state" ; opt=Optional; - arg=With_arg ""; - doc="Requested state. Default is 1."; } ; - ] - end; - - (* Handle options *) - let basis_file = Util.of_some @@ Command_line.get "basis" in - - let aux_basis_filename = Util.of_some @@ Command_line.get "aux_basis" in - - let nuclei_file = Util.of_some @@ Command_line.get "xyz" in - - let charge = - match Command_line.get "charge" with - | Some x -> ( if x.[0] = 'm' then - ~- (int_of_string (String.sub x 1 (String.length x - 1))) - else - int_of_string x ) - | None -> 0 - in - - - let expo = - match Command_line.get "expo" with - | Some x -> float_of_string x - | None -> 1.0 - in - - let state = - match Command_line.get "state" with - | Some x -> int_of_string x - | None -> 1 - in - - let multiplicity = - match Command_line.get "multiplicity" with - | Some x -> int_of_string x - | None -> 1 - in - - let ppf = - if Parallel.master then Format.std_formatter - else Printing.ppf_dev_null - in - - let f12 = - F12factor.gaussian_geminal expo - in - - let simulation = - Simulation.of_filenames ~f12 ~charge ~multiplicity ~nuclei:nuclei_file basis_file - in - - let hf = HartreeFock.make ~guess:`Hcore simulation in - if Parallel.master then - Format.fprintf ppf "@[%a@]@." HartreeFock.pp hf; - - let mo_basis = - MOBasis.of_hartree_fock hf - in - - let frozen_core = - Command_line.get_bool "frozen-core" - in - - let fcif12 = - F12CI.make ~simulation ~frozen_core ~mo_basis ~aux_basis_filename ~state () - in - - let ci = F12CI.ci fcif12 in - if Parallel.master then - Format.fprintf ppf "FCI energy : "; - Vec.iteri (fun i x -> if i <= state then - Format.fprintf ppf "%20.16f@; " (x +. Simulation.nuclear_repulsion simulation) ) - (CI.eigenvalues ci); - Format.fprintf ppf "@."; - - let _, e_cif12 = F12CI.eigensystem fcif12 in - if Parallel.master then - Format.fprintf ppf "FCI-F12 energy : "; - Vec.iteri (fun i x -> if i <= state then - Format.fprintf ppf "%20.16f@; " (x +. Simulation.nuclear_repulsion simulation) ) - e_cif12; - Format.fprintf ppf "@." - - diff --git a/run_hartree_fock.ml b/run_hartree_fock.ml deleted file mode 100644 index 2a9f8df..0000000 --- a/run_hartree_fock.ml +++ /dev/null @@ -1,78 +0,0 @@ -open Lacaml.D - -let () = - let open Command_line in - begin - set_header_doc (Sys.argv.(0) ^ " - QCaml command"); - set_description_doc "Runs a Hartree-Fock calculation"; - set_specs - [ { short='b' ; long="basis" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the basis set"; } ; - - { short='x' ; long="xyz" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the nuclear coordinates in xyz format"; } ; - - { short='m' ; long="multiplicity" ; opt=Optional; - arg=With_arg ""; - doc="Spin multiplicity (2S+1). Default is singlet"; } ; - - { short='c' ; long="charge" ; opt=Optional; - arg=With_arg ""; - doc="Total charge of the molecule. Default is 0"; } ; - - { short='g' ; long="guess" ; opt=Optional; - arg=With_arg ""; - doc="Guess with another basis set."; } ; - ] - end; - - let ppf = - if Parallel.master then Format.std_formatter - else Printing.ppf_dev_null - in - - let basis_file = Util.of_some @@ Command_line.get "basis" in - - let nuclei_file = Util.of_some @@ Command_line.get "xyz" in - - let charge = - match Command_line.get "charge" with - | Some x -> int_of_string x - | None -> 0 - in - - let multiplicity = - match Command_line.get "multiplicity" with - | Some x -> int_of_string x - | None -> 1 - in - - let s = Simulation.of_filenames - ~charge ~multiplicity ~nuclei:nuclei_file basis_file in - - let guess = - match Command_line.get "guess" with - | None -> `Huckel - | Some filename -> - let s_guess = Simulation.of_filenames - ~charge ~multiplicity ~nuclei:nuclei_file filename in - let hf = HartreeFock.make s_guess in - Format.fprintf ppf "@[%a@]@." HartreeFock.pp hf; - let guess_mos = - MOBasis.of_hartree_fock hf - |> MOBasis.of_mo_basis s - in - `Matrix (MOBasis.mo_coef guess_mos) - in - - let hf = HartreeFock.make ~guess s in - - Format.fprintf ppf "@[%a@]@." HartreeFock.pp hf - (* - ; let mos = MOBasis.of_hartree_fock hf in - Format.fprintf ppf "@[%a@]@." (fun ppf x -> MOBasis.pp_mo ppf x) mos - *) - - diff --git a/run_integrals.ml b/run_integrals.ml deleted file mode 100644 index b75b6f8..0000000 --- a/run_integrals.ml +++ /dev/null @@ -1,70 +0,0 @@ -let out_file : string option ref = ref None -let basis_file : string option ref = ref None -let nuclei_file : string option ref = ref None -let charge : int option ref = ref None -let multiplicity : int option ref = ref None -let range_separation : float option ref = ref None - - -let speclist = [ - ( "-b" , Arg.String (fun x -> basis_file := Some x), - "File containing the atomic basis set") ; - ( "-c" , Arg.Int (fun x -> charge := Some x), - "Total charge of the system") ; - ( "-m" , Arg.Int (fun x -> multiplicity := Some x), - "Multiplicity of the system") ; - ( "-x" , Arg.String (fun x -> nuclei_file := Some x), - "File containing the nuclear coordinates") ; - ( "-u" , Arg.Float (fun x -> range_separation := Some x), - "Value of mu, the range separation factor") ; -] - -let run () = - let basis_file = - match !basis_file with - | None -> raise (Invalid_argument "Basis set file should be specified with -b") - | Some x -> x - and nuclei_file = - match !nuclei_file with - | None -> raise (Invalid_argument "Coordinate file should be specified with -x") - | Some x -> x - and range_separation = !range_separation - and charge = !charge - and multiplicity = !multiplicity - in - - let s = - Simulation.of_filenames ?range_separation ?charge ?multiplicity - ~nuclei:nuclei_file basis_file - in - - print_endline @@ Nuclei.to_string @@ Simulation.nuclei s; - print_endline "Nuclear repulsion : "; - print_float @@ Simulation.nuclear_repulsion s; print_newline (); - print_endline @@ Basis.to_string @@ Simulation.basis s; - - let ao_basis = Simulation.ao_basis s in - let overlap = AOBasis.overlap ao_basis in - let eN_ints = AOBasis.eN_ints ao_basis in - let kin_ints = AOBasis.kin_ints ao_basis in - let ee_ints = AOBasis.ee_ints ao_basis in - let multipole = AOBasis.multipole ao_basis in - Overlap.to_file ~filename:("Ov.dat") overlap; - NucInt.to_file ~filename:("Nuc.dat") eN_ints; - KinInt.to_file ~filename:("Kin.dat") kin_ints; - ERI.to_file ~filename:("ERI.dat") ee_ints; - Multipole.to_file ~filename:("x.dat") (Multipole.matrix_x multipole); - Multipole.to_file ~filename:("y.dat") (Multipole.matrix_y multipole); - Multipole.to_file ~filename:("z.dat") (Multipole.matrix_z multipole); - - match range_separation with - | Some _mu -> - ERI_lr.to_file ~filename:("ERI_lr.dat") (AOBasis.ee_lr_ints ao_basis) - | None -> () - - -let () = - let usage_msg = "Available options:" in - Arg.parse speclist (fun _ -> ()) usage_msg; - run () - diff --git a/run_mp2.ml b/run_mp2.ml deleted file mode 100644 index adc5ffc..0000000 --- a/run_mp2.ml +++ /dev/null @@ -1,81 +0,0 @@ -open Lacaml.D - -let () = - let open Command_line in - begin - set_header_doc (Sys.argv.(0) ^ " - QCaml command"); - set_description_doc "Runs a Hartree-Fock calculation"; - set_specs - [ { short='b' ; long="basis" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the basis set"; } ; - - { short='x' ; long="xyz" ; opt=Mandatory; - arg=With_arg ""; - doc="Name of the file containing the nuclear coordinates in xyz format"; } ; - - { short='m' ; long="multiplicity" ; opt=Optional; - arg=With_arg ""; - doc="Spin multiplicity (2S+1). Default is singlet"; } ; - - { short='c' ; long="charge" ; opt=Optional; - arg=With_arg ""; - doc="Total charge of the molecule. Default is 0"; } ; - - { short='g' ; long="guess" ; opt=Optional; - arg=With_arg ""; - doc="Guess with another basis set."; } ; - ] - end; - - let ppf = - if Parallel.master then Format.std_formatter - else Printing.ppf_dev_null - in - - let basis_file = Util.of_some @@ Command_line.get "basis" in - - let nuclei_file = Util.of_some @@ Command_line.get "xyz" in - - let charge = - match Command_line.get "charge" with - | Some x -> int_of_string x - | None -> 0 - in - - let multiplicity = - match Command_line.get "multiplicity" with - | Some x -> int_of_string x - | None -> 1 - in - - let s = Simulation.of_filenames - ~charge ~multiplicity ~nuclei:nuclei_file basis_file in - - let guess = - match Command_line.get "guess" with - | None -> `Huckel - | Some filename -> - let s_guess = Simulation.of_filenames - ~charge ~multiplicity ~nuclei:nuclei_file filename in - let hf = HartreeFock.make s_guess in - Format.fprintf ppf "@[%a@]@." HartreeFock.pp hf; - let guess_mos = - MOBasis.of_hartree_fock hf - |> MOBasis.of_mo_basis s - in - `Matrix (MOBasis.mo_coef guess_mos) - in - - let hf = HartreeFock.make ~guess s in - - Format.fprintf ppf "@[%a@]@." HartreeFock.pp hf; - - let e_hf = HartreeFock.energy hf in - - let mp2 = MP2.make ~frozen_core:true hf in - Format.fprintf ppf "@[MP2 = %15.10f@]@." mp2; - Format.fprintf ppf "@[E+MP2 = %15.10f@]@." (mp2 +. e_hf) - - - diff --git a/run_parallel.ml b/run_parallel.ml deleted file mode 100644 index 9231e7c..0000000 --- a/run_parallel.ml +++ /dev/null @@ -1,44 +0,0 @@ - -let pouet () = - Printf.printf "Hello from rank %d of %d.\n" Parallel.rank Parallel.size; - let () = Parallel.barrier () in -(* -let v = Parallel.Vec.init 47 (fun i -> float_of_int i) in -*) - let a = Array.init 41 (fun i -> float_of_int (i+1)) |> Lacaml.D.Vec.of_array in - let b = Array.init 41 (fun i -> float_of_int (3*i+1)) |> Lacaml.D.Vec.of_array in - let v1 = Parallel.Vec.of_vec a in - let v2 = Parallel.Vec.of_vec b in - let d1 = Parallel.dot v1 v2 |> Parallel.broadcast_float in - let d2 = Lacaml.D.dot a b in - (* - let w = Parallel.Vec.to_vec v in - Format.printf "%a" Parallel.Vec.pp v; - if Parallel.master then - Format.printf "@[%a@]@;" (Lacaml.Io.pp_lfvec ()) w; - *) - Printf.printf "%f %f\n" d1 d2; - print_newline () - - -let pouet2 () = - let f (a,b) = (Parallel.rank, a+b) in - let input = Stream.of_list - [ (1,2) ; (3,4) ; (5,6) ; (7,8) ; (9,10) - ; (1,2) ; (3,4) ; (5,6) ; (7,8) ; (9,10) - ; (1,2) ; (3,4) ; (5,6) ; (7,8) ; (9,10) - ; (1,2) ; (3,4) ; (5,6) ; (7,8) ; (9,10) ] - in - let stream = - Farm.run ~f input - in - Stream.iter (fun (x,y) -> Printf.printf "%d %d\n%!" x y) stream - - -open Printf -let () = - printf "%d : %s\n" Parallel.rank Parallel.Node.name; - let value = Parallel.broadcast (lazy Parallel.rank) in - printf "%d : %d\n" Parallel.rank value; - let value = Parallel.Node.broadcast (lazy Parallel.rank) in - printf "%d : %d\n" Parallel.rank value diff --git a/run_test_f12.ml b/run_test_f12.ml deleted file mode 100644 index d73d625..0000000 --- a/run_test_f12.ml +++ /dev/null @@ -1,2309 +0,0 @@ - -let png_image = print_endline ;; - - -open Lacaml.D - - -let basis_filename = "/home/scemama/qp2/data/basis/6-31g" -let aux_basis_filename = "/home/scemama/qp2/data/basis/cc-pvdz" -let nuclei = Nuclei.of_zmt_string "li" -let frozen_core = false -let multiplicity = 2 -let state = 1 - -let f12 = F12factor.gaussian_geminal 1.0 -let basis = Basis.of_nuclei_and_basis_filenames ~f12 ~nuclei [basis_filename] -let charge = 0 - - -let simulation = - Simulation.make - ~charge ~multiplicity ~nuclei - ~cartesian:true - basis - - -let n_elec_alfa, n_elec_beta, n_elec = - let e = Simulation.electrons simulation in - Electrons.(n_alfa e, n_beta e, n_elec e) - -let hf = HartreeFock.make ~guess:`Hcore ~max_scf:1 simulation ;; - -let mo_basis = MOBasis.of_hartree_fock hf - -let f12 = Util.of_some @@ Simulation.f12 simulation - -let mo_num = MOBasis.size mo_basis - -let pp_spindet = Spindeterminant.pp mo_num - -let pp_det = Determinant.pp mo_num - -;; - - - -let simulation_aux = - let charge = Charge.to_int @@ Simulation.charge simulation - and multiplicity = Electrons.multiplicity @@ Simulation.electrons simulation - and nuclei = Simulation.nuclei simulation - in - let general_basis = - Basis.general_basis @@ Simulation.basis simulation - in - GeneralBasis.combine [ - general_basis ; GeneralBasis.read aux_basis_filename - ] - |> Basis.of_nuclei_and_general_basis ~f12 nuclei - |> Simulation.make ~charge ~multiplicity ~nuclei - - -let aux_basis = - MOBasis.of_mo_basis simulation_aux mo_basis - -let aux_num = - MOBasis.size aux_basis - - -let () = ignore @@ MOBasis.f12_ints aux_basis -let () = ignore @@ MOBasis.two_e_ints aux_basis - -let cancel_singles = false - -let mos_cabs = - Util.list_range (mo_num+1) aux_num - -let mos_abs = - Util.list_range 1 aux_num - -let mos_in = - Util.list_range 1 mo_num - -let mos_a k = - Determinant.alfa k - |> Spindeterminant.to_list - -let mos_b k = - Determinant.beta k - |> Spindeterminant.to_list - - -let h_one = - let h = - MOBasis.one_e_ints aux_basis - in fun i j _ -> h.{i,j} - -let h_two = - let two_e_ints = MOBasis.two_e_ints aux_basis in - let h2 i j k l (s:Spin.t) (s':Spin.t) = - if s' <> s then - ERI.get_phys two_e_ints i j k l - else - (ERI.get_phys two_e_ints i j k l) -. - (ERI.get_phys two_e_ints i j l k) - in - h2 - - - - -let f_two = - let two_e_ints = MOBasis.f12_ints aux_basis in - let f2 i j k l (s:Spin.t) (s':Spin.t) = - if s' <> s then - 0.5 *. F12.get_phys two_e_ints i j k l - else - 0.5 *. ( - (F12.get_phys two_e_ints i j k l) -. - (F12.get_phys two_e_ints i j l k) ) - in - let f3 i j k l (s:Spin.t) (s':Spin.t) = - if (i=k && j<>l) || (j=l && i<>k) then - 0. - else - f2 i j k l s s' - in - if cancel_singles then f3 else f2 - -let f_one = fun _ _ _ -> 0. - -(* -let f_two = h_two - -let f_one = h_one -*) - -let f12_integrals mo_basis = - ( f_one, f_two, None ) - -let h_ij mo_basis ki kj = - let integrals = - List.map (fun f -> f mo_basis) - [ CI.h_integrals ] - in - CIMatrixElement.make integrals ki kj - |> List.hd - - -let f_ij mo_basis ki kj = - let integrals = - List.map (fun f -> f mo_basis) - [ f12_integrals ] - in - CIMatrixElement.make integrals ki kj - |> List.hd - - -let hf_ij mo_basis ki kj = - let integrals = - List.map (fun f -> f mo_basis) - [ CI.h_integrals ; f12_integrals ] - in - CIMatrixElement.make integrals ki kj - - - - -let is_a_double det_space = - let mo_class = DeterminantSpace.mo_class det_space in - let mo_num = Array.length @@ MOClass.mo_class_array mo_class in - let m l = - List.fold_left (fun accu i -> - let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j) - ) (Bitstring.zero mo_num) l - in - let aux_mask = m (MOClass.auxiliary_mos mo_class) in - fun k -> - let alfa = - Determinant.alfa k - |> Spindeterminant.bitstring - in - let beta = - Determinant.beta k - |> Spindeterminant.bitstring - in - let a = Bitstring.logand aux_mask alfa - and b = Bitstring.logand aux_mask beta - in - match Bitstring.popcount a + Bitstring.popcount b with - | 2 | 1 -> true - | 0 | _ -> false - - - -let in_space = - DeterminantSpace.fci_f12_of_mo_basis aux_basis ~frozen_core mo_num - -let aux_space = - DeterminantSpace.fci_of_mo_basis aux_basis ~frozen_core - -let det_space_in () = - DeterminantSpace.determinant_stream in_space - -let det_space_out () = - let s = - DeterminantSpace.determinant_stream aux_space - in - Stream.from (fun _ -> - try - let is_a_double = is_a_double in_space in - let rec result () = - let ki = Stream.next s in - if is_a_double ki then - Some (ki,ki) - else - result () - in - result () - with Stream.Failure -> None - ) - - -let ci = CI.make ~n_states:state in_space - -let ci_coef, ci_energy = Lazy.force ci.eigensystem - -let _ = print_newline () - -let p12 det_space = - let mo_class = DeterminantSpace.mo_class det_space in - let mo_num = Array.length @@ MOClass.mo_class_array mo_class in - let m l = - List.fold_left (fun accu i -> - let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j) - ) (Bitstring.zero mo_num) l - in - let aux_mask = m (MOClass.auxiliary_mos mo_class) in - let not_aux_mask = - Bitstring.(shift_left_one mo_num (mo_num-1) |> minus_one |> logxor aux_mask) - in - fun k -> - let alfa = - Determinant.alfa k - |> Spindeterminant.bitstring - in - let beta = - Determinant.beta k - |> Spindeterminant.bitstring - in - let a = Bitstring.logand aux_mask alfa - and b = Bitstring.logand aux_mask beta - in - match Bitstring.popcount a, Bitstring.popcount b with - | 2, 0 - | 0, 2 -> Some (Determinant.negate_phase k) - | 1, 1 -> Some (Determinant.of_spindeterminants - (Spindeterminant.of_bitstring @@ - Bitstring.(logor b (logand not_aux_mask alfa)) ) - (Spindeterminant.of_bitstring @@ - Bitstring.(logor a (logand not_aux_mask beta)) - ) ) - | 1, 0 - | 0, 1 -> Some k - | _ -> None - - - -let out_list = - Util.stream_to_list (det_space_out ()) - -let in_list = - Util.stream_to_list (det_space_in ()) - -let det_a = Array.of_list out_list - |> Array.map (fun (i,_) -> i) - -let det_I = - let n = 123456789 in - in_list - |> List.map (fun k -> (Random.int n, k)) - |> List.sort compare - |> List.map (fun (_,k) -> k) - |> Array.of_list - - -let generate_alphas ki kj exc cabs l r = - (* Check input excitation degree *) - let d = Determinant.degree ki kj in - if d <> exc then - Printf.sprintf "Invalid excitation degree. Expected %d and found %d." exc d - |> failwith; - - (* Generate single excitations *) - let all_singles ki = - let mos_a, mos_b = Determinant.to_lists ki in - [ List.map (fun hole -> - List.map (fun particle -> - if hole = particle then None else - Some (Determinant.single_excitation Spin.Alfa hole particle ki) - ) mos_abs - ) mos_a - ; - List.map (fun hole -> - List.map (fun particle -> - if hole = particle then None else - Some (Determinant.single_excitation Spin.Beta hole particle ki) - ) mos_abs - ) mos_b - ] - |> List.concat - |> List.concat - |> Util.list_some - |> List.filter (fun x -> Determinant.is_none x = false) - |> List.map (fun x -> Determinant.set_phase Phase.Pos x) - in - - (* Generate double excitations *) - let all_doubles ki = - let mos_a, mos_b = Determinant.to_lists ki in - [ List.map (fun hole -> (* Alpha-Alpha *) - List.map (fun particle -> - List.map (fun hole' -> - List.map (fun particle' -> - if hole = particle || hole' = particle' then None else - if hole' > hole && particle' < particle then - Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Alfa hole' particle' ki) - else None - ) mos_abs - ) mos_a - ) mos_abs - ) mos_a - ; - List.map (fun hole -> (* Beta-Beta *) - List.map (fun particle -> - List.map (fun hole' -> - List.map (fun particle' -> - if hole' > hole && particle' < particle && hole <> particle && hole' <> particle' then - Some (Determinant.double_excitation Spin.Beta hole particle Spin.Beta hole' particle' ki) - else None - ) mos_abs - ) mos_b - ) mos_abs - ) mos_b - ; - List.map (fun hole -> (* Alpha-Beta *) - List.map (fun particle -> - List.map (fun hole' -> - List.map (fun particle' -> - if hole = particle || hole' = particle' then None else - Some (Determinant.double_excitation Spin.Alfa hole particle Spin.Beta hole' particle' ki) - ) mos_abs - ) mos_b - ) mos_abs - ) mos_a - ] - |> List.concat - |> List.concat - |> List.concat - |> List.concat - |> Util.list_some - |> List.filter (fun x -> Determinant.is_none x = false) - |> List.map (fun x -> Determinant.set_phase Phase.Pos x) - in - - (* Generate left and right excitations *) - let al = - match l with - | 1 -> all_singles ki - | 2 -> all_doubles ki - | _ -> assert false - in - let ar = - match r with - | 1 -> all_singles kj - | 2 -> all_doubles kj - | _ -> assert false - in - - let mo_class = DeterminantSpace.mo_class in_space in - let m l = - List.fold_left (fun accu i -> - let j = i-1 in Bitstring.logor accu (Bitstring.shift_left_one mo_num j) - ) (Bitstring.zero mo_num) l - in - let aux_mask = m (MOClass.auxiliary_mos mo_class) in - let good_cabs k = - let alfa = - Determinant.alfa k - |> Spindeterminant.bitstring - in - let beta = - Determinant.beta k - |> Spindeterminant.bitstring - in - let a = Bitstring.logand aux_mask alfa - and b = Bitstring.logand aux_mask beta - in - Bitstring.popcount a + Bitstring.popcount b = cabs - in - let good_lr k = - Determinant.degree ki k = l && - Determinant.degree k kj = r - in - - - - (* Merge lists in a set of unique determinants *) - List.concat [ al; ar ] - |> List.sort_uniq compare - - (* Filter out all determinants with incorrect numbers of electrons in the CABS *) - |> List.filter good_cabs - - (* Filter out all determinants with incorrect excitation numbers *) - |> List.filter good_lr - - -let compute_HaaF ki alphas kj = - List.fold_left (fun accu alpha -> accu - +. h_ij aux_basis ki alpha - *. f_ij aux_basis alpha kj - ) 0. alphas - - -let check n integral_value exc cabs lexc rexc = - let cpudet, cpuint = ref 0., ref 0. in - let det_list = - match n with - | 0 -> det_I - | n -> Array.sub det_I 0 n - in - let result = - if Parallel.master then Printf.printf "Checking ... \n%!"; - let percent = ref 0 in - let task (i,ki) = - (let p = (10 * (i+1))/(Array.length det_list) in - if p <> !percent then - ( percent := p ; if Parallel.master then Printf.printf " - %3d %%\n%!" (p*10) )); - Array.mapi (fun j kj -> - if i > j || Determinant.degree ki kj <> exc then - (0,0,0.,0.) - else - begin - let alphas = generate_alphas ki kj exc cabs lexc rexc in - let det_value = - let t0 = Unix.gettimeofday () in - let result = compute_HaaF ki alphas kj in - cpudet := !cpudet +. Unix.gettimeofday () -. t0; - result - in - let int_value = - let t0 = Unix.gettimeofday () in - let result = integral_value ki kj in - cpuint := !cpuint +. Unix.gettimeofday () -. t0; - result - in -(* Printf.printf "%d %d %e %e\n%!" i j det_value int_value; *) - (i,j,det_value,int_value) - end - ) det_list - in - det_list - |> Array.mapi (fun i ki -> (i,ki)) - |> Array.to_list - |> Stream.of_list - |> Farm.run ~f:task - |> Util.stream_to_list - |> Array.concat - in - let i,j,d,v = - let rec aux k imax jmax emax dmax vmax = - if k = -1 then - imax, jmax, dmax, vmax - else - let i, j, d, v = result.(k) in - let e = abs_float (d -. v) in - if e >= emax then - aux (k-1) i j e d v - else - aux (k-1) imax jmax emax dmax vmax - in - aux (Array.length result - 1) 0 0 0. 0. 0. - in - let error = abs_float (d -. v) in - if error < epsilon_float then - (* - Printf.printf "OK: %e\n%!" error - *) - if Parallel.master then Printf.printf "OK: (%d, %d) | %e %e | %e | cpu : %f %f\n%!" i j d v error !cpudet !cpuint - else - if Parallel.master then Printf.printf "Failed: (%d, %d) | %e %e | %e | cpu : %f %f\n%!" i j d v error !cpudet !cpuint - - -let sum l f = List.fold_left (fun accu i -> accu +. f i) 0. l - -let array_3_init d1 d2 d3 f = - let result = - Bigarray.(Array3.create Float64 fortran_layout) d1 d2 d3 - in - for k=1 to d3 do - for j=1 to d2 do - for i=1 to d1 do - result.{i,j,k} <- f i j k - done - done - done; - result - - -let array_4_init d1 d2 d3 d4 f = - let result = - Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4 |] - in - for l=1 to d4 do - for k=1 to d3 do - for j=1 to d2 do - for i=1 to d1 do - result.{i,j,k,l} <- f i j k l - done - done - done - done; - result - - -let array_5_init d1 d2 d3 d4 d5 f = - let result = - Bigarray.(Genarray.create Float64 fortran_layout) [| d1;d2;d3;d4;d5 |] - in - for m=1 to d5 do - for l=1 to d4 do - for k=1 to d3 do - for j=1 to d2 do - for i=1 to d1 do - result.{i,j,k,l,m} <- f i j k l m - done - done - done - done - done; - result - -(* ----- *) - -let _ = png_image "0_1_11.png" - -let integral_value ki kj = - (* Alpha-Beta *) - let s, s' = Spin.(Alfa, Beta) in - let mos_a, mos_b = mos_a ki, mos_b ki in - - sum mos_cabs (fun a -> - sum mos_a (fun i -> - (h_one i a s +. - sum mos_a (fun j -> h_two i j a j s s ) +. - sum mos_b (fun j -> h_two i j a j s s') ) *. - (f_one a i s +. - sum mos_a (fun j -> f_two a j i j s s ) +. - sum mos_b (fun j -> f_two a j i j s s') ) - ) - +. - sum mos_b (fun i -> - (h_one i a s +. - sum mos_b (fun j -> h_two i j a j s' s') +. - sum mos_a (fun j -> h_two i j a j s' s ) ) *. - (f_one a i s +. - sum mos_a (fun j -> f_two a j i j s' s ) +. - sum mos_b (fun j -> f_two a j i j s' s') ) - ) - ) - -let _ = - check 0 integral_value 0 1 1 1 - - -let m_0111_1H_1F = - Vec.init mo_num (fun i -> - sum mos_cabs (fun a -> - h_one i a Spin.Alfa *. f_one a i Spin.Alfa )) - - -let m_0111_1H_2Fa = - Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a -> - h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Alfa )) - - -let m_0111_1H_2Fb = - Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a -> - h_one i a Spin.Alfa *. f_two a j i j Spin.Alfa Spin.Beta )) - - -let m_0111_2Ha_1F = - Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa )) - - -let m_0111_2Hb_1F = - Mat.init_cols mo_num mo_num (fun i j -> sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Beta *. f_one a j Spin.Alfa )) - - -let m_0111_2Ha_2Fa = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Alfa *. - f_two a k i k Spin.Alfa Spin.Alfa - ) - ) - - -let m_0111_2Hb_2Fa = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Beta *. - f_two a k i k Spin.Alfa Spin.Alfa - ) - ) - - -let m_0111_2Ha_2Fb = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Alfa *. - f_two a k i k Spin.Alfa Spin.Beta - ) - ) - - -let m_0111_2Hb_2Fb = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Beta *. - f_two a k i k Spin.Alfa Spin.Beta - ) - ) - - - -let integral_value ki kj = - - let mos_a, mos_b = mos_a ki, mos_b ki in - - sum mos_a (fun i -> - m_0111_1H_1F.{i} +. - sum mos_a (fun j -> - m_0111_1H_2Fa.{i,j} +. m_0111_2Ha_1F.{i,j} +. - sum mos_a (fun k -> m_0111_2Ha_2Fa.{i,j,k}) +. - sum mos_b (fun k -> m_0111_2Ha_2Fb.{i,j,k})) +. - sum mos_b (fun j -> - m_0111_1H_2Fb.{i,j} +. m_0111_2Hb_1F.{i,j} +. - sum mos_a (fun k -> m_0111_2Hb_2Fa.{i,j,k}) +. - sum mos_b (fun k -> m_0111_2Hb_2Fb.{i,j,k})) - ) - +. - sum mos_b (fun i -> - m_0111_1H_1F.{i} +. - sum mos_b (fun j -> - m_0111_1H_2Fa.{i,j} +. m_0111_2Ha_1F.{i,j} +. - sum mos_b (fun k -> m_0111_2Ha_2Fa.{i,j,k}) +. - sum mos_a (fun k -> m_0111_2Ha_2Fb.{i,j,k})) +. - sum mos_a (fun j -> - m_0111_1H_2Fb.{i,j} +. m_0111_2Hb_1F.{i,j} +. - sum mos_b (fun k -> m_0111_2Hb_2Fa.{i,j,k}) +. - sum mos_a (fun k -> m_0111_2Hb_2Fb.{i,j,k})) - ) - -let _ = - check 0 integral_value 0 1 1 1 - - -let _ = png_image "0_1_22.png" - -let integral_value ki kj = - (* mos unoccupied in both I and J *) - let mos_virt_a, mos_virt_b = - Array.init mo_num (fun i -> Some (i+1)) , - Array.init mo_num (fun i -> Some (i+1)) - in - List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki); - List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj); - List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki); - List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj); - - let mos_virt_a, mos_virt_b = - Array.to_list mos_virt_a |> Util.list_some, - Array.to_list mos_virt_b |> Util.list_some - in - - (* Alpha-Beta *) - let s, s' = Spin.(Alfa, Beta) in - sum mos_cabs (fun a -> - sum (mos_b ki) (fun j -> - sum (mos_a ki) (fun i -> - sum mos_virt_b (fun k -> - h_two i j a k s s' *. f_two a k i j s s' - ))) - +. - sum (mos_a ki) (fun j -> - sum (mos_b ki) (fun i -> - sum mos_virt_a (fun k -> - h_two i j a k s s' *. f_two a k i j s s' - )))) - +. - (* Alpha-Alpha / Beta-Beta *) - List.fold_left (fun accu (mos_virt,mos,s) -> - let s' = s in accu +. - sum mos (fun j -> - sum mos (fun i -> if i < j then 0. else - sum mos_virt (fun k -> - sum mos_cabs (fun a -> - h_two i j a k s s' *. f_two a k i j s s' - )))) - ) 0. [ (mos_virt_a,mos_a ki,Spin.Alfa) ; (mos_virt_b,mos_b ki,Spin.Beta)] - -let _ = - check 0 integral_value 0 1 2 2 - - -let m_0122_Haa = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two i j a k Spin.Alfa Spin.Alfa *. f_two a k i j Spin.Alfa Spin.Alfa - ) ) - -let m_0122_Hab = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two i j a k Spin.Alfa Spin.Beta *. f_two a k i j Spin.Alfa Spin.Beta - ) ) - - -let integral_value ki kj = - (* mos unoccupied in both I and J *) - let mos_virt_a, mos_virt_b = - Array.init mo_num (fun i -> Some (i+1)) , - Array.init mo_num (fun i -> Some (i+1)) - in - List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki); - List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj); - List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki); - List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj); - - let mos_virt_a, mos_virt_b = - Array.to_list mos_virt_a |> Util.list_some, - Array.to_list mos_virt_b |> Util.list_some - in - - let result = - sum (mos_a ki) (fun i -> - sum (mos_b ki) (fun j -> - sum mos_virt_b (fun k -> m_0122_Hab.{i,j,k} ))) - +. - sum (mos_b ki) (fun i -> - sum (mos_a ki) (fun j -> - sum mos_virt_a (fun k -> m_0122_Hab.{i,j,k} ))) - +. - (* Alpha-Alpha / Beta-Beta *) - List.fold_left (fun accu (mos_virt,mos) -> - accu +. - sum mos (fun j -> - sum mos (fun i -> if i <= j then 0. else - sum mos_virt (fun k -> m_0122_Haa.{i,j,k} ))) - ) 0. [ (mos_virt_a,mos_a ki) ; (mos_virt_b,mos_b ki)] - in - result - -let _ = - check 0 integral_value 0 1 2 2 - - -let _ = png_image "0_2_22.png" - -let integral_value ki kj = - (* Alpha-Beta *) - let s, s' = Spin.(Alfa, Beta) in - sum mos_cabs (fun a -> - sum mos_cabs (fun b -> - sum (mos_a ki) (fun i -> - sum (mos_b ki) (fun j -> - h_two i j a b s s' *. f_two a b i j s s' - )))) - +. - (* Alpha-Alpha / Beta-Beta *) - List.fold_left (fun accu (mos,s) -> - let s' = s in accu +. - sum mos_cabs (fun b -> - sum mos_cabs (fun a -> if b > a then 0. else - sum mos (fun j -> - sum mos (fun i -> if i < j then 0. else - h_two i j a b s s' *. f_two a b i j s s' - )))) - ) 0. [ (mos_a ki,Spin.Alfa) ; (mos_b ki,Spin.Beta)] - -let _ = - check 0 integral_value 0 2 2 2 - - -let m_0222_Haa = - Mat.init_cols mo_num mo_num (fun i j -> - sum mos_cabs (fun a -> - sum mos_cabs (fun b -> if b >= a then 0. else - h_two i j a b Spin.Alfa Spin.Alfa *. f_two a b i j Spin.Alfa Spin.Alfa - ) ) - ) - -let m_0222_Hab = - Mat.init_cols mo_num mo_num (fun i j -> - sum mos_cabs (fun a -> - sum mos_cabs (fun b -> - h_two i j a b Spin.Alfa Spin.Beta *. f_two a b i j Spin.Alfa Spin.Beta - ) ) - ) - -let integral_value ki kj = - (* Alpha-Beta *) - sum (mos_a ki) (fun i -> - sum (mos_b ki) (fun j -> - m_0222_Hab.{i,j} - )) - +. - (* Alpha-Alpha / Beta-Beta *) - List.fold_left (fun accu (mos) -> - accu +. - sum mos (fun j -> - sum mos (fun i -> if i < j then 0. else - m_0222_Haa.{i,j} - )) - ) 0. [ (mos_a ki) ; (mos_b ki)] - -let _ = - check 0 integral_value 0 2 2 2 - - -let _ = png_image "1_1_11.png" - -let integral_value ki kj = - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - let mos_i, mos_i' = - match s with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - let mos_j, mos_j' = - match s with - | Spin.Alfa -> mos_a kj, mos_b kj - | Spin.Beta -> mos_b kj, mos_a kj - in - - let result = - let s' = Spin.other s in - - sum mos_cabs (fun a -> - (h_one i a s +. - sum mos_i (fun j -> h_two i j a j s s ) +. - sum mos_i' (fun j -> h_two i j a j s s') ) *. - (f_one a k s +. - sum mos_j (fun j -> f_two a j k j s s ) +. - sum mos_j' (fun j -> f_two a j k j s s') ) - ) - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 1 1 1 1 - -let m_1111_1H_1F = - Mat.init_cols mo_num mo_num (fun i k -> - sum mos_cabs (fun a -> - h_one i a Spin.Alfa *. f_one a k Spin.Alfa )) - - -let m_1111_1H_2Fa = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Alfa )) - - -let m_1111_1H_2Fb = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_one i a Spin.Alfa *. f_two a j k j Spin.Alfa Spin.Beta )) - - -let m_1111_2Ha_1F = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa )) - - -let m_1111_2Hb_1F = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa )) - - -let m_1111_2Ha_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Alfa *. - f_two a l k l Spin.Alfa Spin.Alfa - ) - ) - - -let m_1111_2Hb_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Beta *. - f_two a l k l Spin.Alfa Spin.Alfa - ) - ) - - -let m_1111_2Ha_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Alfa *. - f_two a l k l Spin.Alfa Spin.Beta - ) - ) - - -let m_1111_2Hb_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_two i j a j Spin.Alfa Spin.Beta *. - f_two a l k l Spin.Alfa Spin.Beta - ) - ) - - -let integral_value ki kj = - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - let mos_a, mos_b = - match s with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - - let result = - m_1111_1H_1F.{i,k} +. - sum mos_a (fun j -> if j = i then 0. else - m_1111_1H_2Fa.{i,j,k} +. m_1111_2Ha_1F.{i,j,k} +. - sum mos_a (fun l -> if l = i then 0. else m_1111_2Ha_2Fa.{i,j,k,l}) +. - sum mos_b (fun l -> m_1111_2Ha_2Fb.{i,j,k,l})) +. - sum mos_b (fun j -> - m_1111_1H_2Fb.{i,j,k} +. m_1111_2Hb_1F.{i,j,k} +. - sum mos_a (fun l -> if l = i then 0. else m_1111_2Hb_2Fa.{i,j,k,l}) +. - sum mos_b (fun l -> m_1111_2Hb_2Fb.{i,j,k,l})) - in - - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - -let _ = - check 0 integral_value 1 1 1 1 - - -let _ = png_image "1_1_12.png" - -let integral_value ki kj = - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - let mos_j, mos_j' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logand i j) - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logand i j) - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - let mos_i, mos_i' = - match s with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - - let result = - let s' = Spin.other s in - sum mos_cabs (fun a -> - sum mos_j (fun j -> - (h_one j a s +. - sum mos_i (fun m -> h_two j m a m s s ) +. - sum mos_i' (fun m -> h_two j m a m s s') ) *. - (f_two a i j k s s ) - ) - +. - sum mos_j' (fun j -> - (h_one j a s +. - sum mos_i (fun m -> h_two j m a m s' s ) +. - sum mos_i' (fun m -> h_two j m a m s' s') ) *. - (f_two a i j k s' s ) - ) - ) - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 1 1 1 2 - -let m_1112_1H_2Fa = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_one j a Spin.Alfa *. f_two a i j k Spin.Alfa Spin.Alfa )) - - -let m_1112_1H_2Fb = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_one j a Spin.Beta *. f_two a i j k Spin.Alfa Spin.Beta )) - - -let m_1112_2Ha_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two j m a m Spin.Alfa Spin.Alfa *. - f_two a i j k Spin.Alfa Spin.Alfa - ) - ) - - -let m_1112_2Hb_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two j m a m Spin.Alfa Spin.Beta *. - f_two a i j k Spin.Alfa Spin.Alfa - ) - ) - -let m_1112_2Ha_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two j m a m Spin.Alfa Spin.Alfa *. - f_two a i j k Spin.Alfa Spin.Beta - ) - ) - - -let m_1112_2Hb_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two j m a m Spin.Alfa Spin.Beta *. - f_two a i j k Spin.Alfa Spin.Beta - ) - ) - - -let integral_value ki kj = - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - let mos_j, mos_j' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logand i j) - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logand i j) - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - let mos_i, mos_i' = - match s with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - - let result = - sum mos_j (fun j -> - m_1112_1H_2Fa.{i,j,k} +. - sum mos_i (fun m -> m_1112_2Ha_2Fa.{i,j,k,m}) +. - sum mos_i' (fun m -> m_1112_2Hb_2Fa.{i,j,k,m})) +. - sum mos_j' (fun j -> - m_1112_1H_2Fb.{i,j,k} +. - sum mos_i (fun m -> m_1112_2Hb_2Fb.{i,j,k,m}) +. - sum mos_i' (fun m -> m_1112_2Ha_2Fb.{i,j,k,m})) - in - - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - - -let _ = check 0 integral_value 1 1 1 2 - -let _ = png_image "1_1_21.png" - -let integral_value ki kj = - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - let mos_j, mos_j' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logand i j) - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logand i j) - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - let mos_i, mos_i' = - match s with - | Spin.Alfa -> mos_a kj, mos_b kj - | Spin.Beta -> mos_b kj, mos_a kj - in - - let result = - let s' = Spin.other s in - sum mos_cabs (fun a -> - sum mos_j (fun j -> - (h_two i j k a s s ) *. - (f_one a j s +. - sum mos_i (fun m -> f_two m a m j s s) +. - sum mos_i' (fun m -> f_two m a m j s' s) ) - ) - +. - sum mos_j' (fun j -> - (h_two i j k a s s') *. - (f_one a j s' +. - sum mos_i (fun m -> f_two m a m j s s') +. - sum mos_i' (fun m -> f_two m a m j s' s') ) - )) - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 1 1 2 1 - -let m_1121_2Ha_1F = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two i j k a Spin.Alfa Spin.Alfa *. f_one a j Spin.Alfa)) - - -let m_1121_2Hb_1F = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - h_two i j k a Spin.Alfa Spin.Beta *. f_one a j Spin.Beta)) - - -let m_1121_2Ha_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two i j k a Spin.Alfa Spin.Alfa *. - f_two m a m j Spin.Alfa Spin.Alfa - ) - ) - - -let m_1121_2Hb_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two i j k a Spin.Alfa Spin.Beta *. - f_two m a m j Spin.Alfa Spin.Alfa - ) - ) - -let m_1121_2Ha_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two i j k a Spin.Alfa Spin.Alfa *. - f_two m a m j Spin.Alfa Spin.Beta - ) - ) - - -let m_1121_2Hb_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two i j k a Spin.Alfa Spin.Beta *. - f_two m a m j Spin.Alfa Spin.Beta - ) - ) - - -let integral_value ki kj = - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - let mos_j, mos_j' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logand i j) - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logand i j) - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - let mos_i, mos_i' = - match s with - | Spin.Alfa -> mos_a kj, mos_b kj - | Spin.Beta -> mos_b kj, mos_a kj - in - - let result = - sum mos_j (fun j -> - m_1121_2Ha_1F.{i,j,k} +. - sum mos_i (fun m -> m_1121_2Ha_2Fa.{i,j,k,m}) +. - sum mos_i' (fun m -> m_1121_2Ha_2Fb.{i,j,k,m})) +. - sum mos_j' (fun j -> - m_1121_2Hb_1F.{i,j,k} +. - sum mos_i (fun m -> m_1121_2Hb_2Fb.{i,j,k,m}) +. - sum mos_i' (fun m -> m_1121_2Hb_2Fa.{i,j,k,m})) - in - - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - - -let _ = check 0 integral_value 1 1 2 1 - -let _ = png_image "1_1_22.png" - -(* -let ki = det_I.(6) -let kj = det_I.(58) - -let _ = - Format.printf "|I> -> |J> : %a |\n@." Excitation.pp (Excitation.of_det ki kj) ; -generate_alphas ki kj 1 1 2 2 -|> Array.of_list -|> Array.mapi (fun kk alpha -> - -(* -let _ = Determinant.to_lists ki -let _ = Determinant.to_lists alpha -let _ = Determinant.to_lists kj - - -let _ = - Format.printf "|I> -> |J> : %a\n@." Excitation.pp (Excitation.of_det ki kj); - Format.printf "|I> -> |a> : %a\n@." Excitation.pp (Excitation.of_det ki alpha); - Format.printf "|a> -> |J> : %a\n@." Excitation.pp (Excitation.of_det alpha kj) -*) - - let integral_value ki kj = - - let exc0 = Array.init (aux_num+1) (fun _ -> [|"-";"-"|]) in - let exc1 = Array.init (aux_num+1) (fun _ -> [|"-";"-"|]) in - let exc2 = Array.init (aux_num+1) (fun _ -> [|"-";"-"|]) in - - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin } )) -> - hole, particle, spin, phase - | _ -> assert false - in - let spin = function - | Spin.Alfa -> 0 - | _ -> 1 - in - exc0.(i).(spin s ) <- "i" - ; exc0.(k).(spin s ) <- "k" - ; - let s0 = s in - - let i, j, k, l, s, s', p1 = - match Excitation.of_det ki alpha with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - - if exc0.(i).(spin s ) = "-" then exc0.(i).(spin s ) <- "n"; - if exc0.(j).(spin s') = "-" then exc0.(j).(spin s') <- "n"; - if exc0.(k).(spin s ) = "-" then exc0.(k).(spin s ) <- if k > mo_num then "a" else "m"; - if exc0.(l).(spin s') = "-" then exc0.(l).(spin s') <- if l > mo_num then "a" else "m"; - - let string_h = - Printf.sprintf "h_two %s %s %s %s %s %s *. " - exc0.(i).(spin s ) - exc0.(j).(spin s') - exc0.(k).(spin s ) - exc0.(l).(spin s') - (if s = s0 then "s " else "s'") - (if s' = s0 then "s " else "s'") - (* - (if exc0.(i).(spin s ) = "i" || exc0.(k).(spin s ) = "k" then "s " else - if exc0.(i).(spin s ) = "j" || exc0.(k).(spin s ) = "l" then "s' " else "s''") - (if exc0.(j).(spin s') = "i" || exc0.(l).(spin s') = "k" then "s " else - if exc0.(j).(spin s') = "j" || exc0.(l).(spin s') = "l" then "s' " else "s''") - *) - in - - let i, j, k, l, s, s', p2 = - match Excitation.of_det alpha kj with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - - let string_f = - Printf.sprintf "f_two %s %s %s %s %s %s" - exc0.(i).(spin s ) - exc0.(j).(spin s') - exc0.(k).(spin s ) - exc0.(l).(spin s') - (* - (if exc0.(i).(spin s ) = "i" || exc0.(k).(spin s ) = "k" then "s " else - if exc0.(i).(spin s ) = "j" || exc0.(k).(spin s ) = "l" then "s' " else - if exc0.(i).(spin s ) = "n" || exc0.(k).(spin s ) = "n" then "s''" else - if s = s0 then "s" else "s'") - (if exc0.(j).(spin s') = "i" || exc0.(l).(spin s') = "k" then "s " else - if exc0.(j).(spin s') = "j" || exc0.(l).(spin s') = "l" then "s' " else - if exc0.(j).(spin s') = "n" || exc0.(l).(spin s') = "n" then "s''" else - if s' = s0 then "s" else "s'") - *) - (if s = s0 then "s " else "s'") - (if s' = s0 then "s " else "s'") - in - - Format.printf "|I> -> |a> : %a | %s\n@." Excitation.pp (Excitation.of_det ki alpha) string_h ; - Format.printf "|a> -> |J> : %a | %s\n@." Excitation.pp (Excitation.of_det alpha kj) string_f ; - - let sign = - if Phase.add p1 p2 = phase then "+. " else "-. " - in -sign ^ string_h ^ string_f -(* - - let mos, mos' = - match s with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - - let result = - let k=4 and l=5 in - let i=1 and j=2 in - let n=2 and a=7 in - let s = Spin.Alfa - and s' = Spin.Alfa - and s'' = Spin.Beta - in - (* - h_two j n l a s' s'' *. f_two a i n k s s'' - *) - h_two i n k a s s'' *. f_two j a l n s s'' - in - - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - *) - -in -integral_value ki kj -(* -let a = (compute_HaaF ki [alpha] kj) -and b = (integral_value ki kj) -in -if kk = 31 then - Format.printf "%6d %e %e@.@." (kk) a b - *) -) -|> Array.to_list -|> List.sort_uniq compare - -let _ = compute_HaaF ki (generate_alphas ki kj 1 1 2 2) kj - -let _ = integral_value ki kj - -*) - -let integral_value ki kj = - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - (* MOs unoccupied in both I and J *) - let mos_virt_a, mos_virt_b = - Array.init mo_num (fun i -> Some (i+1)) , - Array.init mo_num (fun i -> Some (i+1)) - in - List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki); - List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj); - List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki); - List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj); - - let mos_virt_a, mos_virt_b = - Array.to_list mos_virt_a |> Util.list_some, - Array.to_list mos_virt_b |> Util.list_some - in - - let mos_virt, mos_virt' = - match s with - | Spin.Alfa -> mos_virt_a, mos_virt_b - | Spin.Beta -> mos_virt_b, mos_virt_a - in - - let mos_j, mos_j' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logand i j) - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logand i j) - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - let result = - let s' = Spin.other s in - sum mos_cabs (fun a -> - sum mos_j (fun n -> - sum mos_virt (fun m -> - h_two n i a m s s *. f_two m a k n s s - ))) +. - sum mos_cabs (fun a' -> - sum mos_j' (fun n' -> - sum mos_virt (fun m -> - h_two i n' m a' s s' *. f_two m a' k n' s s' - ))) +. - sum mos_cabs (fun a -> - sum mos_j' (fun n' -> - sum mos_virt' (fun m' -> - h_two i n' a m' s s' *. f_two a m' k n' s s' - ))) -. - sum mos_cabs (fun a -> - sum mos_j (fun n -> - sum mos_j (fun l -> if l <=n then 0. else - h_two n l a k s s *. f_two i a l n s s - ))) -. - sum mos_cabs (fun a' -> - sum mos_j' (fun n' -> - sum mos_j (fun l -> - h_two l n' k a' s s' *. f_two i a' l n' s s' - ))) - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - -let _ = check 0 integral_value 1 1 2 2 - - - -let m_1122_va = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two j i a m Spin.Alfa Spin.Alfa *. - f_two m a k j Spin.Alfa Spin.Alfa - ) - ) - -let m_1122_v2 = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two i j m a Spin.Alfa Spin.Beta *. - f_two m a k j Spin.Alfa Spin.Beta - ) - ) - -let m_1122_v3 = - array_4_init mo_num mo_num mo_num mo_num (fun i j k m -> - sum mos_cabs (fun a -> - h_two i j a m Spin.Alfa Spin.Beta *. - f_two a m k j Spin.Alfa Spin.Beta - ) - ) - -let m_1122_oa = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_two j l a k Spin.Alfa Spin.Alfa *. - f_two i a l j Spin.Alfa Spin.Alfa - ) - ) - -let m_1122_o = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_two l j k a Spin.Alfa Spin.Beta *. - f_two i a l j Spin.Alfa Spin.Beta - ) - ) - - -let integral_value ki kj = - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - (* MOs unoccupied in both I and J *) - let mos_virt_a, mos_virt_b = - Array.init mo_num (fun i -> Some (i+1)) , - Array.init mo_num (fun i -> Some (i+1)) - in - List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki); - List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj); - List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki); - List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj); - - let mos_virt_a, mos_virt_b = - Array.to_list mos_virt_a |> Util.list_some, - Array.to_list mos_virt_b |> Util.list_some - in - - let mos_virt, mos_virt' = - match s with - | Spin.Alfa -> mos_virt_a, mos_virt_b - | Spin.Beta -> mos_virt_b, mos_virt_a - in - - let mos_j, mos_j' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logand i j) - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logand i j) - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - let result = - sum mos_j (fun j -> - sum mos_virt (fun m -> - m_1122_va.{i,j,k,m} - )) +. - sum mos_j' (fun j -> - sum mos_virt (fun m -> - m_1122_v2.{i,j,k,m} - )) +. - sum mos_j' (fun j -> - sum mos_virt' (fun m -> - m_1122_v3.{i,j,k,m} - )) -. - sum mos_j (fun j -> - sum mos_j (fun l -> if l <= j then 0. else - m_1122_oa.{i,j,k,l} - )) -. - sum mos_j' (fun j -> - sum mos_j (fun l -> - m_1122_o.{i,j,k,l} - )) - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 1 1 2 2 - - - - -let _ = png_image "1_2_22.png" - -let integral_value ki kj = - let h, p, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - let mos, mos' = - match s with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - - - - let result = - (* Alpha-Beta *) - let s' = Spin.other s in - sum mos_cabs (fun b -> - sum mos_cabs (fun a -> - sum mos' (fun j -> h_two h j a b s s' *. f_two a b p j s s') - )) - +. - (* Alpha-Alpha / Beta-Beta *) - sum mos_cabs (fun b -> - sum mos_cabs (fun a -> if b >= a then 0. else - sum mos (fun j -> h_two h j a b s s *. f_two a b p j s s) - )) - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 1 2 2 2 - -let m_1222a = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - sum mos_cabs (fun b -> if b > a then 0. else - h_two i j a b Spin.Alfa Spin.Alfa *. - f_two a b k j Spin.Alfa Spin.Alfa - ) - ) - ) - -let m_1222 = - array_3_init mo_num mo_num mo_num (fun i j k -> - sum mos_cabs (fun a -> - sum mos_cabs (fun b -> - h_two i j a b Spin.Alfa Spin.Beta *. - f_two a b k j Spin.Alfa Spin.Beta - ) - ) - ) - - -let integral_value ki kj = - let i, k, s, phase = - match Excitation.of_det ki kj with - | Excitation.(Single (phase, { hole ; particle ; spin })) -> - hole, particle, spin, phase - | _ -> assert false - in - - (* MOs unoccupied in both I and J *) - let mos_j, mos_j' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logand i j) - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logand i j) - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - let result = - sum mos_j (fun j -> m_1222a.{i,j,k} ) +. - sum mos_j' (fun j -> m_1222.{i,j,k} ) - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 1 2 2 2 - - - - -let _ = png_image "2_1_12.png" - -let integral_value ki kj = - let i, j, k, l, s, s', phase = - match Excitation.of_det ki kj with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - - let mos, mos' = - match s with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - - let mos2, mos2' = - match s' with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - - let result = - sum mos_cabs (fun a -> - let s'' = Spin.other s in - ( h_one i a s +. - sum mos (fun n -> h_two i n a n s s ) +. - sum mos' (fun n -> h_two i n a n s s'') - ) *. f_two a j k l s s' - ) +. - sum mos_cabs (fun a -> - let s'' = Spin.other s' in - ( h_one j a s' +. - sum mos2 (fun n -> h_two j n a n s' s' ) +. - sum mos2' (fun n -> h_two j n a n s' s'') - ) *. f_two i a k l s s' - ) - in - - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 2 1 1 2 - -let m_2112_1H_2Fa = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Alfa +. - h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Alfa ) - ) - -let m_2112_1H_2Fb = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_one i a Spin.Alfa *. f_two a j k l Spin.Alfa Spin.Beta +. - h_one j a Spin.Alfa *. f_two i a k l Spin.Alfa Spin.Beta) - ) - -let m_2112_2Ha_2Fa = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n -> - sum mos_cabs (fun a -> - h_two i n a n Spin.Alfa Spin.Alfa *. - f_two a j k l Spin.Alfa Spin.Alfa ) - ) - -let m_2112_2Hb_2Fa = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n -> - sum mos_cabs (fun a -> - h_two i n a n Spin.Alfa Spin.Beta *. - f_two a j k l Spin.Alfa Spin.Alfa ) - ) - -let m_2112_2Ha_2Fb = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n -> - sum mos_cabs (fun a -> - h_two i n a n Spin.Alfa Spin.Alfa *. - f_two a j k l Spin.Alfa Spin.Beta ) - ) - -let m_2112_2Hb_2Fb = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n -> - sum mos_cabs (fun a -> - h_two i n a n Spin.Alfa Spin.Beta *. - f_two a j k l Spin.Alfa Spin.Beta ) - ) - -let integral_value ki kj = - let i, j, k, l, s, s', phase = - match Excitation.of_det ki kj with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - let mos, mos' = - match s with - | Spin.Alfa -> mos_a ki, mos_b ki - | Spin.Beta -> mos_b ki, mos_a ki - in - - let result = - if s = s' then - m_2112_1H_2Fa.{i,j,k,l} +. - sum mos (fun n -> - m_2112_2Ha_2Fa.{i,j,k,l,n} +. m_2112_2Ha_2Fa.{j,i,l,k,n} - ) +. - sum mos' (fun n -> - m_2112_2Hb_2Fa.{i,j,k,l,n} +. m_2112_2Hb_2Fa.{j,i,l,k,n} - ) - else - m_2112_1H_2Fb.{i,j,k,l} +. - sum mos (fun n -> - m_2112_2Ha_2Fb.{i,j,k,l,n} +. m_2112_2Hb_2Fb.{j,i,l,k,n} - ) +. - sum mos' (fun n -> - m_2112_2Hb_2Fb.{i,j,k,l,n} +. m_2112_2Ha_2Fb.{j,i,l,k,n} - ) - in - - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 2 1 1 2 - - - - -let _ = png_image "2_1_21.png" - -let integral_value ki kj = - let i, j, k, l, s, s', phase = - match Excitation.of_det ki kj with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - - let result = - - let mos, mos', s'' = - match s with - | Spin.Alfa -> mos_a kj, mos_b kj, Spin.Beta - | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa - in - sum mos_cabs (fun a -> - h_two i j a l s s' *. - ( f_one a k s +. - sum mos (fun n -> f_two a n k n s s) +. - sum mos' (fun n -> f_two a n k n s s'') - ) ) +. - - let mos, mos', s'' = - match s' with - | Spin.Alfa -> mos_a kj, mos_b kj, Spin.Beta - | Spin.Beta -> mos_b kj, mos_a kj, Spin.Alfa - in - sum mos_cabs (fun a -> - h_two j i a k s' s *. - ( f_one a l s' +. - sum mos (fun n -> f_two a n l n s' s') +. - sum mos' (fun n -> f_two a n l n s' s'') - ) - ) - in - - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 2 1 2 1 - -let m_2121_2Ha_1F = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_two i j a l Spin.Alfa Spin.Alfa *. f_one a k Spin.Alfa +. - h_two i j k a Spin.Alfa Spin.Alfa *. f_one a l Spin.Alfa) - ) - -let m_2121_2Hb_1F = - array_4_init mo_num mo_num mo_num mo_num (fun i j k l -> - sum mos_cabs (fun a -> - h_two i j a l Spin.Alfa Spin.Beta *. f_one a k Spin.Alfa +. - h_two i j k a Spin.Alfa Spin.Beta *. f_one a l Spin.Alfa) - ) - -let m_2121_2Ha_2Fa = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n -> - sum mos_cabs (fun a -> - h_two i j a l Spin.Alfa Spin.Alfa *. - f_two a n k n Spin.Alfa Spin.Alfa ) - ) - -let m_2121_2Hb_2Fa = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n -> - sum mos_cabs (fun a -> - h_two i j a l Spin.Alfa Spin.Beta *. - f_two a n k n Spin.Alfa Spin.Alfa ) - ) - -let m_2121_2Ha_2Fb = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n -> - sum mos_cabs (fun a -> - h_two i j a l Spin.Alfa Spin.Alfa *. - f_two a n k n Spin.Alfa Spin.Beta ) - ) - -let m_2121_2Hb_2Fb = - array_5_init mo_num mo_num mo_num mo_num mo_num (fun i j k l n -> - sum mos_cabs (fun a -> - h_two i j a l Spin.Alfa Spin.Beta *. - f_two a n k n Spin.Alfa Spin.Beta ) - ) - -let integral_value ki kj = - let i, j, k, l, s, s', phase = - match Excitation.of_det ki kj with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - let mos, mos' = - match s with - | Spin.Alfa -> mos_a kj, mos_b kj - | Spin.Beta -> mos_b kj, mos_a kj - in - - let result = - if s = s' then - m_2121_2Ha_1F.{i,j,k,l} +. - sum mos (fun n -> - m_2121_2Ha_2Fa.{i,j,k,l,n} +. m_2121_2Ha_2Fa.{j,i,l,k,n} - ) +. - sum mos' (fun n -> - m_2121_2Ha_2Fb.{i,j,k,l,n} +. m_2121_2Ha_2Fb.{j,i,l,k,n} - ) - else - m_2121_2Hb_1F.{i,j,k,l} +. - sum mos (fun n -> - m_2121_2Hb_2Fa.{i,j,k,l,n} +. m_2121_2Hb_2Fb.{j,i,l,k,n} - ) +. - sum mos' (fun n -> - m_2121_2Hb_2Fb.{i,j,k,l,n} +. m_2121_2Hb_2Fa.{j,i,l,k,n} - ) - in - - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 2 1 2 1 - - - - -let _ = png_image "2_1_22.png" - -let integral_value ki kj = - let i, j, k, l, s, s', phase = - match Excitation.of_det ki kj with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - - let mos_virt_a, mos_virt_b = - Array.init mo_num (fun i -> Some (i+1)) , - Array.init mo_num (fun i -> Some (i+1)) - in - List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a ki); - List.iter (fun i -> mos_virt_a.(i-1) <- None) (mos_a kj); - List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b ki); - List.iter (fun i -> mos_virt_b.(i-1) <- None) (mos_b kj); - - let mos_virt_a, mos_virt_b = - Array.to_list mos_virt_a |> Util.list_some, - Array.to_list mos_virt_b |> Util.list_some - in - - let result = - - let mos_virt, mos_virt' = - match s with - | Spin.Alfa -> mos_virt_a, mos_virt_b - | Spin.Beta -> mos_virt_b, mos_virt_a - in - - let mos, mos' = - let alfa = - let i = Spindeterminant.bitstring @@ Determinant.alfa ki in - let j = Spindeterminant.bitstring @@ Determinant.alfa kj in - Bitstring.to_list (Bitstring.logand i j) - in - let beta = - let i = Spindeterminant.bitstring @@ Determinant.beta ki in - let j = Spindeterminant.bitstring @@ Determinant.beta kj in - Bitstring.to_list (Bitstring.logand i j) - in - match s with - | Spin.Alfa -> alfa, beta - | Spin.Beta -> beta, alfa - in - - if s = s' then - let s'' = Spin.other s' in - sum mos_cabs (fun a -> - sum mos (fun n -> - h_two i n a k s s *. f_two j a n l s s - +. h_two i n a l s s *. f_two j a k n s s - -. h_two j n a k s s *. f_two i a n l s s - -. h_two j n a l s s *. f_two i a k n s s - ) - +. sum mos_virt (fun m -> - -. h_two i j a m s s *. f_two m a k l s s ) - +. sum mos' (fun n -> - h_two i n k a s s'' *. f_two j a l n s s'' - +. h_two j n l a s s'' *. f_two i a k n s s'' - -. h_two i n l a s s'' *. f_two j a k n s s'' - -. h_two j n k a s s'' *. f_two i a l n s s'' - ) - ) - else - sum mos_cabs (fun a -> - sum mos_virt' (fun m -> - h_two i j a m s s' *. f_two a m k l s s' ) +. - sum mos_virt (fun m -> - h_two i j m a s s' *. f_two m a k l s s' ) +. - sum mos (fun n -> - h_two n i a k s s *. f_two a j n l s s' - +. h_two n j a l s s' *. f_two i a k n s s - -. h_two n j k a s s' *. f_two i a n l s s' - ) +. - sum mos' (fun n -> if n >= j then 0. else - h_two i n k a s s' *. f_two j a l n s' s' - +. h_two n j a l s' s' *. f_two i a k n s s' ) +. - sum mos' (fun n -> if n <= j then 0. else - -. h_two i n k a s s' *. f_two j a n l s' s' - -. h_two j n a l s' s' *. f_two i a k n s s' ) +. - sum mos' (fun n -> - -. h_two i n a l s s' *. f_two a j k n s s' - ) - ) - in - - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 2 1 2 2 - -let _ = png_image "2_2_22.png" - -let integral_value ki kj = - let h, h', p, p', s, s', phase = - match Excitation.of_det ki kj with - | Excitation.(Double (phase, - { hole=h ; particle=p ; spin=s }, - { hole=h'; particle=p'; spin=s'}) ) -> h, h', p, p', s, s', phase - | _ -> assert false - in - - let result = - if s <> s' then (* Alpha-Beta *) - sum mos_cabs (fun b -> - sum mos_cabs (fun a -> - h_two h h' a b s s' *. f_two a b p p' s s' - )) - else (* Alpha-Alpha / Beta-Beta *) - sum mos_cabs (fun b -> - sum mos_cabs (fun a -> if b >= a then 0. else - h_two h h' a b s s' *. f_two a b p p' s s' - )) - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 2 2 2 2 - -let _ = png_image "3_1_22.png" - -let integral_value ki kj = - let i, j, m, k, l, n, s1, s2, s3, phase = - match Excitation.of_det ki kj with - | Excitation.(Triple (phase, - { hole=h1 ; particle=p1 ; spin=s1 }, - { hole=h2 ; particle=p2 ; spin=s2 }, - { hole=h3 ; particle=p3 ; spin=s3 }) ) -> h1, h2, h3, p1, p2, p3, s1, s2, s3, phase - | _ -> assert false - in - - let result = - let open Spin in - match s1, s2, s3 with - | Alfa, Alfa, Alfa - | Beta, Beta, Beta -> - sum mos_cabs (fun a -> - h_two i j a k s1 s2 *. f_two m a l n s3 s3 - +. h_two i j a n s1 s2 *. f_two m a k l s3 s2 - +. h_two i m a l s1 s3 *. f_two j a k n s2 s3 - +. h_two j m a k s2 s3 *. f_two i a l n s1 s3 - +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 - -. h_two i j a l s1 s2 *. f_two m a k n s3 s3 - -. h_two i m a k s1 s3 *. f_two j a l n s2 s3 - -. h_two i m a n s1 s3 *. f_two j a k l s2 s2 - -. h_two j m a l s2 s3 *. f_two i a k n s1 s3 ) - | Alfa, Alfa, Beta - | Beta, Beta, Alfa -> - sum mos_cabs (fun a -> - h_two i j a l s1 s2 *. f_two a m k n s1 s3 - +. h_two i m k a s1 s3 *. f_two j a l n s2 s3 - +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 - +. h_two j m l a s2 s3 *. f_two i a k n s1 s3 - -. h_two i j a k s1 s2 *. f_two a m l n s1 s3 - -. h_two i m a n s1 s3 *. f_two j a k l s2 s2 - -. h_two i m l a s1 s3 *. f_two j a k n s2 s3 - -. h_two j m k a s2 s3 *. f_two i a l n s1 s3 - ) - | Alfa, Beta, Beta - | Beta, Alfa, Alfa -> - sum mos_cabs (fun a -> - h_two i j a l s1 s2 *. f_two a m k n s1 s3 - +. h_two i m a n s1 s3 *. f_two a j k l s1 s2 - +. h_two i m k a s1 s3 *. f_two j a l n s2 s3 - +. h_two j m a n s2 s3 *. f_two i a k l s1 s2 - -. h_two i j a n s1 s2 *. f_two a m k l s1 s2 - -. h_two i j k a s1 s2 *. f_two m a l n s2 s3 - -. h_two i m a l s1 s3 *. f_two a j k n s1 s3 - -. h_two j m a l s2 s3 *. f_two i a k n s1 s3 - ) - | Beta, Alfa, Beta - | Alfa, Beta, Alfa -> 0. (*TODO *) - in - match phase with - | Phase.Pos -> result - | Phase.Neg -> -. result - - -let _ = check 0 integral_value 3 1 2 2 - -let ki = det_I.(129) -let kj = det_I.(349) - -let alpha_to_string alpha = - - let exc0 = Array.init (aux_num+1) (fun _ -> [|"-";"-"|]) in - - let i, j, m, k, l, n, s, s', s'', phase = - match Excitation.of_det ki kj with - | Excitation.(Triple (phase, - { hole ; particle ; spin }, - {hole=hole' ; particle=particle' ; spin=spin' }, - {hole=hole''; particle=particle''; spin=spin''} )) -> - hole, hole', hole'', particle, particle', particle'', spin, spin', spin'', phase - | _ -> assert false - in - let spin = function - | Spin.Alfa -> 0 - | _ -> 1 - in - exc0.(i).(spin s ) <- "i" - ; exc0.(j).(spin s' ) <- "j" - ; exc0.(k).(spin s ) <- "k" - ; exc0.(l).(spin s' ) <- "l" - ; exc0.(m).(spin s'') <- "m" - ; exc0.(n).(spin s'') <- "n" - ; - let s0, s0', s0'' = s, s', s'' in - - let i, j, k, l, s, s', p1 = - match Excitation.of_det ki alpha with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - - if exc0.(i).(spin s ) = "-" then exc0.(i).(spin s ) <- "p"; - if exc0.(j).(spin s') = "-" then exc0.(j).(spin s') <- "p"; - if exc0.(k).(spin s ) = "-" then exc0.(k).(spin s ) <- if k > mo_num then "a" else "q"; - if exc0.(l).(spin s') = "-" then exc0.(l).(spin s') <- if l > mo_num then "a" else "q"; - - let string_h = - Printf.sprintf "h_two %s %s %s %s %s %s *. " - exc0.(i).(spin s ) - exc0.(j).(spin s') - exc0.(k).(spin s ) - exc0.(l).(spin s') - (if s = s0 then "s " else if s = s0' then "s'" else "s''") - (if s' = s0' then "s'" else if s = s0'' then "s''" else "s" ) - in - - let i, j, k, l, s, s', p2 = - match Excitation.of_det alpha kj with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - - let string_f = - Printf.sprintf "f_two %s %s %s %s %s %s" - exc0.(i).(spin s ) - exc0.(j).(spin s') - exc0.(k).(spin s ) - exc0.(l).(spin s') - (if s = s0 then "s " else if s = s0' then "s'" else "s''") - (if s' = s0' then "s'" else if s = s0'' then "s''" else "s" ) - in - (* - Format.printf "|I> -> |a> : %a | %s\n@." Excitation.pp (Excitation.of_det ki alpha) string_h ; - Format.printf "|a> -> |J> : %a | %s\n@." Excitation.pp (Excitation.of_det alpha kj) string_f ; - *) - - - let sign = - if Phase.add p1 p2 = phase then "+." else "-." - in - sign ^ string_h ^ string_f - - -let alpha_debug alpha = - - let i, j, k, l, s, s', p1 = - match Excitation.of_det ki alpha with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - Printf.printf "%d %d %d %d " i j k l; - - let i, j, k, l, s, s', p2 = - match Excitation.of_det alpha kj with - | Excitation.(Double (phase, { hole ; particle ; spin }, {hole=hole' ; particle=particle' ; spin=spin' })) -> - hole, hole', particle, particle', spin, spin', phase - | _ -> assert false - in - (* - Format.printf "|I> -> |a> : %a | \n@." Excitation.pp (Excitation.of_det ki alpha) ; - Format.printf "|a> -> |J> : %a | \n@." Excitation.pp (Excitation.of_det alpha kj) ; - *) - Printf.printf "%d %d %d %d \n%!" i j k l - - -let strings = - Format.printf "|I> -> |J> : %a |\n@." Excitation.pp (Excitation.of_det ki kj) ; - generate_alphas ki kj 3 1 2 2 - |> Array.of_list - |> Array.mapi (fun kk alpha -> alpha_to_string alpha) - |> Array.to_list - |> List.sort_uniq compare - |> Array.of_list - -let _ = Array.iteri (fun i x -> Printf.printf "%d %s \n%!" i x) strings - -let _ = - let v = - let alphas = - generate_alphas ki kj 3 1 2 2 - (* - |> List.filter (fun alpha -> - let x = alpha_to_string alpha in - x = strings.(6) - ) - *) - in - (* - List.iter alpha_debug alphas ; - Printf.printf "\n%!"; - *) - compute_HaaF ki alphas kj - in - let x = (integral_value ki kj) in - Printf.printf "%20.8e %20.8e %20.8e\n%!" x v (v-. x) - - - diff --git a/run_tests.ml b/run_tests.ml deleted file mode 100644 index f6213f6..0000000 --- a/run_tests.ml +++ /dev/null @@ -1,54 +0,0 @@ - -let () = - - - (* H2O / cc-pVDZ *) - let test_integrals_water, test_guess_water = - let basis_file = "test_files/cc-pvdz" - and nuclei_file = "test_files/water.xyz" - in - - let simulation_closed_shell = - Simulation.of_filenames ~charge:0 ~multiplicity:1 ~nuclei:nuclei_file basis_file - in - - let ao_basis = - Simulation.ao_basis simulation_closed_shell - in - (fun () -> AOBasis.test_case "water" ao_basis), - (fun () -> Guess.test_case ao_basis); - in - - - (* LiH / cc-pVTZ *) - let test_integrals_lih = - let basis_file = "test_files/cc-pvdz" - and nuclei_file = "test_files/lih.xyz" - in - - let simulation_closed_shell = - Simulation.of_filenames ~range_separation:0.5 ~charge:0 ~cartesian:true ~multiplicity:1 ~nuclei:nuclei_file basis_file - in - - let ao_basis = - Simulation.ao_basis simulation_closed_shell - in - (fun () -> AOBasis.test_case "lih" ao_basis) - in - - Alcotest.run "Unit tests" [ - "Util", Util.test_case (); - "Bitstring", Bitstring.test_case (); - "Spindeterminant", Spindeterminant.test_case (); - "Determinant", Determinant.test_case (); - "Excitation", Excitation.test_case (); - "Sparse vectors", Vector.test_case (); - "Sparse matrices", Matrix.test_case (); - "Cholesky", Cholesky.test_case (); - "Guess water", test_guess_water (); - "AO Integrals water", test_integrals_water (); - "AO Integrals LiH", test_integrals_lih (); - ] - - - diff --git a/style.css b/style.css deleted file mode 100644 index eb3b25a..0000000 --- a/style.css +++ /dev/null @@ -1,86 +0,0 @@ -img.ltxhtml { vertical-align : middle } -.keyword { font-weight : bold ; color : Red } -.keywordsign { color : #C04600 } -.comment { color : Green } -.constructor { color : Blue } -.type { color : #5C6585 } -.string { color : Maroon } -.warning { color : Red ; font-weight : bold } -.info { margin-left : 3em; margin-right: 3em } -.param_info { margin-top: 4px; margin-left : 3em; margin-right : 3em } -.code { color : #465F91 ; } -.typetable { border-style : hidden } -.paramstable { border-style : hidden ; padding: 5pt 5pt} -tr { } -td.typefieldcomment { font-size: smaller ;} -div.sig_block {margin-left: 2em} -*:target { background: yellow; } -body { - font: 10pt sans-serif; - color: black; - text-align: left; - padding: 5px; - margin: 1.375em 5%; - min-width: 40ex; - max-width: 100ex; - background-color: White; -} -h1 { - font-size : 1.5em; - text-align: left; - margin-top: 0.5em; - padding-top: 0.8em; - margin-bottom: 1.0em; - padding-bottom: 0.0em; - border-top-style:solid; - border-width:1px; - border-color:#AAA; -} -h2 { - font-size : 1.3em; - text-align: left; - margin-top: 0.5em; - padding-top: 0.8em; - margin-bottom: 1.0em; - padding-bottom: 0.0em; - border-top-style:solid; - border-width:1px; - border-color:#AAA; -} -h3 { - font-size : 1.2em; - text-align: left; - margin-top: 0.5em; - padding-top: 0.8em; - margin-bottom: 1.0em; - padding-bottom: 0.0em; - font-style: italic; - font-weight: normal -} -a {color: #416DFF; text-decoration: none} -a:hover {background-color: #ddd; text-decoration: underline} -pre -{ - font-family: monospace; -} -pre.verbatim, pre.codepre { - padding: 1.0em; - padding-right: 1.0em; - background-color:#F8F8F8; -} -.indextable { - border: 1px #ddd solid; - border-collapse: collapse; - font-size: 1.0em; -} -.indextable td, .indextable th {border: 1px #ddd solid; min-width: 80px} -.indextable td.module {background-color: #eee ; padding-left: 2px; padding-right: 2px} -.indextable td.module a {color: #4E6272; text-decoration: none; display: block; width: 100%} -.indextable td.module a:hover {text-decoration: underline; background-color: transparent} -.deprecated {color: #888; font-style: italic} -.indextable tr td div.info { margin-left: 2px; margin-right: 2px } -ul.indexlist { margin-left: 0; padding-left: 0;} -ul.indexlist li { list-style-type: none ; margin-left: 0; padding-left: 0; } -ul.info-attributes {list-style: none; margin: 0; padding: 0; } -div.info > p:first-child { margin-top:0; } -div.info-desc > p:first-child { margin-top:0; margin-bottom:0; } diff --git a/test_files/caffeine.xyz b/test/caffeine.xyz similarity index 85% rename from test_files/caffeine.xyz rename to test/caffeine.xyz index f197322..fc375e6 100644 --- a/test_files/caffeine.xyz +++ b/test/caffeine.xyz @@ -1,8 +1,8 @@ 24 -Caffeine -1 -3.3804130 -1.1272367 0.5733036 -7 0.9668296 -1.0737425 -0.8198227 -6 0.0567293 0.8527195 0.3923156 +Caffeine test file +H -3.3804130 -1.1272367 0.5733036 +N 0.9668296 -1.0737425 -0.8198227 +C 0.0567293 0.8527195 0.3923156 N -1.3751742 -1.0212243 -0.0570552 C -1.2615018 0.2590713 0.5234135 C -0.3068337 -1.6836331 -0.7169344 @@ -24,3 +24,6 @@ N 2.2861252 0.9968439 -0.2440298 H -0.1687028 4.0436553 0.9301094 H 0.3535322 3.2979060 2.5177747 H -1.2074498 2.7537592 1.7203047 + + + diff --git a/test/cc-pvdz b/test/cc-pvdz new file mode 100644 index 0000000..3d1a77e --- /dev/null +++ b/test/cc-pvdz @@ -0,0 +1,3609 @@ +!---------------------------------------------------------------------- +! Basis Set Exchange +! Version 2.1.0+44.g1191679.dirty +! https://www.basissetexchange.org +!---------------------------------------------------------------------- +! Basis set: cc-pVDZ +! Description: cc-pVDZ +! Role: orbital +! Version: 1 (Data from ccRepo/Grant Hill) +!---------------------------------------------------------------------- + + +$DATA + +HYDROGEN +S 4 +1 1.301000E+01 1.968500E-02 +2 1.962000E+00 1.379770E-01 +3 4.446000E-01 4.781480E-01 +4 1.220000E-01 5.012400E-01 +S 1 +1 1.220000E-01 1.000000E+00 +P 1 +1 7.270000E-01 1.0000000 + +HELIUM +S 4 +1 3.836000E+01 2.380900E-02 +2 5.770000E+00 1.548910E-01 +3 1.240000E+00 4.699870E-01 +4 2.976000E-01 5.130270E-01 +S 1 +1 2.976000E-01 1.000000E+00 +P 1 +1 1.275000E+00 1.0000000 + +LITHIUM +S 9 +1 1.469000E+03 7.660000E-04 +2 2.205000E+02 5.892000E-03 +3 5.026000E+01 2.967100E-02 +4 1.424000E+01 1.091800E-01 +5 4.581000E+00 2.827890E-01 +6 1.580000E+00 4.531230E-01 +7 5.640000E-01 2.747740E-01 +8 7.345000E-02 9.751000E-03 +9 2.805000E-02 -3.180000E-03 +S 9 +1 1.469000E+03 -1.200000E-04 +2 2.205000E+02 -9.230000E-04 +3 5.026000E+01 -4.689000E-03 +4 1.424000E+01 -1.768200E-02 +5 4.581000E+00 -4.890200E-02 +6 1.580000E+00 -9.600900E-02 +7 5.640000E-01 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b/test/run_tests.ml new file mode 100644 index 0000000..bd3ad61 --- /dev/null +++ b/test/run_tests.ml @@ -0,0 +1,13 @@ +(* + Run all the OCaml test suites defined in the project. +*) + +let test_suites: unit Alcotest.test list = [ + "Common.Bitstring", Test_common.Bitstring.tests; + "Common.Util", Test_common.Math_functions.tests; + "Particles.Nuclei", Test_particles.Nuclei.tests; + "Particles.Electrons", Test_particles.Electrons.tests; + "Gaussian_basis.General_basis", Test_gaussian_basis.General_basis.tests; +] + +let () = Alcotest.run "QCaml" test_suites diff --git a/test_files/water.xyz b/test/water.xyz similarity index 98% rename from test_files/water.xyz rename to test/water.xyz index 0d078a3..ca7842c 100644 --- a/test_files/water.xyz +++ b/test/water.xyz @@ -3,3 +3,5 @@ Water O 0. 0. 0. H -0.756950272703377558 0. -0.585882234512562827 H 0.756950272703377558 0. -0.585882234512562827 + + diff --git a/test_files/cc-pvdz b/test_files/cc-pvdz deleted file mode 100644 index 1685d42..0000000 --- a/test_files/cc-pvdz +++ /dev/null @@ -1,3371 +0,0 @@ -HYDROGEN -S 3 - 1 13.0100000 0.0196850 - 2 1.9620000 0.1379770 - 3 0.4446000 0.4781480 -S 1 - 1 0.1220000 1.0000000 -P 1 - 1 0.7270000 1.0000000 - -HELIUM -S 3 - 1 38.3600000 0.0238090 - 2 5.7700000 0.1548910 - 3 1.2400000 0.4699870 -S 1 - 1 0.2976000 1.0000000 -P 1 - 1 1.2750000 1.0000000 - -LITHIUM -S 8 - 1 1469.0000000 0.0007660 - 2 220.5000000 0.0058920 - 3 50.2600000 0.0296710 - 4 14.2400000 0.1091800 - 5 4.5810000 0.2827890 - 6 1.5800000 0.4531230 - 7 0.5640000 0.2747740 - 8 0.0734500 0.0097510 -S 8 - 1 1469.0000000 -0.0001200 - 2 220.5000000 -0.0009230 - 3 50.2600000 -0.0046890 - 4 14.2400000 -0.0176820 - 5 4.5810000 -0.0489020 - 6 1.5800000 -0.0960090 - 7 0.5640000 -0.1363800 - 8 0.0734500 0.5751020 -S 1 - 1 0.0280500 1.0000000 -P 3 - 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