Four-idx transformation

This commit is contained in:
Anthony Scemama 2018-07-20 16:09:06 +02:00
parent 955f9d014b
commit 4f41af9e31
14 changed files with 307 additions and 17 deletions

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@ -13,6 +13,7 @@ module Psp = PrimitiveShellPair
type t = Mat.t
external matrix : t -> Mat.t = "%identity"
external of_matrix : Mat.t -> t = "%identity"
let cutoff = integrals_cutoff

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@ -11,4 +11,7 @@ val to_file : filename:string -> t -> unit
(** Write the integrals in a file. *)
val matrix : t -> Mat.t
(** Returns the matrix suitable for Lacaml *)
(** Returns the matrix suitable for Lacaml. *)
val of_matrix : Mat.t -> t
(** Build from a Lacaml matrix. *)

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@ -6,6 +6,7 @@ open Lacaml.D
type t = Mat.t
external matrix : t -> Mat.t = "%identity"
external of_matrix : Mat.t -> t = "%identity"
module Am = AngularMomentum
module Bs = Basis

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@ -4,6 +4,7 @@ open Lacaml.D
type t = Mat.t
external matrix : t -> Mat.t = "%identity"
external of_matrix : Mat.t -> t = "%identity"
module Am = AngularMomentum

181
MOBasis/MOBasis.ml Normal file
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@ -0,0 +1,181 @@
open Lacaml.D
open Util
(** One-electron orthogonal basis set, corresponding to Molecular Orbitals. *)
module HF = HartreeFock_type
module Si = Simulation
type mo_class =
| Core of int
| Inactive of int
| Active of int
| Virtual of int
| Deleted of int
type mo_type =
| RHF | ROHF | CASSCF
| Natural of string
| Localized of string
type t =
{
ao_basis : AOBasis.t; (* Atomic basis set on which the MOs are built. *)
mo_type : mo_type; (* Kind of MOs (RHF, CASSCF, Localized... *)
mo_class : mo_class array; (* CI-Class of the MOs *)
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 *)
kin_ints : KinInt.t lazy_t; (* Kinetic energy integrals *)
}
let mo_matrix_of_ao_matrix ~mo_coef ao_matrix =
gemm ~transa:`T mo_coef @@
gemm ao_matrix mo_coef
let ao_matrix_of_mo_matrix ~mo_coef ~ao_overlap mo_matrix =
let sc = gemm ao_overlap mo_coef in
gemm sc @@
gemm ~transb:`T mo_matrix sc
let four_index_transform ~mo_coef eri_ao =
let ao_num = Mat.dim1 mo_coef in
let mo_num = Mat.dim2 mo_coef in
let eri_mo = ERI.create ~size:mo_num `Dense 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 ~start:1 mo_num in
let range_ao = list_range ~start: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
Printf.eprintf "Transforming %d integrals : %!" mo_num;
List.iter (fun delta ->
Printf.eprintf "%d %!" delta;
Mat.fill u 0.;
List.iter (fun l ->
let jk = ref 0 in
List.iter (fun k ->
List.iter (fun j ->
incr jk;
ERI.get_phys_all_i eri_ao ~j ~k ~l
|> Array.iteri (fun i x -> o.{i+1,!jk} <- x)
) range_ao
) range_ao;
(* o_i_jk *)
let p =
gemm ~transa:`T ~c:p o mo_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' mo_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. ~c:u q' mo_coef
(* u_alphabeta_gamma = \sum_k q_k_alphabeta c_k_gamma *)
) range_ao;
let u =
Bigarray.reshape
(Bigarray.genarray_of_array2 u)
[| mo_num ; mo_num ; mo_num |]
|> Bigarray.array3_of_genarray
in
List.iter (fun gamma ->
List.iter (fun beta ->
List.iter (fun alpha ->
let x = u.{alpha,beta,gamma} in
if x <> 0. then
ERI.set_phys eri_mo alpha beta gamma delta x
) range_mo
) range_mo
) range_mo
) range_mo;
Printf.eprintf "\n%!";
eri_mo
let make ~ao_basis ~mo_type ~mo_class ~mo_occupation ~mo_coef () =
let eN_ints = lazy (
Lazy.force ao_basis.AOBasis.eN_ints
|> NucInt.matrix
|> mo_matrix_of_ao_matrix ~mo_coef
|> NucInt.of_matrix
)
and kin_ints = lazy (
Lazy.force ao_basis.AOBasis.kin_ints
|> KinInt.matrix
|> mo_matrix_of_ao_matrix ~mo_coef
|> KinInt.of_matrix
)
and ee_ints = lazy (
Lazy.force ao_basis.AOBasis.ee_ints
|> four_index_transform ~mo_coef
)
in
{ ao_basis ; mo_type ; mo_class ; mo_occupation ; mo_coef ;
eN_ints ; ee_ints ; kin_ints }
let of_rhf ~frozen_core hf =
let simulation = hf.HF.simulation in
let nocc = hf.HF.nocc in
let ncore =
if frozen_core then Nuclei.small_core simulation.Si.nuclei
else 0
in
let mo_num = Vec.dim hf.HF.eigenvalues in
let ao_basis = simulation.Si.ao_basis in
let mo_type = RHF in
let mo_class =
Array.init mo_num (fun i ->
if (i < ncore) then Core i
else
if (i < nocc ) then Inactive i
else Virtual i)
in
let mo_occupation =
Array.init mo_num (fun i ->
if i < nocc then 2. else 0.)
|> Vec.of_array
in
let mo_coef = hf.HF.eigenvectors in
make ~ao_basis ~mo_type ~mo_class ~mo_occupation ~mo_coef ()
let of_hartree_fock ~frozen_core = function
| HF.RHF hf -> of_rhf ~frozen_core hf
| _ -> assert false

43
MOBasis/MOBasis.mli Normal file
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@ -0,0 +1,43 @@
(** Data structure to represent the molecular orbitals. *)
open Lacaml.D
type mo_class =
| Core of int
| Inactive of int
| Active of int
| Virtual of int
| Deleted of int
type mo_type =
| RHF | ROHF | CASSCF
| Natural of string
| Localized of string
type t = private
{
ao_basis : AOBasis.t; (* Atomic basis set on which the MOs are built. *)
mo_type : mo_type; (* Kind of MOs (RHF, CASSCF, Localized... *)
mo_class : mo_class array; (* CI-Class of the MOs *)
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 *)
kin_ints : KinInt.t lazy_t; (* Kinetic energy integrals *)
}
val make : ao_basis:AOBasis.t ->
mo_type:mo_type ->
mo_class:mo_class array ->
mo_occupation:Vec.t ->
mo_coef:Mat.t ->
unit -> t
(** Function to build a data structure representing the molecular orbitals. *)
val of_hartree_fock : frozen_core:bool -> HartreeFock_type.t -> t
(** Build MOs from a Restricted Hartree-Fock calculation. *)

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@ -1,6 +1,6 @@
.NOPARALLEL:
INCLUDE_DIRS=Nuclei,Utils,Basis,SCF
INCLUDE_DIRS=Nuclei,Utils,Basis,SCF,MOBasis
LIBS=
PKGS=
OCAMLBUILD=ocamlbuild -j 0 -cflags $(ocamlcflags) -lflags $(ocamlcflags) $(ocamldocflags) -Is $(INCLUDE_DIRS) -ocamlopt $(ocamloptflags)

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@ -1,8 +1,9 @@
open Lacaml.D
open Util
type t =
type s =
{
simulation : Simulation.t;
guess : Guess.t;
eigenvectors : Lacaml.D.Mat.t ;
eigenvalues : Lacaml.D.Vec.t ;
@ -17,6 +18,12 @@ type t =
}
type t =
| RHF of s (** Restricted Hartree-Fock *)
| ROHF of s (** Restricted Open-shell Hartree-Fock *)
| UHF of s (** Unrestricted Hartree-Fock *)
let iterations_to_string hf_calc =
" # HF energy Convergence HOMO-LUMO
---------------------------------------------------" ::
@ -100,15 +107,21 @@ let mos_to_string hf_calc =
" ]
let to_string hf_calc =
String.concat "\n" [ "
=====================================================
Hartree-Fock
=====================================================" ; "" ;
iterations_to_string hf_calc ; "" ;
summary hf_calc ; "" ;
mos_to_string hf_calc ; "" ;
]
let to_string hf =
let aux hf_calc r =
String.concat "\n" [ Printf.sprintf "
=====================================================
%s Hartree-Fock
=====================================================" r ; "" ;
iterations_to_string hf_calc ; "" ;
summary hf_calc ; "" ;
mos_to_string hf_calc ; "" ;
]
in
match hf with
| RHF hf_calc -> aux hf_calc "Restricted"
| UHF hf_calc -> aux hf_calc "Unrestricted"
| ROHF hf_calc -> aux hf_calc "Restricted Open-shell"

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@ -1,7 +1,8 @@
(** Data structure representing the output of a Hartree-Fock caculation *)
type t =
type s =
{
simulation : Simulation.t; (** Simulation which was used for HF calculation *)
guess : Guess.t; (** Initial guess *)
eigenvectors : Lacaml.D.Mat.t ; (** Final eigenvectors *)
eigenvalues : Lacaml.D.Vec.t ; (** Final eigenvalues *)
@ -16,6 +17,12 @@ type t =
(** Energy, convergence and HOMO-LUMO gap of all iterations *)
}
type t =
| RHF of s (** Restricted Hartree-Fock *)
| ROHF of s (** Restricted Open-shell Hartree-Fock *)
| UHF of s (** Unrestricted Hartree-Fock *)
val to_string : t -> string
(** Results of a Hartree-Fock calculation pretty-printed in a string. *)

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@ -158,7 +158,9 @@ let make ?guess:(guess=`Huckel) ?max_scf:(max_scf=64) ?level_shift:(level_shift=
List.rev ( (energy, error, gap) :: iterations )
|> Array.of_list
in
{ HartreeFock_type.
HartreeFock_type.(RHF
{
simulation;
nocc;
guess ;
eigenvectors = m_C ;
@ -170,7 +172,7 @@ let make ?guess:(guess=`Huckel) ?max_scf:(max_scf=64) ?level_shift:(level_shift=
eN_energy = Mat.gemm_trace m_P m_V;
coulomb_energy = 0.5 *. Mat.gemm_trace m_P m_J;
exchange_energy = 0.5 *. Mat.gemm_trace m_P m_K;
}
})
in

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@ -166,6 +166,23 @@ type element = (** Element for the stream *)
}
let get_phys_all_i d ~j ~k ~l =
Array.init d.size (fun i -> get_phys d (i+1) j k l)
let get_chem_all_i d ~j ~k ~l =
Array.init d.size (fun i -> get_chem d (i+1) j k l)
let get_phys_all_ji d ~k ~l =
Array.init d.size (fun j -> get_phys_all_i d ~j:(j+1) ~k ~l)
let get_chem_all_ji d ~k ~l =
Array.init d.size (fun j -> get_chem_all_i d ~j:(j+1) ~k ~l)
let to_stream d =
let i = ref 0

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@ -36,6 +36,18 @@ val set_chem : t -> int -> int -> int -> int -> float -> unit
val set_phys : t -> int -> int -> int -> int -> float -> unit
(** Set an integral using the Physicist's convention {% $\langle ij|kl \rangle$ %}. *)
val get_chem_all_i : t -> j:int -> k:int -> l:int -> float array
(** Get all integrals in an array [a.(i-1) =] {% $(\cdot j|kl)$ %} . *)
val get_phys_all_i : t -> j:int -> k:int -> l:int -> float array
(** Get all integrals in an array [a.(i-1) =] {% $\langle \cdot j|kl \rangle$ %} . *)
val get_chem_all_ji : t -> k:int -> l:int -> float array array
(** Get all integrals in an array [a.(j-1).(i-1) =] {% $(\cdot \cdot|kl)$ %} . *)
val get_phys_all_ji : t -> k:int -> l:int -> float array array
(** Get all integrals in an array [a.(j-1).(i-1) =] {% $\langle \cdot \cdot|kl \rangle$ %} . *)
val to_stream : t -> element Stream.t
(** Retrun the data structure as a stream. *)

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@ -169,7 +169,7 @@ let list_some l =
(** {2 Stream functions} *)
let range ?(start=0) n =
let stream_range ?(start=0) n =
Stream.from (fun i ->
let result = i+start in
if result < n then
@ -178,6 +178,10 @@ let range ?(start=0) n =
)
let list_range ?(start=0) n =
Array.init n (fun i -> start+i) |> Array.to_list
(** {2 Linear algebra} *)

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@ -63,8 +63,13 @@ val list_some : 'a option list -> 'a list
(** Filters out all [None] elements of the list, and returns the elements without
the [Some]. *)
val list_range : ?start:int -> int -> int list
(** Returns a list [start ; start+1 ; ... ; start+(n-1)]. Default is [start=0]. *)
(** {2 Useful streams} *)
val range : ?start:int -> int -> int Stream.t
val stream_range : ?start:int -> int -> int Stream.t
(** Returns a stream <start ; start+1 ; ... ; start+(n-1)>. Default is [start=0]. *)
(** {2 Linear algebra } *)