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Dressed integrals in F12

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This commit is contained in:
Anthony Scemama 2019-10-03 16:58:15 +02:00
parent 72307bcec8
commit 8b49ac8f77
5 changed files with 236 additions and 269 deletions
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307
CI/F12CI.ml
View File

@ -1,314 +1,83 @@
open Lacaml.D open Lacaml.D
module Ds = DeterminantSpace
type t = type t =
{ {
mo_basis : MOBasis.t ; mo_basis : MOBasis.t ;
aux_basis : MOBasis.t ;
det_space : DeterminantSpace.t ; det_space : DeterminantSpace.t ;
ci : CI.t ; ci : CI.t ;
hf12_integrals : HF12.t ;
eigensystem : (Mat.t * Vec.t) lazy_t; eigensystem : (Mat.t * Vec.t) lazy_t;
} }
let ci t = t.ci let ci t = t.ci
let mo_basis t = t.mo_basis let mo_basis t = t.mo_basis
let det_space t = t.det_space let det_space t = t.det_space
let mo_class t = DeterminantSpace.mo_class @@ det_space t let mo_class t = Ds.mo_class @@ det_space t
let eigensystem t = Lazy.force t.eigensystem let eigensystem t = Lazy.force t.eigensystem
let f12_integrals mo_basis =
let two_e_ints = MOBasis.f12_ints mo_basis in let hf_ij_non_zero hf12_integrals deg_a deg_b ki kj =
( (fun _ _ _ -> 0.), let integrals = [
(fun i j k l s s' -> let one_e _ _ _ = 0. in
if (i=k && j<>l) || (j=l && i<>k) then let hf12_s, hf12_o = hf12_integrals in
0. let two_e i j k l s s' =
else
begin
let ijkl = F12.get_phys two_e_ints i j k l
in
(*
if s' = Spin.other s then if s' = Spin.other s then
(* Minus sign because we swap spin variables hf12_o.{i,j,k,l}
instead of orbital variables *)
0.375 *. ijkl +. 0.125 *. ijlk
else else
0.25 *. (ijkl -. ijlk) hf12_s.{i,j,k,l}
*)
if s' = Spin.other s then
ijkl
else
let ijlk = F12.get_phys two_e_ints i j l k
in in
ijkl -. ijlk (one_e, two_e)
end ]
) )
let h_ij mo_basis ki kj =
let integrals =
List.map (fun f -> f mo_basis)
[ CI.h_integrals ]
in in
CIMatrixElement.make integrals ki kj CIMatrixElement.non_zero integrals deg_a deg_b 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 |> List.hd
let hf_ij mo_basis ki kj = let dressing_vector ~frozen_core hf12_integrals f12_amplitudes ci =
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 -> true
| _ -> false
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 |> minus_one)
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 (Determinant.negate_phase k)
| 0, 1 -> Some (Determinant.vac 1)
*)
| _ -> None
let dressing_vector ~frozen_core aux_basis f12_amplitudes ci =
if Parallel.master then if Parallel.master then
Printf.printf "Building matrix\n%!"; Printf.printf "Building matrix\n%!";
let det_space =
(* Determinants of the FCI space as a list *) ci.CI.det_space
let in_dets =
DeterminantSpace.determinant_stream ci.CI.det_space
|> Util.stream_to_list
in in
(* Stream that generates only singly and doubly excited determinants
wrt FCI space *)
let out_dets_stream =
(* Stream that generates all determinants of FCI space *)
let s =
DeterminantSpace.fci_of_mo_basis ~frozen_core aux_basis
|> DeterminantSpace.determinant_stream
in
(* Select only doubly excited determinants wrt FCI space *)
Stream.from (fun _ ->
try
let p12 = p12 ci.CI.det_space in
let rec result () =
let ki = Stream.next s in
match p12 ki with
| Some ki' -> Some (ki, ki')
| None -> result ()
in
result ()
with Stream.Failure -> None
)
in
let make_h_and_f alpha_list =
let rec col_vecs_list accu_H accu_F = function
| [] ->
List.rev accu_H,
List.rev accu_F
| (ki, ki') :: rest ->
begin
let h, f =
List.map (fun kj ->
match hf_ij aux_basis kj ki with
| [ a ; b ] -> a, b
| _ -> assert false ) in_dets
|> List.split
in
let f' =
List.map (fun kj -> f_ij aux_basis kj ki') in_dets
in
let h = Vec.of_list h in
let f = Vec.of_list f in
let f' = Vec.of_list f' in
scal 0.375 f;
scal 0.125 f';
let f = Vec.add f f' in
col_vecs_list (h::accu_H) (f::accu_F) rest
end
in
let h, f =
col_vecs_list [] [] alpha_list
in
Mat.of_col_vecs_list h,
Mat.of_col_vecs_list f
in
let m_HF = let m_HF =
let batch_size = 1 + 1_000_000 / (Mat.dim1 f12_amplitudes) in
let input_stream = let f =
Stream.from (fun i -> match Ds.determinants det_space with
let rec make_batch accu = function | Ds.Arbitrary _ -> CI.create_matrix_arbitrary
| 0 -> accu | Ds.Spin _ -> CI.create_matrix_spin_computed
| n -> try
let alpha = Stream.next out_dets_stream in
let accu = alpha :: accu in
make_batch accu (n-1)
with Stream.Failure -> accu
in in
let result = make_batch [] batch_size in f (fun deg_a deg_b ki kj ->
if result = [] then None else Some result hf_ij_non_zero hf12_integrals deg_a deg_b ki kj
) ) det_space
in in
let iteration input = Matrix.mm (Lazy.force m_HF) (Matrix.dense_of_mat f12_amplitudes)
Printf.printf ".%!";
let m_H_aux, m_F_aux = make_h_and_f input in
let m_HF =
gemm m_H_aux m_F_aux ~transb:`T
in
gemm m_HF f12_amplitudes
in
let result =
let x =
try [ Stream.next out_dets_stream ]
with Stream.Failure -> failwith "Auxiliary basis set does not produce any excited determinant"
in
iteration x
in
input_stream
|> Farm.run ~ordered:false ~f:iteration
|> Stream.iter (fun hf ->
ignore @@ Mat.add result hf ~c:result );
Printf.printf "\n";
Parallel.broadcast (lazy result)
in
if Parallel.master then Printf.printf "Done\n%!";
Matrix.dense_of_mat m_HF
let make ~simulation ?(threshold=1.e-12) ~frozen_core ~mo_basis ~aux_basis_filename ?(state=1) () = let make ~simulation ?(threshold=1.e-12) ~frozen_core ~mo_basis ~aux_basis_filename ?(state=1) () =
let f12 = Util.of_some @@ Simulation.f12 simulation in
let mo_num = MOBasis.size mo_basis in
Printf.printf "Add aux basis\n%!";
(* Add auxiliary basis set *)
let s =
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 nuclei
|> Simulation.make ~f12 ~charge ~multiplicity ~nuclei
in
let aux_basis =
MOBasis.of_mo_basis s mo_basis
in
let () =
ignore @@ MOBasis.f12_ints aux_basis
in
let () =
ignore @@ MOBasis.two_e_ints aux_basis
in
let det_space = let det_space =
DeterminantSpace.fci_f12_of_mo_basis aux_basis ~frozen_core mo_num DeterminantSpace.fci_of_mo_basis mo_basis ~frozen_core
in in
let ci = CI.make ~n_states:state det_space in let ci = CI.make ~n_states:state det_space in
let hf12_integrals =
HF12.make ~simulation ~mo_basis ~aux_basis_filename ()
in
let ci_coef, ci_energy = let ci_coef, ci_energy =
let x = Lazy.force ci.eigensystem in let x = Lazy.force ci.eigensystem in
Parallel.broadcast (lazy x) Parallel.broadcast (lazy x)
in in
let e_shift =
let det =
DeterminantSpace.determinant_stream det_space
|> Stream.next
in
h_ij aux_basis det det
in
let eigensystem = lazy ( let eigensystem = lazy (
let m_H = let m_H =
Lazy.force ci.CI.m_H Lazy.force ci.CI.m_H
@ -320,7 +89,7 @@ Printf.printf "Add aux basis\n%!";
let delta = let delta =
(* delta_i = {% $\sum_j c_j H_{ij}$ %} *) (* delta_i = {% $\sum_j c_j H_{ij}$ %} *)
dressing_vector ~frozen_core aux_basis psi ci dressing_vector ~frozen_core hf12_integrals psi ci
|> Matrix.to_mat |> Matrix.to_mat
in in
@ -449,14 +218,14 @@ Printf.printf "Add aux basis\n%!";
(Mat.to_col_vecs eigenvectors).(0) ) (Mat.to_col_vecs eigenvectors).(0) )
in in
if Parallel.master then if Parallel.master then
Printf.printf "F12 Convergence : %e %f\n" conv (eigenvalues.{state} +. e_shift Printf.printf "F12 Convergence : %e %f\n" conv (eigenvalues.{state}
+. Simulation.nuclear_repulsion simulation); +. Simulation.nuclear_repulsion simulation);
if conv > threshold then if conv > threshold then
iteration ~state eigenvectors iteration ~state eigenvectors
else else
let eigenvalues = let eigenvalues =
Vec.map (fun x -> x +. e_shift) eigenvalues Vec.map (fun x -> x +. ci.CI.e_shift) eigenvalues
in in
eigenvectors, eigenvalues eigenvectors, eigenvalues
in in
@ -464,6 +233,8 @@ Printf.printf "Add aux basis\n%!";
) )
in in
{ mo_basis ; aux_basis ; det_space ; ci ; eigensystem } { mo_basis ; det_space ; ci ; hf12_integrals ; eigensystem }

186
MOBasis/HF12.ml Normal file
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@ -0,0 +1,186 @@
(** %{ $ \langle ij | H F | kl \rangle $ %} integrals. *)
open Lacaml.D
module Fis = FourIdxStorage
type t = (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t
* (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Genarray.t
let make ~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 aux_basis =
let s =
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 nuclei
|> Simulation.make ~f12 ~charge ~multiplicity ~nuclei
in
MOBasis.of_mo_basis s mo_basis
in
let aux_num = MOBasis.size aux_basis in
(* Fire calculation of F12 and ERI *)
let f12 =
MOBasis.f12_ints aux_basis
in
let eri =
MOBasis.two_e_ints aux_basis
in
(* Compute the <ij|QHF|kl> integrals *)
if Parallel.master then Printf.eprintf "Computing HF12 integrals\n%!";
let result_s, result_o =
Bigarray.Genarray.create Float64 Bigarray.fortran_layout [| mo_num ; mo_num ; mo_num ; mo_num |] ,
Bigarray.Genarray.create Float64 Bigarray.fortran_layout [| mo_num ; mo_num ; mo_num ; mo_num |]
in
let h_s = Bigarray.Array3.create Float64 Bigarray.fortran_layout mo_num aux_num aux_num in
let f_s = Bigarray.Array3.create Float64 Bigarray.fortran_layout aux_num aux_num mo_num in
let h_o = Bigarray.Array3.create Float64 Bigarray.fortran_layout mo_num aux_num aux_num in
let f_o = Bigarray.Array3.create Float64 Bigarray.fortran_layout aux_num aux_num mo_num in
let hf_s = Mat.create mo_num mo_num in
let hf_o = Mat.create mo_num mo_num in
for a=1 to mo_num do
for b=1 to mo_num do
for i=1 to mo_num do
h_s.{i, a, b} <- 0. ;
h_o.{i, a, b} <- 0.
done
done
done;
for k=1 to mo_num do
for b=1 to mo_num do
for a=1 to mo_num do
f_s.{a, b, k} <- 0. ;
f_o.{a, b, k} <- 0.
done
done
done;
let task (j,l) =
let h i a b =
h_s.{i, a, b} <- ERI.get_phys eri i j a b -. ERI.get_phys eri i j b a ;
h_o.{i, a, b} <- ERI.get_phys eri i j a b
and f a b k =
f_s.{a, b, k} <- 0.25 *. (F12.get_phys f12 a b k l -. F12.get_phys f12 a b l k) ;
f_o.{a, b, k} <- 0.375 *. F12.get_phys f12 a b k l +. 0.125 *. F12.get_phys f12 b a k l
in
for a=mo_num+1 to aux_num do
for b=mo_num+1 to aux_num do
for i=1 to mo_num do
h i a b
done
done
done;
for k=1 to mo_num do
for b=mo_num+1 to aux_num do
for a=mo_num+1 to aux_num do
f a b k
done
done
done;
(*
for a=1 to mo_num do
for b=mo_num+1 to aux_num do
for i=1 to mo_num do
if i <> a then
h i a b
done
done
done;
for k=1 to mo_num do
for b=mo_num+1 to aux_num do
for a=1 to mo_num do
if k <> a then
f a b k
done
done
done;
*)
let h_o =
Bigarray.(reshape (genarray_of_array3 h_o)) [| mo_num ; aux_num*aux_num |]
|> Bigarray.array2_of_genarray
in
let f_o =
Bigarray.(reshape (genarray_of_array3 f_o)) [| aux_num*aux_num ; mo_num |]
|> Bigarray.array2_of_genarray
in
let h_s =
Bigarray.(reshape (genarray_of_array3 h_s)) [| mo_num ; aux_num*aux_num |]
|> Bigarray.array2_of_genarray
in
let f_s =
Bigarray.(reshape (genarray_of_array3 f_s)) [| aux_num*aux_num ; mo_num |]
|> Bigarray.array2_of_genarray
in
let hf_s = gemm ~alpha:1.0 ~c:hf_s h_s f_s in
let hf_o = gemm ~alpha:1.0 ~c:hf_o h_o f_o in
hf_s, hf_o, j, l
in
let tasks =
let rec next accu = function
| _, 0 -> accu
| 0, l -> next accu (mo_num, l-1)
| j, l -> next ((j,l) :: accu) ((j-1), l)
in
next [] (mo_num, mo_num)
|> Stream.of_list
in
Farm.run ~f:task ~ordered:true tasks
|> Stream.iter (fun (hf_s, hf_o, j, l) ->
(*
Printf.printf "%d %d\n" j l ;
*)
for k=1 to mo_num do
for i=1 to mo_num do
result_s.{i,k,j,l} <- hf_s.{i,k} ;
result_o.{i,k,j,l} <- hf_o.{i,k}
done
done );
(*
for l=1 to mo_num do
for k=1 to mo_num do
for j=1 to mo_num do
for i=1 to mo_num do
Printf.printf "%d %d %d %d %e\n" i j k l result.{i,j,k,l}
done
done
done
done;
Printf.printf "%!";
*)
Parallel.broadcast (lazy (result_s, result_o) )

3
Utils/FourIdxStorage.ml
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@ -258,6 +258,9 @@ let get_phys t i j k l = get ~r1:{ first=i ; second=k } ~r2:{ first=j ; second=l
let set_chem t i j k l value = set ~r1:{ first=i ; second=j } ~r2:{ first=k ; second=l } ~value 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 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 *) type element = (** Element for the stream *)

6
Utils/FourIdxStorage.mli
View File

@ -38,6 +38,12 @@ val set_chem : t -> int -> int -> int -> int -> float -> unit
val set_phys : 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 {% $\langle ij|kl \rangle$ %}. *) (** Set an integral using the Physicist's convention {% $\langle ij|kl \rangle$ %}. *)
val increment_chem : t -> int -> int -> int -> int -> float -> unit
(** Increments an integral using the Chemist's convention {% $(ij|kl)$ %}. *)
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 -> Vec.t
(** Get all integrals in an array [a.{i} =] {% $(\cdot j|kl)$ %} . *) (** Get all integrals in an array [a.{i} =] {% $(\cdot j|kl)$ %} . *)

1
run_fci_f12.ml
View File

@ -87,6 +87,7 @@ let () =
MOBasis.of_hartree_fock hf MOBasis.of_hartree_fock hf
in in
let fcif12 = let fcif12 =
F12CI.make ~simulation ~frozen_core:false ~mo_basis ~aux_basis_filename ~state () F12CI.make ~simulation ~frozen_core:false ~mo_basis ~aux_basis_filename ~state ()
in in