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263 lines
8.4 KiB
OCaml
263 lines
8.4 KiB
OCaml
(** Electron-electron repulsion integrals *)
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open Util
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open Constants
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open Bigarray
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type t = (float, float32_elt, fortran_layout) Genarray.t
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(* Input type *)
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type input_data =
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{
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i : int;
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j : int;
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shell_pairs : ContractedShellPair.t array array ;
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schwartz : (float Zmap.t * float) array array;
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cutoff : float
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}
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(* Output type *)
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type output_integral = (* <ij|kl> *)
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{
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i1 : int ; (* Function i for electron 1 *)
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j2 : int ; (* Function j for electron 2 *)
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k1 : int ; (* Function k for electron 1 *)
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l2 : int ; (* Function l for electron 2 *)
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swap : bool ; (* If true, Compute (kl|ij) instead of (ij|kl) *)
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cls : float Zmap.t;
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}
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type output_data = output_integral list
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(** (00|00)^m : Fundamental electron repulsion integral
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$ \int \int \phi_p(r1) 1/r_{12} \phi_q(r2) dr_1 dr_2 $
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maxm : Maximum total angular momentum
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expo_pq_inv : $1./p + 1/q$ where $p$ and $q$ are the exponents of
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$\phi_p$ and $\phi_q$
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norm_pq_sq : square of the distance between the centers of $\phi_p$
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and $\phi_q$
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*)
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let zero_m ~maxm ~expo_pq_inv ~norm_pq_sq =
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let exp_pq = 1. /. expo_pq_inv in
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let t = norm_pq_sq *. exp_pq in
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let f = two_over_sq_pi *. (sqrt exp_pq) in
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let result = boys_function ~maxm t in
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let rec aux accu k = function
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| 0 -> result.(k) <- result.(k) *. accu
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| l ->
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begin
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result.(k) <- result.(k) *. accu;
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let new_accu = -. accu *. exp_pq in
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aux new_accu (k+1) (l-1)
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end
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in
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aux f 0 maxm;
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result
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(** Compute all the integrals of a contracted class when shell pairs are not yet available *)
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let contracted_class shell_a shell_b shell_c shell_d : float Zmap.t =
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TwoElectronRR.contracted_class ~zero_m shell_a shell_b shell_c shell_d
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(** Compute all the integrals of a contracted class *)
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let contracted_class_shell_pairs_vec ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
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TwoElectronRRVectorized.contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
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(** Compute all the integrals of a contracted class *)
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let contracted_class_shell_pairs ?schwartz_p ?schwartz_q shell_p shell_q : float Zmap.t =
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TwoElectronRR.contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
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(** Creates the input data structure from the basis set. *)
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let make_input basis =
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let shell = Basis.contracted_shells basis in
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(* Pre-compute all shell pairs *)
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let shell_pairs =
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ContractedShellPair.shell_pairs shell
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in
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(* Pre-compute diagonal integrals for Schwartz screening *)
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let t0 = Unix.gettimeofday () in
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let schwartz =
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Array.map (fun pair_array ->
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Array.map (fun pair ->
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let cls = contracted_class_shell_pairs pair pair in
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let m = Zmap.fold (fun _ value accu ->
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max (abs_float value) accu) cls 0.
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in (cls, m)
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) pair_array
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) shell_pairs
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in
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(* Count number of significant shell pairs. *)
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let icount = ref 0 in
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for i=0 to (Array.length shell) - 1 do
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print_int (Contracted_shell.index shell.(i)) ; print_newline ();
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for j=0 to i do
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let schwartz_p, schwartz_p_max = schwartz.(i).(j) in
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if (schwartz_p_max >= cutoff) then
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icount := !icount + 1;
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done;
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done;
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Printf.printf "%d shell pairs computed in %f seconds\n" !icount (Unix.gettimeofday () -. t0);
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List.init (Array.length shell) (fun i ->
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List.init (i+1) (fun j ->
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{ i ; j ; shell_pairs ; schwartz ; cutoff } ) )
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|> List.fold_left List.rev_append []
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exception NullIntegral
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let slave_job { i ; j ; shell_pairs ; schwartz ; cutoff} =
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let shell_p = shell_pairs.(i).(j) in
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let schwartz_p, schwartz_p_max = schwartz.(i).(j) in
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if schwartz_p_max < cutoff then [] else
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let schwartz_cutoff = cutoff *. cutoff in
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let sp = shell_p.ContractedShellPair.shell_pairs in
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let f k l =
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let schwartz_q, schwartz_q_max = schwartz.(k).(l) in
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if schwartz_p_max *. schwartz_q_max < schwartz_cutoff then
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raise NullIntegral;
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let shell_q = shell_pairs.(k).(l) in
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let sq = shell_q.ContractedShellPair.shell_pairs in
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let swap = Array.length sp > Array.length sq in
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(* Compute all the integrals of the class *)
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let cls =
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if swap then
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if Array.length sp + Array.length sq = 2 then
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contracted_class_shell_pairs ~schwartz_p:schwartz_q ~schwartz_q:schwartz_p shell_q shell_p
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else
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contracted_class_shell_pairs_vec ~schwartz_p:schwartz_q ~schwartz_q:schwartz_p shell_q shell_p
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else
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if Array.length sp + Array.length sq = 2 then
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contracted_class_shell_pairs ~schwartz_p ~schwartz_q shell_p shell_q
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else
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contracted_class_shell_pairs_vec ~schwartz_p ~schwartz_q shell_p shell_q
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in
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{ i1=i ; j2=k ; k1=j ; l2=l ; swap ; cls }
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in
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let rec loop accu k l =
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match k, l with
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| -1, -1 -> accu
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| k, -1 -> loop accu (k-1) (k-1)
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| k, l ->
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let new_accu =
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let _, schwartz_q_max = schwartz.(k).(l) in
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if schwartz_p_max *. schwartz_q_max > schwartz_cutoff then
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f k l :: accu
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else accu
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in
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loop new_accu k (l-1)
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in
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loop [] i i
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let of_basis basis =
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let shell = Basis.contracted_shells basis in
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(* 4D data initialization *)
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let eri_array =
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let n = Basis.size basis in
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Genarray.create Float32 fortran_layout [| n ; n ; n ; n|]
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in
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Genarray.fill eri_array 0.;
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(* Compute ERIs *)
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let to_int_tuple x =
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let open Zkey in
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match to_int_tuple Kind_3 x with
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| Three x -> x
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| _ -> assert false
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in
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let t0 = Unix.gettimeofday () in
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let inn = ref 0 in
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let out = ref 0 in
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make_input basis
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|> List.map slave_job
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|> List.iter (fun output_ij ->
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List.iter (fun { i1=i ; j2=k ; k1=j ; l2=l ; swap ; cls } ->
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Array.iteri (fun i_c powers_i ->
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let i_c = (Contracted_shell.index shell.(i)) + i_c + 1 in
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let xi = to_int_tuple powers_i in
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Array.iteri (fun j_c powers_j ->
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let j_c = (Contracted_shell.index shell.(j)) + j_c + 1 in
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let xj = to_int_tuple powers_j in
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Array.iteri (fun k_c powers_k ->
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let k_c = (Contracted_shell.index shell.(k)) + k_c + 1 in
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let xk = to_int_tuple powers_k in
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Array.iteri (fun l_c powers_l ->
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let l_c = (Contracted_shell.index shell.(l)) + l_c + 1 in
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let xl = to_int_tuple powers_l in
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let key =
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if swap then
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Zkey.of_int_tuple (Zkey.Twelve (xk,xl,xi,xj))
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else
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Zkey.of_int_tuple (Zkey.Twelve (xi,xj,xk,xl))
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in
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let value =
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Zmap.find cls key
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in
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eri_array.{i_c,k_c,j_c,l_c} <- value;
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eri_array.{j_c,k_c,i_c,l_c} <- value;
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eri_array.{i_c,l_c,j_c,k_c} <- value;
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eri_array.{j_c,l_c,i_c,k_c} <- value;
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eri_array.{k_c,i_c,l_c,j_c} <- value;
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eri_array.{k_c,j_c,l_c,i_c} <- value;
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eri_array.{l_c,i_c,k_c,j_c} <- value;
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eri_array.{l_c,j_c,k_c,i_c} <- value;
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if (abs_float value > cutoff) then
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(inn := !inn + 1;
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)
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else
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out := !out + 1;
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) (Contracted_shell.powers shell.(l))
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) (Contracted_shell.powers shell.(k))
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) (Contracted_shell.powers shell.(j))
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) (Contracted_shell.powers shell.(i));
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) output_ij
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);
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Printf.printf "In: %d Out:%d\n" !inn !out ;
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Printf.printf "Computed ERIs in %f seconds\n%!" (Unix.gettimeofday () -. t0);
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eri_array
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(** Write all integrals to a file with the <ij|kl> convention *)
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let to_file ~filename eri_array =
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let oc = open_out filename in
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(* Print ERIs *)
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for l_c=1 to (Genarray.nth_dim eri_array 3) do
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for k_c=1 to l_c do
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for j_c=1 to l_c do
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for i_c=1 to k_c do
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let value = eri_array.{i_c,j_c,k_c,l_c} in
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if (abs_float value > cutoff) then
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Printf.fprintf oc " %5d %5d %5d %5d%20.15f\n" i_c j_c k_c l_c value;
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done;
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done;
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done;
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done;
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close_out oc
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