open Qcaml_common let max_index = 1 lsl 14 type index_pair = { first : int ; second : int } type 'a storage_t = | Dense of ('a,'a) Matrix.t | Sparse of (int, float) Hashtbl.t type 'a t = { size : int ; two_index : ('a,'a) Matrix.t; two_index_anti : ('a,'a) Matrix.t; three_index : ('a,'a) Matrix.t; three_index_anti : ('a,'a) Matrix.t; four_index : 'a 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_inplace 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_inplace 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_inplace |> Bigarray.genarray_of_array1 in Bigarray.reshape_2 result d.size d.size |> Matrix.of_bigarray_inplace else match d.four_index with | Dense a -> let kl = sym_index k l in let result = Matrix.col a kl |> Vector.to_bigarray_inplace |> Bigarray.genarray_of_array1 in Bigarray.reshape_2 result d.size d.size |> Matrix.of_bigarray_inplace | 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_inplace 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_inplace 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