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Added RR

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Anthony Scemama 2020-09-26 16:45:52 +02:00
parent 58d4c2695a
commit 70fe4145f3
8 changed files with 1675 additions and 3 deletions
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2
README.md
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@ -85,7 +85,7 @@ 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 .
$ opam pin add QCaml .
```
For more information on `opam pin`, please consult the opam documentation.

183
gaussian_integrals/lib/two_electron_integrals.ml Normal file
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(** Two electron integrals
*)
open Qcaml_common
open Qcaml_linear_algebra
open Qcaml_gaussian_basis
open Constants
let cutoff = integrals_cutoff
module Bs = Basis
module Cs = Contracted_shell
module Csp = Contracted_shell_pair
module Cspc = Contracted_shell_pair_couple
module Fis = Four_idx_storage
module type Two_ei_structure =
sig
val name : string
val class_of_contracted_shell_pair_couple :
basis:Basis.t -> Cspc.t -> float Zmap.t
end
module Make(T : Two_ei_structure) = struct
include Four_idx_storage
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
if abs_float value > cutoff then
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 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
|> filter_contracted_shell_pairs ~basis ~cutoff
in
Printf.printf "%d significant shell pairs computed in %f seconds\n"
(List.length shell_pairs) (Unix.gettimeofday () -. t0);
let ishell = ref max_int in
let t0 = Unix.gettimeofday () in
let f shell_p =
let () =
(*
if Parallel.rank < 2 && Cs.index (Csp.shell_a shell_p) < !ishell then
*)
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 -> ()
in
(*
List.rev shell_pairs
*)
shell_pairs
(*
|> Parallel.list_iter f ;
*)
|> List.iter f;
Printf.printf "Computed %s Integrals in parallel in %f seconds\n%!"
T.name (Unix.gettimeofday () -. t0);
eri_array
end

39
gaussian_integrals/lib/two_electron_integrals.mli Normal file
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(** 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
*)
open Qcaml_common
open Qcaml_gaussian_basis
open Qcaml_linear_algebra
module type Two_ei_structure =
sig
val name : string
(** Name of the kind of integrals, for printing purposes. *)
val class_of_contracted_shell_pair_couple :
basis:Basis.t -> Contracted_shell_pair_couple.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 : Two_ei_structure) ->
sig
include module type of Four_idx_storage
val filter_contracted_shell_pairs :
?cutoff:float -> basis:Basis.t ->
Contracted_shell_pair.t list -> Contracted_shell_pair.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

523
gaussian_integrals/lib/two_electron_rr.ml Normal file
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open Qcaml_common
open Qcaml_gaussian_basis
module Am = Angular_momentum
module Asp = Atomic_shell_pair
module Aspc = Atomic_shell_pair_couple
module Co = Coordinate
module Cs = Contracted_shell
module Csp = Contracted_shell_pair
module Cspc = Contracted_shell_pair_couple
module Po = Powers
module Psp = Primitive_shell_pair
module Pspc = Primitive_shell_pair_couple
module Ps = Primitive_shell
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 = (Util.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 =
(Util.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 =
(Util.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

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gaussian_integrals/lib/two_electron_rr_vectorized.ml Normal file
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open Qcaml_common
open Qcaml_gaussian_basis
open Qcaml_linear_algebra
module Am = Angular_momentum
module Co = Coordinate
module Cs = Contracted_shell
module Csp = Contracted_shell_pair
module Cspc = Contracted_shell_pair_couple
module Po = Powers
module Psp = Primitive_shell_pair
module Ps = Primitive_shell
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 = Util.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 = (Util.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 = (Util.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 =
Vector.init np (fun ab -> Psp.exponent_inv sp.(ab-1))
and expo_q_inv =
Vector.init nq (fun cd -> Psp.exponent_inv sq.(cd-1))
in
let coef =
Matrix.outer_product (Vector.of_array @@ cq) (Vector.of_array @@ cp)
in
let coefx = Matrix.to_bigarray coef in
let zm_array = Matrix.init_cols np nq (fun i j ->
try
if (abs_float coefx.{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
Matrix.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

30
gaussian_integrals/lib/zero_m_parameters.ml Normal file
View File

@ -0,0 +1,30 @@
open Qcaml_common
open Qcaml_gaussian_basis
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 ;
}

11
linear_algebra/lib/matrix.ml
View File

@ -108,6 +108,10 @@ let gemm ?m ?n ?k ?beta ?c ?(transa=`N) ?(alpha=1.0) a ?(transb=`N) b =
in
gemm ?m ?n ?k ?beta ?c ~transa ~alpha a ~transb b
let gemm_trace ?(transa=`N) a ?(transb=`N) b =
Mat.gemm_trace ~transa a ~transb b
let init_cols = Mat.init_cols
let of_col_vecs a =
@ -173,6 +177,13 @@ let sysv ~b a =
let debug_matrix name a =
Format.printf "@[%s =\n@[%a@]@]@." name pp a
let outer_product_inplace m ?(alpha=1.0) u v =
ger ~alpha (Vector.to_bigarray u) (Vector.to_bigarray v) m
let outer_product ?(alpha=1.0) u v =
let m = make0 (Vector.dim u) (Vector.dim v) in
outer_product_inplace m ~alpha u v;
m
let matrix_of_file filename =
let ic = Scanf.Scanning.open_in filename in

15
linear_algebra/lib/matrix.mli
View File

@ -140,18 +140,29 @@ val scale_cols_inplace: t -> Vector.t -> unit
val sycon: t -> float
(** Returns the condition number of a matrix *)
val outer_product : ?alpha:float -> Vector.t -> Vector.t -> t
(** Computes M = %{ $\alpha u.v^t$ %} *)
val outer_product_inplace : t -> ?alpha:float -> Vector.t -> Vector.t -> unit
(** Computes M = %{ $\alpha u.v^t$ %} *)
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:
(** Performs the Lapack GEMM 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:
(** Performs the Lapack GEMM operation. Default values:
[beta=0.] [transa=`N] [alpha=1.0] [transb=`N]
[gemm ~beta ~alpha a b]: %{ $C = \beta C + \alpha A B$ *)
val gemm_trace: ?transa:[`N | `T] -> t -> ?transb:[`N | `T] -> t -> float
(** Computes the trace of a GEMM. Default values:
[transa=`N] [transb=`N]
[gemm_trace a b]: %{ $C = Tr(A B)$ *)
val svd: t -> t * Vector.t * t
(** Singular value decomposition. *)