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Added ScreenedERI

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This commit is contained in:
Anthony Scemama 2020-02-17 19:45:53 +01:00
parent 01b56ea5f8
commit 4e8efef264
14 changed files with 216 additions and 66 deletions
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22
Basis/AOBasis.ml
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@ -3,13 +3,14 @@ open Util
type t =
{
basis : Basis.t ;
overlap : Overlap.t lazy_t;
ortho : Orthonormalization.t lazy_t;
eN_ints : NucInt.t lazy_t;
kin_ints : KinInt.t lazy_t;
ee_ints : ERI.t lazy_t;
f12_ints : F12.t lazy_t;
basis : Basis.t ;
overlap : Overlap.t lazy_t;
ortho : Orthonormalization.t lazy_t;
eN_ints : NucInt.t lazy_t;
kin_ints : KinInt.t lazy_t;
ee_ints : ERI.t lazy_t;
f12_ints : F12.t lazy_t;
f12_over_r12_ints : ScreenedERI.t lazy_t;
cartesian : bool;
}
@ -20,6 +21,7 @@ let eN_ints t = Lazy.force t.eN_ints
let kin_ints t = Lazy.force t.kin_ints
let ee_ints t = Lazy.force t.ee_ints
let f12_ints t = Lazy.force t.f12_ints
let f12_over_r12_ints t = Lazy.force t.f12_over_r12_ints
let cartesian t = t.cartesian
@ -50,7 +52,11 @@ let make ~cartesian ~basis ?f12 nuclei =
F12.of_basis basis
) in
{ basis ; overlap ; ortho ; eN_ints ; kin_ints ; ee_ints ; f12_ints ;
let f12_over_r12_ints = lazy (
ScreenedERI.of_basis basis
) in
{ basis ; overlap ; ortho ; eN_ints ; kin_ints ; ee_ints ; f12_ints ; f12_over_r12_ints ;
cartesian ;
}

2
Basis/F12.ml
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@ -14,7 +14,7 @@ module T = struct
let class_of_contracted_shell_pair_couple shell_pair_couple =
let g = f12_factor.F12factor.gaussian in
F12RR.contracted_class_shell_pair_couple
g.GaussianOperator.expo_sg_inv
g.GaussianOperator.expo_g_inv
g.GaussianOperator.coef_g
shell_pair_couple

11
Basis/F12RR.ml
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@ -12,7 +12,6 @@ module Po = Powers
module Psp = PrimitiveShellPair
module Pspc = PrimitiveShellPairCouple
module Ps = PrimitiveShell
module Zp = Zero_m_parameters
let cutoff = Constants.integrals_cutoff
let cutoff2 = cutoff *. cutoff
@ -83,7 +82,7 @@ let rec hvrr angMom_a angMom_b angMom_c angMom_d
let v1 =
vrr (angMom_a-1) 0
in
let a = float_of_int (angMom_a-1) in
let a = float_of_int_fast (angMom_a-1) in
let v2 =
vrr (angMom_a-2) 0
in
@ -92,7 +91,7 @@ let rec hvrr angMom_a angMom_b angMom_c angMom_d
let v1 =
vrr angMom_a 0
in
let a = float_of_int angMom_a in
let a = float_of_int_fast angMom_a in
let v2 =
vrr (angMom_a-1) 0
in
@ -102,7 +101,7 @@ let rec hvrr angMom_a angMom_b angMom_c angMom_d
let v1 =
vrr 0 (angMom_c-1)
in
let b = float_of_int (angMom_c-1) in
let b = float_of_int_fast (angMom_c-1) in
let v3 =
vrr 0 (angMom_c-2)
in
@ -112,8 +111,8 @@ let rec hvrr angMom_a angMom_b angMom_c angMom_d
let v1 =
vrr angMom_a (angMom_c-1)
in
let a = float_of_int angMom_a in
let b = float_of_int (angMom_c-1) in
let a = float_of_int_fast angMom_a in
let b = float_of_int_fast (angMom_c-1) in
let v2 =
vrr (angMom_a-1) (angMom_c-1)
in

18
Basis/GaussianOperator.ml
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@ -4,16 +4,16 @@ open Constants
type t =
{
coef_g : float array;
expo_sg : float array;
expo_sg_inv : float array;
coef_g : float array;
expo_g : float array;
expo_g_inv : float array;
}
let make coef_g expo_sg =
let expo_sg_inv =
Array.map (fun x -> 1. /. x ) expo_sg
let make coef_g expo_g =
let expo_g_inv =
Array.map (fun x -> 1. /. x ) expo_g
in
{ coef_g ; expo_sg ; expo_sg_inv }
{ coef_g ; expo_g ; expo_g_inv }
let one_over_r =
@ -25,13 +25,13 @@ let one_over_r =
0.169933732064 ; 0.130190978230 ; 0.099652303426 ; 0.075428246546 ;
0.0555635614051 ; 0.0386791283055 ; 0.0237550435652 ; 0.010006278387 ;
|]
and expo_sg =
and expo_g =
[| 84135.654509 ; 2971.58727634 ; 474.716025959 ; 130.676724560 ;
47.3938388887 ; 20.2078651631 ; 9.5411021938 ; 4.8109546955 ;
2.52795733067 ; 1.35894103210 ; 0.73586710268 ; 0.39557629706 ;
0.20785895177 ; 0.104809693858 ; 0.049485682527 ; 0.021099788990 ;
0.007652472186 ; 0.0021065225215 ; 0.0003365204879 ; 0.0000118855674 |]
in make coef_g expo_sg
in make coef_g expo_g

4
Basis/KinInt.ml
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@ -90,8 +90,8 @@ let contracted_class shell_a shell_b : float Zmap.t =
and s2 = ov (Po.get xyz angMomA + 1) (Po.get xyz angMomB - 1) k
and s3 = ov (Po.get xyz angMomA - 1) (Po.get xyz angMomB + 1) k
and s4 = ov (Po.get xyz angMomA + 1) (Po.get xyz angMomB + 1) k
and a = float_of_int (Po.get xyz angMomA)
and b = float_of_int (Po.get xyz angMomB)
and a = float_of_int_fast (Po.get xyz angMomA)
and b = float_of_int_fast (Po.get xyz angMomB)
in
0.5 *. a *. b *. s1 -. expo_a *. b *. s2 -. expo_b *. a *. s3 +.
2.0 *. expo_a *. expo_b *. s4

2
Basis/OneElectronRR.ml
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@ -58,7 +58,7 @@ let hvrr_one_e angMom_a angMom_b
vrr amm
in
let v1 = vrr am in
let f3 = float_of_int amxyz *. expo_inv_p *. 0.5 in
let f3 = float_of_int_fast amxyz *. expo_inv_p *. 0.5 in
Array.init (maxsze - angMom_a.Po.tot)
(fun m -> f1 *. v1.(m) -. f2 *. v1.(m+1) +.
f3 *. (v3.(m) -. expo_inv_p *. v3.(m+1))

2
Basis/Overlap_primitives.ml
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@ -10,7 +10,7 @@ let hvrr (angMom_a, angMom_b) (expo_inv_p) (center_ab, center_pa)
if angMom_a > 0 then
chop center_pa (fun () -> vrr (angMom_a-1))
+. chop (0.5 *. float_of_int (angMom_a-1) *. expo_inv_p)
+. chop (0.5 *. float_of_int_fast (angMom_a-1) *. expo_inv_p)
(fun () -> vrr (angMom_a-2))
else if angMom_a = 0 then 1.
else 0.

95
Basis/ScreenedERI.ml Normal file
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@ -0,0 +1,95 @@
(** Screened Electron-electron repulsion integrals (Yukawa potential). Required for F12/r12. *)
open Constants
open Util
module Csp = ContractedShellPair
module Cspc = ContractedShellPairCouple
module T = struct
let name = "Screened electron repulsion integrals"
let f12_factor = F12factor.gaussian_geminal 1.0
open Zero_m_parameters
let zero_m z =
let expo_pq_inv = z.expo_p_inv +. z.expo_q_inv in
assert (expo_pq_inv <> 0.);
(*
let f12_factor =
match z.f12_factor with
| Some f -> f
| None -> assert false
in
*)
let expo_G_inv, coef_G =
f12_factor.F12factor.gaussian.GaussianOperator.expo_g_inv,
f12_factor.F12factor.gaussian.GaussianOperator.coef_g
in
let expo_pq = 1. /. expo_pq_inv in
let maxm = z.maxm in
let result = Array.init (maxm+1) (fun _ -> 0.) in
array_range 0 (Array.length coef_G)
|> Array.iter (fun i ->
let fG_inv = expo_pq_inv +. expo_G_inv.(i) in
let fG = 1. /. fG_inv in
let t =
if z.norm_pq_sq > integrals_cutoff then
z.norm_pq_sq *. (expo_pq -. fG)
else 0.
in
let fm = boys_function ~maxm t in
let tmp_array =
let result = Array.init (maxm+1) (fun k -> 1.) in
array_range 1 maxm
|> Array.iter (fun k -> result.(k) <- result.(k-1) *. expo_pq *. expo_G_inv.(i));
result
in
let tmp_result = Array.init (maxm+1) (fun _ -> 0.) in
let rec aux accu m = function
| 0 -> tmp_result.(m) <- fm.(m) *. accu
| j ->
begin
let f =
array_range 0 m
|> Array.fold_left (fun v k ->
v +. (binom_float m k) *. tmp_array.(k) *. fm.(k)) 0.
in
tmp_result.(m) <- accu *. f;
let new_accu = -. accu *. expo_pq in
(aux [@tailcall]) new_accu (m+1) (j-1)
end
in
let f =
two_over_sq_pi *. (sqrt expo_pq) *. fG *. expo_G_inv.(i) *. exp (-.fG *. z.norm_pq_sq)
in
aux f 0 maxm;
Array.iteri (fun k v ->
result.(k) <- result.(k) +. coef_G.(i) *. v
) tmp_result) ;
result
let class_of_contracted_shell_pair_couple shell_pair_couple =
let shell_p = Cspc.shell_pair_p shell_pair_couple
and shell_q = Cspc.shell_pair_q shell_pair_couple
in
if Array.length (Csp.shell_pairs shell_p) +
(Array.length (Csp.shell_pairs shell_q)) < 4 then
TwoElectronRR.contracted_class_shell_pair_couple
~zero_m shell_pair_couple
else
TwoElectronRRVectorized.contracted_class_shell_pairs
~zero_m shell_p shell_q
end
module M = TwoElectronIntegrals.Make(T)
include M

8
Basis/TwoElectronIntegrals.ml
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@ -27,7 +27,7 @@ module Make(T : TwoEI_structure) = struct
List.map (fun pair ->
match Cspc.make ~cutoff pair pair with
| Some cspc ->
let cls = class_of_contracted_shell_pair_couple cspc in
let cls = class_of_contracted_shell_pair_couple 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.)
@ -96,9 +96,9 @@ module Make(T : TwoEI_structure) = struct
let eri_array =
Fis.create ~size:n `Dense
(*
Fis.create ~size:n `Sparse
*)
(*
Fis.create ~size:n `Sparse
*)
in
let t0 = Unix.gettimeofday () in

25
Basis/TwoElectronRR.ml
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@ -15,6 +15,7 @@ module Zp = Zero_m_parameters
let cutoff = Constants.integrals_cutoff
let cutoff2 = cutoff *. cutoff
exception NullQuartet
@ -105,7 +106,7 @@ let rec hvrr_two_e
let amm = Po.decr xyz am in
let v3 = vrr0 amm in
let v1 = vrr0 am in
let f3 = (float_of_int amxyz) *. expo_p_inv *. 0.5 in
let f3 = (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
@ -142,7 +143,7 @@ let rec hvrr_two_e
begin
let am = Po.decr xyz angMom_a in
let f5 =
(float_of_int axyz) *. expo_p_inv *. expo_q_inv *. 0.5
(float_of_int_fast axyz) *. expo_p_inv *. expo_q_inv *. 0.5
in
if (abs_float f5 > cutoff) then
let v5 =
@ -154,7 +155,7 @@ let rec hvrr_two_e
if cmxyz > 0 then
begin
let f3 =
(float_of_int cmxyz) *. expo_q_inv *. 0.5
(float_of_int_fast cmxyz) *. expo_q_inv *. 0.5
in
if (abs_float f3 > cutoff) ||
(abs_float (f3 *. expo_q_inv) > cutoff) then
@ -206,7 +207,7 @@ let rec hvrr_two_e
let result =
if cmxyz < 1 then result else
let f = 0.5 *. (float_of_int cmxyz) *. expo_q_inv in
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
@ -226,7 +227,7 @@ let rec hvrr_two_e
in
let result =
if axyz < 1 then result else
let f = 0.5 *. (float_of_int axyz) *. expo_q_inv in
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
@ -333,17 +334,16 @@ let contracted_class_shell_pair_couple ~zero_m shell_pair_couple : float Zmap.t
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_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 normalization = Psp.normalization sp_ab *. Psp.normalization sp_cd in
let zero_m_array =
zero_m Zp.{
let zero = Zp.zero 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 ; normalization ;
}
@ -456,8 +456,9 @@ let contracted_class_atomic_shell_pair_couple ~zero_m atomic_shell_pair_couple :
let expo_q_inv = Psp.exponent_inv sp_cd in
let normalization = Psp.normalization sp_ab *. Psp.normalization sp_cd in
let zero_m_array =
zero_m Zp.{
let zero = Zp.zero 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 ; normalization ;
}

29
Basis/TwoElectronRRVectorized.ml
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@ -112,7 +112,7 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
else
begin
let amm = Po.decr xyz am in
let amxyz = float_of_int amxyz in
let amxyz = 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
@ -231,7 +231,7 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
let p2 =
if cxyz < 2 then p1 else
let cmm = Po.decr xyz cm in
let fcm = (float_of_int (cxyz-1)) *. 0.5 in
let fcm = (float_of_int_fast (cxyz-1)) *. 0.5 in
let f1 =
Array.init nq (fun k ->
let x = fcm *. expo_q_inv.(k) in
@ -356,7 +356,7 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
| Some p2 -> p2
in
for l=0 to np-1 do
let fa = (float_of_int axyz) *. expo_p_inv.(l) *. 0.5 in
let fa = (float_of_int_fast axyz) *. expo_p_inv.(l) *. 0.5 in
let p2_l = p2.(l)
and v_l = v.(l)
in
@ -396,7 +396,7 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
let result =
if cmxyz < 1 then result else
begin
let f = 0.5 *. (float_of_int cmxyz) in
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
@ -473,7 +473,7 @@ let hvrr_two_e_vector (angMom_a, angMom_b, angMom_c, angMom_d)
let result =
if axyz < 1 then result else
begin
let f = 0.5 *. (float_of_int axyz) in
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
@ -655,9 +655,11 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
Psp.normalization sq.(i-1)
in
let zero = Zp.zero zero_m in
let zero_m_array =
zero_m Zp.{
maxm=0 ; expo_p_inv ; expo_q_inv ; norm_pq_sq ;
zero_m
{zero with
expo_p_inv ; expo_q_inv ; norm_pq_sq ;
center_pq ; center_pa ; center_qc ; normalization ;
}
in
@ -787,12 +789,13 @@ let contracted_class_shell_pairs ~zero_m ?schwartz_p ?schwartz_q shell_p shell_q
let normalization = Psp.normalization shell_ab *.
Psp.normalization shell_cd
in
zero_m Zp.{
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) ;
normalization ;
}
let zero = Zp.zero 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) ;
normalization ;
}
) sq
in
(* Transpose result *)

6
Basis/Zero_m_parameters.ml
View File

@ -8,10 +8,14 @@ type t =
center_pq : Coordinate.t ;
center_pa : Coordinate.t ;
center_qc : Coordinate.t ;
f12_factor : F12factor.t option;
zero_m_func : t -> float array ;
}
let zero =
let zero ?f12_factor zero_m_func =
{
zero_m_func ;
f12_factor ;
maxm=0 ;
expo_p_inv = 0.;
expo_q_inv = 0.;

48
Utils/Util.ml
View File

@ -45,12 +45,22 @@ let () =
;;
let memo_float_of_int =
Array.init 64 float_of_int
let float_of_int_fast i =
if Int.logand i 63 = i then
memo_float_of_int.(i)
else
float_of_int i
let factmax = 150
(* Incomplete gamma function : Int_0^x exp(-t) t^(a-1) dt
p: 1 / Gamma(a) * Int_0^x exp(-t) t^(a-1) dt
q: 1 / Gamma(a) * Int_x^inf exp(-t) t^(a-1) dt
(* Incomplete gamma function :
{% $\gamma(\alpha,x) = \int_0^x e^{-t} t^{\alpha-1} dt$ %}
{% $p: \frac{1}{\Gamma(\alpha)} \int_0^x e^{-t} t^{\alpha-1} dt$ %}
{% $q: \frac{1}{\Gamma(\alpha)} \int_x^\infty e^{-t} t^{\alpha-1} dt$ %}
reference - Haruhiko Okumura: C-gengo niyoru saishin algorithm jiten
(New Algorithm handbook in C language) (Gijyutsu hyouron
@ -123,7 +133,7 @@ let fact = function
| i -> fact_memo.(i)
let binom n k =
let binom_func n k =
(*TODO : slow function *)
assert (n >= k);
let rec aux n k =
@ -133,6 +143,23 @@ let binom n k =
aux (n-1) (k-1) + aux (n-1) k
in aux n k
let binom =
let memo =
Array.init 64 (fun n -> Array.init 64 (fun k ->
if n >= k then binom_func n k else 0) )
in
fun n k ->
if n < 64 then
begin
assert (n >= k);
memo.(n).(k)
end
else
binom_func n k
let binom_float n k =
binom n k
|> float_of_int_fast
let rec pow a = function
| 0 -> 1.
@ -157,6 +184,14 @@ let chop f g =
(** Generalized Boys function.
maxm : Maximum total angular momentum
{% $F_m(x) = \frac{\gamma(m+1/2,x)}{2x^{m+1/2}}$ %}
where %{ $\gamma$ %} is the incomplete gamma function.
{% $F_0(0.) = 1$ %}
{% $F_0(t) = \frac{\sqrt{\pi}}{2\sqrt{t}} \text{erf} ( \sqrt{t} )$ %}
{% $F_m(0.) = \frac{1}{2m+1}$ %}
{% $F_m(t) = \frac{\gamma{m+1/2,t}}{2t^{m+1/2}}
{% $F_m(t) = \frac{ 2t\, F_{m+1}(t) + e^{-t} }{2m+1}$ %}
*)
let boys_function ~maxm t =
match maxm with
@ -182,10 +217,9 @@ let boys_function ~maxm t =
let dm = 0.5 +. n in
let f = (pow t_inv (maxm+maxm+1) ) in
match classify_float f with
| FP_normal -> (incomplete_gamma dm t) *. 0.5 *. f
| FP_zero
| FP_subnormal
| FP_normal ->
(incomplete_gamma dm t) *. 0.5 *. f
| FP_subnormal -> 0.
| _ -> invalid_arg "zero_m overflow"
in
let emt = exp (-. t) in

10
Utils/Util.mli
View File

@ -49,6 +49,9 @@ val fact : int -> float
val binom : int -> int -> int
(** Binomial coefficient. [binom n k] {% $= C_n^k$ %}. *)
val binom_float : int -> int -> float
(** Binomial coefficient. [binom n k] {% $= C_n^k$ %}. *)
val pow : float -> int -> float
(** Fast implementation of the power function for small integer powers *)
@ -57,8 +60,10 @@ val chop : float -> (unit -> float) -> float
than {!Constants.epsilon}, and return [a *. f ()].
*)
val of_some : 'a option -> 'a
val float_of_int_fast : int -> float
(* Faster implementation of float_of_int for small positive ints *)
val of_some : 'a option -> 'a
(** {2 Functions related to the Boys function} *)
@ -77,6 +82,9 @@ val boys_function : maxm:int -> float -> float array
(** {2 Extension of the Array module} *)
val array_range : int -> int -> int array
(** [array_range first last] returns an array [| first; first+1 ; ... ; last-1 ; last |]. *)
val array_sum : float array -> float
(** Returns the sum of all the elements of the array *)