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Merge branch 'master' of gitlab.com:scemama/QCaml
This commit is contained in:
commit
3901749698
@ -3,13 +3,14 @@ open Util
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type t =
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{
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basis : Basis.t ;
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overlap : Overlap.t lazy_t;
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ortho : Orthonormalization.t lazy_t;
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eN_ints : NucInt.t lazy_t;
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kin_ints : KinInt.t lazy_t;
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ee_ints : ERI.t lazy_t;
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f12_ints : F12.t lazy_t;
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basis : Basis.t ;
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overlap : Overlap.t lazy_t;
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ortho : Orthonormalization.t lazy_t;
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eN_ints : NucInt.t lazy_t;
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kin_ints : KinInt.t lazy_t;
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ee_ints : ERI.t lazy_t;
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f12_ints : F12.t lazy_t;
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f12_over_r12_ints : ScreenedERI.t lazy_t;
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cartesian : bool;
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}
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@ -20,6 +21,7 @@ let eN_ints t = Lazy.force t.eN_ints
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let kin_ints t = Lazy.force t.kin_ints
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let ee_ints t = Lazy.force t.ee_ints
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let f12_ints t = Lazy.force t.f12_ints
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let f12_over_r12_ints t = Lazy.force t.f12_over_r12_ints
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let cartesian t = t.cartesian
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@ -50,7 +52,11 @@ let make ~cartesian ~basis ?f12 nuclei =
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F12.of_basis basis
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) in
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{ basis ; overlap ; ortho ; eN_ints ; kin_ints ; ee_ints ; f12_ints ;
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let f12_over_r12_ints = lazy (
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ScreenedERI.of_basis basis
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) in
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{ basis ; overlap ; ortho ; eN_ints ; kin_ints ; ee_ints ; f12_ints ; f12_over_r12_ints ;
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cartesian ;
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}
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@ -14,7 +14,7 @@ module T = struct
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let class_of_contracted_shell_pair_couple shell_pair_couple =
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let g = f12_factor.F12factor.gaussian in
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F12RR.contracted_class_shell_pair_couple
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g.GaussianOperator.expo_sg_inv
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g.GaussianOperator.expo_g_inv
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g.GaussianOperator.coef_g
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shell_pair_couple
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@ -12,7 +12,6 @@ module Po = Powers
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module Psp = PrimitiveShellPair
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module Pspc = PrimitiveShellPairCouple
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module Ps = PrimitiveShell
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module Zp = Zero_m_parameters
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let cutoff = Constants.integrals_cutoff
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let cutoff2 = cutoff *. cutoff
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@ -83,7 +82,7 @@ let rec hvrr angMom_a angMom_b angMom_c angMom_d
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let v1 =
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vrr (angMom_a-1) 0
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in
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let a = float_of_int (angMom_a-1) in
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let a = float_of_int_fast (angMom_a-1) in
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let v2 =
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vrr (angMom_a-2) 0
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in
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@ -92,7 +91,7 @@ let rec hvrr angMom_a angMom_b angMom_c angMom_d
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let v1 =
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vrr angMom_a 0
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in
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let a = float_of_int angMom_a in
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let a = float_of_int_fast angMom_a in
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let v2 =
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vrr (angMom_a-1) 0
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in
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@ -102,7 +101,7 @@ let rec hvrr angMom_a angMom_b angMom_c angMom_d
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let v1 =
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vrr 0 (angMom_c-1)
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in
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let b = float_of_int (angMom_c-1) in
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let b = float_of_int_fast (angMom_c-1) in
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let v3 =
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vrr 0 (angMom_c-2)
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in
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@ -112,8 +111,8 @@ let rec hvrr angMom_a angMom_b angMom_c angMom_d
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let v1 =
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vrr angMom_a (angMom_c-1)
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in
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let a = float_of_int angMom_a in
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let b = float_of_int (angMom_c-1) in
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let a = float_of_int_fast angMom_a in
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let b = float_of_int_fast (angMom_c-1) in
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let v2 =
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vrr (angMom_a-1) (angMom_c-1)
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in
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@ -4,16 +4,16 @@ open Constants
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type t =
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{
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coef_g : float array;
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expo_sg : float array;
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expo_sg_inv : float array;
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coef_g : float array;
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expo_g : float array;
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expo_g_inv : float array;
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}
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let make coef_g expo_sg =
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let expo_sg_inv =
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Array.map (fun x -> 1. /. x ) expo_sg
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let make coef_g expo_g =
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let expo_g_inv =
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Array.map (fun x -> 1. /. x ) expo_g
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in
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{ coef_g ; expo_sg ; expo_sg_inv }
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{ coef_g ; expo_g ; expo_g_inv }
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let one_over_r =
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@ -25,13 +25,13 @@ let one_over_r =
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0.169933732064 ; 0.130190978230 ; 0.099652303426 ; 0.075428246546 ;
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0.0555635614051 ; 0.0386791283055 ; 0.0237550435652 ; 0.010006278387 ;
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|]
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and expo_sg =
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and expo_g =
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[| 84135.654509 ; 2971.58727634 ; 474.716025959 ; 130.676724560 ;
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47.3938388887 ; 20.2078651631 ; 9.5411021938 ; 4.8109546955 ;
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2.52795733067 ; 1.35894103210 ; 0.73586710268 ; 0.39557629706 ;
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0.20785895177 ; 0.104809693858 ; 0.049485682527 ; 0.021099788990 ;
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0.007652472186 ; 0.0021065225215 ; 0.0003365204879 ; 0.0000118855674 |]
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in make coef_g expo_sg
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in make coef_g expo_g
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@ -90,8 +90,8 @@ let contracted_class shell_a shell_b : float Zmap.t =
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and s2 = ov (Po.get xyz angMomA + 1) (Po.get xyz angMomB - 1) k
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and s3 = ov (Po.get xyz angMomA - 1) (Po.get xyz angMomB + 1) k
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and s4 = ov (Po.get xyz angMomA + 1) (Po.get xyz angMomB + 1) k
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and a = float_of_int (Po.get xyz angMomA)
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and b = float_of_int (Po.get xyz angMomB)
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and a = float_of_int_fast (Po.get xyz angMomA)
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and b = float_of_int_fast (Po.get xyz angMomB)
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in
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0.5 *. a *. b *. s1 -. expo_a *. b *. s2 -. expo_b *. a *. s3 +.
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2.0 *. expo_a *. expo_b *. s4
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@ -58,7 +58,7 @@ let hvrr_one_e angMom_a angMom_b
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vrr amm
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in
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let v1 = vrr am in
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let f3 = float_of_int amxyz *. expo_inv_p *. 0.5 in
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let f3 = float_of_int_fast amxyz *. expo_inv_p *. 0.5 in
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Array.init (maxsze - angMom_a.Po.tot)
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(fun m -> f1 *. v1.(m) -. f2 *. v1.(m+1) +.
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f3 *. (v3.(m) -. expo_inv_p *. v3.(m+1))
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@ -10,7 +10,7 @@ let hvrr (angMom_a, angMom_b) (expo_inv_p) (center_ab, center_pa)
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if angMom_a > 0 then
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chop center_pa (fun () -> vrr (angMom_a-1))
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+. chop (0.5 *. float_of_int (angMom_a-1) *. expo_inv_p)
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+. chop (0.5 *. float_of_int_fast (angMom_a-1) *. expo_inv_p)
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(fun () -> vrr (angMom_a-2))
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else if angMom_a = 0 then 1.
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else 0.
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95
Basis/ScreenedERI.ml
Normal file
95
Basis/ScreenedERI.ml
Normal file
@ -0,0 +1,95 @@
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(** Screened Electron-electron repulsion integrals (Yukawa potential). Required for F12/r12. *)
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open Constants
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open Util
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module Csp = ContractedShellPair
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module Cspc = ContractedShellPairCouple
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module T = struct
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let name = "Screened electron repulsion integrals"
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let f12_factor = F12factor.gaussian_geminal 1.0
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open Zero_m_parameters
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let zero_m z =
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let expo_pq_inv = z.expo_p_inv +. z.expo_q_inv in
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assert (expo_pq_inv <> 0.);
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(*
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let f12_factor =
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match z.f12_factor with
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| Some f -> f
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| None -> assert false
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in
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*)
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let expo_G_inv, coef_G =
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f12_factor.F12factor.gaussian.GaussianOperator.expo_g_inv,
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f12_factor.F12factor.gaussian.GaussianOperator.coef_g
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in
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let expo_pq = 1. /. expo_pq_inv in
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let maxm = z.maxm in
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let result = Array.init (maxm+1) (fun _ -> 0.) in
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array_range 0 (Array.length coef_G)
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|> Array.iter (fun i ->
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let fG_inv = expo_pq_inv +. expo_G_inv.(i) in
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let fG = 1. /. fG_inv in
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let t =
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if z.norm_pq_sq > integrals_cutoff then
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z.norm_pq_sq *. (expo_pq -. fG)
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else 0.
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in
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let fm = boys_function ~maxm t in
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let tmp_array =
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let result = Array.init (maxm+1) (fun k -> 1.) in
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array_range 1 maxm
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|> Array.iter (fun k -> result.(k) <- result.(k-1) *. expo_pq *. expo_G_inv.(i));
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result
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in
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let tmp_result = Array.init (maxm+1) (fun _ -> 0.) in
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let rec aux accu m = function
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| 0 -> tmp_result.(m) <- fm.(m) *. accu
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| j ->
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begin
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let f =
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array_range 0 m
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|> Array.fold_left (fun v k ->
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v +. (binom_float m k) *. tmp_array.(k) *. fm.(k)) 0.
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in
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tmp_result.(m) <- accu *. f;
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let new_accu = -. accu *. expo_pq in
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(aux [@tailcall]) new_accu (m+1) (j-1)
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end
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in
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let f =
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two_over_sq_pi *. (sqrt expo_pq) *. fG *. expo_G_inv.(i) *. exp (-.fG *. z.norm_pq_sq)
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in
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aux f 0 maxm;
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Array.iteri (fun k v ->
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result.(k) <- result.(k) +. coef_G.(i) *. v
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) tmp_result) ;
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result
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|
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let class_of_contracted_shell_pair_couple shell_pair_couple =
|
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let shell_p = Cspc.shell_pair_p shell_pair_couple
|
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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
|
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|
||||
module M = TwoElectronIntegrals.Make(T)
|
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include M
|
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|
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@ -96,9 +96,9 @@ module Make(T : TwoEI_structure) = struct
|
||||
|
||||
let eri_array =
|
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Fis.create ~size:n `Dense
|
||||
(*
|
||||
Fis.create ~size:n `Sparse
|
||||
*)
|
||||
(*
|
||||
Fis.create ~size:n `Sparse
|
||||
*)
|
||||
in
|
||||
|
||||
let t0 = Unix.gettimeofday () in
|
||||
|
||||
@ -16,6 +16,7 @@ module Zp = Zero_m_parameters
|
||||
let cutoff = Constants.integrals_cutoff
|
||||
let cutoff2 = cutoff *. cutoff
|
||||
|
||||
|
||||
exception NullQuartet
|
||||
|
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type four_idx_intermediates =
|
||||
@ -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 ;
|
||||
}
|
||||
|
||||
@ -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 *)
|
||||
|
||||
@ -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.;
|
||||
|
||||
@ -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
|
||||
|
||||
@ -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 *)
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user