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Working on DIIS
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parent
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commit
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@ -1,17 +0,0 @@
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open Lacaml.D
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type guess =
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| Hcore of Mat.t
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type t = guess
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let make ?guess:(guess=`Hcore) simulation =
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let eN_ints = Lazy.force simulation.Simulation.eN_ints
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and kin_ints = Lazy.force simulation.Simulation.kin_ints
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in
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match guess with
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| `Hcore -> Hcore (Mat.add eN_ints kin_ints)
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@ -1,12 +0,0 @@
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(** Guess for Hartree-Fock calculations. *)
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type guess =
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| Hcore of Lacaml.D.Mat.t
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type t = guess
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val make : ?guess:[ `Hcore ] -> Simulation.t -> t
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@ -1,6 +1,6 @@
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.NOPARALLEL:
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INCLUDE_DIRS=Nuclei,Utils,Basis,HartreeFock
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INCLUDE_DIRS=Nuclei,Utils,Basis,SCF
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LIBS=
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PKGS=
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OCAMLBUILD=ocamlbuild -j 0 -cflags $(ocamlcflags) -lflags $(ocamlcflags) $(ocamldocflags) -Is $(INCLUDE_DIRS) -ocamlopt $(ocamloptflags)
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49
SCF/Guess.ml
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49
SCF/Guess.ml
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@ -0,0 +1,49 @@
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open Lacaml.D
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open Util
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type guess =
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| Hcore of Mat.t
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| Huckel of Mat.t
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type t = guess
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module Si = Simulation
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module El = Electrons
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let hcore_guess simulation =
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let eN_ints = Lazy.force simulation.Si.eN_ints
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and kin_ints = Lazy.force simulation.Si.kin_ints
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in
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Mat.add eN_ints kin_ints
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let huckel_guess simulation =
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let c = 0.5 *. 1.75 in
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let ao_num = Basis.size simulation.Si.basis in
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let eN_ints = Lazy.force simulation.Si.eN_ints
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and kin_ints = Lazy.force simulation.Si.kin_ints
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and overlap = Lazy.force simulation.Si.overlap
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and m_X = Lazy.force simulation.Si.overlap_ortho
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in
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let diag = Array.init (ao_num+1) (fun i -> if i=0 then 0. else
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eN_ints.{i,i} +. kin_ints.{i,i})
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in
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let nocc =
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simulation.Si.electrons.El.n_alpha
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in
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let m_F = (Fock.make ~density:(gemm ~alpha:2. ~transb:`T ~k:nocc m_X m_X) simulation).Fock.fock in
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for j=1 to ao_num do
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for i=1 to ao_num do
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if (i <> j) then
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m_F.{i,j} <- c *. overlap.{i,j} *. (diag.(i) +. diag.(j)) (*TODO Pseudo *)
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done;
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done;
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m_F
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let make ~guess simulation =
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match guess with
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| `Hcore -> Hcore (hcore_guess simulation)
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| `Huckel -> Huckel (huckel_guess simulation)
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13
SCF/Guess.mli
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13
SCF/Guess.mli
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@ -0,0 +1,13 @@
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(** Guess for Hartree-Fock calculations. *)
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type guess =
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| Hcore of Lacaml.D.Mat.t
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| Huckel of Lacaml.D.Mat.t
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type t = guess
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val make : guess:[ `Hcore | `Huckel ] -> Simulation.t -> t
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@ -2,7 +2,7 @@ open Util
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open Lacaml.D
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open Simulation
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let make ?guess:(guess=`Hcore) ?max_scf:(max_scf=64)
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let make ?guess:(guess=`Huckel) ?max_scf:(max_scf=64) ?level_shift:(level_shift=0.1)
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?threshold_SCF:(threshold_SCF=1.e-6) simulation =
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(* Number of occupied MOs *)
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@ -21,7 +21,7 @@ let make ?guess:(guess=`Hcore) ?max_scf:(max_scf=64)
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(* Orthogonalization matrix *)
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let m_X =
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Lazy.force simulation.overlap_ortho
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Lazy.force simulation.overlap_ortho
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in
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@ -34,8 +34,16 @@ let make ?guess:(guess=`Hcore) ?max_scf:(max_scf=64)
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and m_V = Lazy.force simulation.eN_ints
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in
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(* Level shift *)
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let m_LS =
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Array.init (Mat.dim2 m_X) (fun i ->
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if i > nocc then level_shift else 0.)
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|> Vec.of_array
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|> Mat.of_diag
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in
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(* SCF iterations *)
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let rec loop nSCF iterations m_C =
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let rec loop nSCF iterations m_C diis =
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(* Density matrix over nocc occupied MOs *)
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let m_P =
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@ -50,9 +58,31 @@ let make ?guess:(guess=`Hcore) ?max_scf:(max_scf=64)
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x.Fock.fock, x.Fock.core, x.Fock.coulomb, x.Fock.exchange
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in
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let error_fock =
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let fps =
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gemm m_F (gemm m_P m_S)
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and spf =
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gemm m_S (gemm m_P m_F)
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in
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Mat.sub fps spf
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in
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let diis =
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DIIS.append ~p:(Mat.as_vec m_F) ~e:(Mat.as_vec error_fock) diis
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in
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let m_F_diis =
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let x =
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Bigarray.genarray_of_array1 (DIIS.next diis)
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in
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Bigarray.reshape_2 x (Mat.dim1 m_F) (Mat.dim2 m_F)
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in
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(* Fock matrix in MO basis *)
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let m_Fmo =
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xt_o_x m_F m_X
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xt_o_x m_F_diis m_C
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|> Mat.add m_LS
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in
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(* MOs in old MO basis *)
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@ -62,7 +92,7 @@ let make ?guess:(guess=`Hcore) ?max_scf:(max_scf=64)
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(* MOs in AO basis *)
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let m_C =
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gemm m_X m_C'
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gemm m_C m_C'
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in
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(* Hartree-Fock energy *)
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@ -72,32 +102,28 @@ let make ?guess:(guess=`Hcore) ?max_scf:(max_scf=64)
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in
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(* Convergence criterion *)
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let commutator =
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let fps =
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gemm m_F (gemm m_P m_S)
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and spf =
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gemm m_S (gemm m_P m_F)
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in
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Mat.sub fps spf
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|> Mat.as_vec
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let error =
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xt_o_x error_fock m_C
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|> Mat.as_vec
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|> amax
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|> abs_float
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in
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let converged =
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nSCF = max_scf || (abs_float commutator) < threshold_SCF
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nSCF = max_scf || error < threshold_SCF
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in
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let gap =
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eigenvalues.{nocc+1} -. eigenvalues.{nocc};
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in
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Printf.printf "%d %16.10f %11.4e %10.4f\n%!" nSCF energy commutator gap;
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Printf.printf "%d %16.10f %11.4e %10.4f\n%!" nSCF energy error gap;
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if not converged then
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loop (nSCF+1) ( (energy, commutator, gap) :: iterations) m_C
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loop (nSCF+1) ( (energy, error, gap) :: iterations) m_C diis
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else
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let iterations =
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List.rev ( (energy, commutator, gap) :: iterations )
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List.rev ( (energy, error, gap) :: iterations )
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|> Array.of_list
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in
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{ HartreeFock_type.
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@ -120,6 +146,7 @@ let make ?guess:(guess=`Hcore) ?max_scf:(max_scf=64)
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let m_H =
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match guess with
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| Guess.Hcore m_H -> m_H
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| Guess.Huckel m_H -> m_H
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in
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let m_Hmo =
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xt_o_x m_H m_X
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@ -131,7 +158,8 @@ let make ?guess:(guess=`Hcore) ?max_scf:(max_scf=64)
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gemm m_X m_C'
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in
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loop 1 [] m_C
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let diis = DIIS.make () in
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loop 1 [] m_C diis
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@ -12,7 +12,7 @@ type t = {
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cartesian : bool;
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}
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let make ?cartesian:(cartesian=true)
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let make ?cartesian:(cartesian=false)
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?multiplicity:(multiplicity=1)
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?charge:(charge=0)
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~nuclei
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60
Utils/DIIS.ml
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60
Utils/DIIS.ml
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open Lacaml.D
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open Util
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type t =
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{
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p : Vec.t list;
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e : Vec.t list;
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m : int;
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mmax : int;
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}
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let make ?mmax:(mmax=15) () =
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assert (mmax > 1);
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{
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p = [];
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e = [];
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m = 0 ;
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mmax;
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}
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let append ~p ~e diis =
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let update v l =
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if diis.m < diis.mmax then
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v :: l
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else
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match List.rev l with
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| [] -> assert false
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| _ :: rest -> v :: List.rev rest
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in
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{ diis with
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p = update p diis.p;
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e = update e diis.e;
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m = min diis.mmax (diis.m+1);
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}
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let next diis =
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let e = Mat.of_col_vecs_list diis.e
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and p = Mat.of_col_vecs_list diis.p
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in
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let a =
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let rec aux m =
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let a = Mat.make (m+1) (m+1) 1. in
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a.{m+1,m+1} <- 0.;
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ignore @@ lacpy ~b:a (gemm ~transa:`T ~m ~n:m e e);
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if sycon (lacpy a) > 1.e-10 then a
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else aux (m-1)
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in
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aux diis.m
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in
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let m = Mat.dim1 a - 1 in
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let c = Mat.make0 (m+1) 1 in
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c.{m+1,1} <- 1.;
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sysv a c;
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gemm p c ~k:m
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|> Mat.as_vec
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@ -29,13 +29,13 @@ Equating zero to the derivatives of {% $\mathcal{L}$ %} with respect to {% $c_i$
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{% \begin{equation*}
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\begin{bmatrix}
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B_{11} & B_{12} & B_{13} & ... & B_{1m} & -1 \\
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B_{21} & B_{22} & B_{23} & ... & B_{2m} & -1 \\
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B_{31} & B_{32} & B_{33} & ... & B_{3m} & -1 \\
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B_{11} & B_{12} & B_{13} & ... & B_{1m} & 1 \\
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B_{21} & B_{22} & B_{23} & ... & B_{2m} & 1 \\
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B_{31} & B_{32} & B_{33} & ... & B_{3m} & 1 \\
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\vdots & \vdots & \vdots & \vdots & \ddots & \vdots \\
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B_{m1} & B_{m2} & B_{m3} & ... & B_{mm} & -1 \\
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B_{m1} & B_{m2} & B_{m3} & ... & B_{mm} & 1 \\
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1 & 1 & 1 & ... & 1 & 0
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\end{bmatrix} \begin{bmatrix} c_1 \\ c_2 \\ c_3 \\ \vdots \\ c_m \\ \lambda \end{bmatrix}=
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\end{bmatrix} \begin{bmatrix} c_1 \\ c_2 \\ c_3 \\ \vdots \\ c_m \\ -\lambda \end{bmatrix}=
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\begin{bmatrix} 0 \\ 0 \\ 0 \\ \vdots \\ 0 \\ 1 \end{bmatrix}
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\end{equation*}
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@ -50,10 +50,10 @@ $$ %}
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type t
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val make : unit -> t
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(** Initialize DIIS *)
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val make : ?mmax:int -> unit -> t
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(** Initialize DIIS with a maximum size.*)
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val append : p:Lacaml.D.Vec.t -> e:Lacaml.D.Vec.t -> t
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val append : p:Lacaml.D.Vec.t -> e:Lacaml.D.Vec.t -> t -> t
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(** Append a parameter vector [p] and the corresponding error vector [e]. *)
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val next : t -> Lacaml.D.Vec.t
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@ -171,9 +171,8 @@ let array_product a =
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let diagonalize_symm m_H =
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let m_V = lacpy m_H in
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let m_W = Vec.create (Mat.dim1 m_H) in
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let result =
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syevd ~vectors:true ~w:m_W m_V
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syevd ~vectors:true m_V
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in
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m_V, result
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@ -200,8 +199,32 @@ let canonical_ortho ?thresh:(thresh=1.e-6) ~overlap c =
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gemm c u
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let string_of_matrix m =
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let open Lacaml.Io in
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let rows = Mat.dim1 m
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and cols = Mat.dim2 m
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in
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let rec aux accu first last =
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if (first > last) then String.concat "\n" (List.rev accu)
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else
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let nw =
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Format.asprintf "\n\n %a\n" (Lacaml.Io.pp_lfmat
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~row_labels:
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(Array.init rows (fun i -> Printf.sprintf "%d " (i + 1)))
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~col_labels:
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(Array.init (min 5 (cols-first+1)) (fun i -> Printf.sprintf "-- %d --" (i + first) ))
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~print_right:false
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~print_foot:false
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() ) (lacpy ~ac:first ~n:(min 5 (cols-first+1)) m)
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in
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aux (nw :: accu) (first+5) last
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in
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aux [] 1 cols
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let debug_matrix name a =
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Format.printf "@[<2>%s =@\n@\n@[%a@]@]@\n@\n" name pp_mat a
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Printf.printf "%s =\n%s\n" name (string_of_matrix a)
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