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mirror of https://gitlab.com/scemama/QCaml.git synced 2024-12-30 16:15:40 +01:00

Documentation

This commit is contained in:
Anthony Scemama 2018-05-30 09:19:49 +02:00
parent 45d0c546ad
commit 25b3c41c50
5 changed files with 70 additions and 61 deletions

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@ -1,10 +1,7 @@
open Util
open Lacaml.D
type t =
| Lowdin of Mat.t
| Canonical of Mat.t
| Svd of Mat.t
type t = Mat.t
module Am = AngularMomentum
module Bs = Basis
@ -12,38 +9,34 @@ module Cs = ContractedShell
let make_canonical_spherical ~thresh ~overlap basis =
let ao_num = Bs.size basis in
let cart_sphe = Mat.make ao_num ao_num 0.
and i = ref 0
and n = ref 0 in
Array.iter (fun shell ->
let submatrix =
SphericalToCartesian.matrix (Cs.ang_mom shell)
in
ignore @@ lacpy ~b:cart_sphe ~br:(!i+1) ~bc:(!n+1) submatrix;
i := !i + Mat.dim1 submatrix;
n := !n + Mat.dim2 submatrix;
) (Bs.contracted_shells basis);
let s = gemm ~transa:`T ~m:!n cart_sphe overlap in
let overlap = gemm s ~n:!n cart_sphe in
let s = canonical_ortho ~thresh ~overlap (Mat.identity !n) in
gemm cart_sphe ~k:!n s
let make_canonical ~thresh ~basis ~cartesian ~overlap =
let make_canonical ~cartesian ~thresh ~basis ~overlap =
let result =
if cartesian then
canonical_ortho ~thresh ~overlap (Mat.identity @@ Mat.dim1 overlap)
else
match basis with
| None -> invalid_arg
"Basis.t is required when cartesian=false in make_canonical"
| Some basis ->
make_canonical_spherical ~thresh ~overlap basis
let make_canonical_spherical basis =
let ao_num = Bs.size basis in
let cart_sphe = Mat.make ao_num ao_num 0.
and i = ref 0
and n = ref 0 in
Array.iter (fun shell ->
let submatrix =
SphericalToCartesian.matrix (Cs.ang_mom shell)
in
ignore @@ lacpy ~b:cart_sphe ~br:(!i+1) ~bc:(!n+1) submatrix;
i := !i + Mat.dim1 submatrix;
n := !n + Mat.dim2 submatrix;
) (Bs.contracted_shells basis);
let s = gemm ~transa:`T ~m:!n cart_sphe overlap in
let overlap = gemm s ~n:!n cart_sphe in
let s = canonical_ortho ~thresh ~overlap (Mat.identity !n) in
gemm cart_sphe ~k:!n s
in
Canonical result
if cartesian then
canonical_ortho ~thresh ~overlap (Mat.identity @@ Mat.dim1 overlap)
else
match basis with
| None -> invalid_arg
"Basis.t is required when cartesian=false in make_canonical"
| Some basis -> make_canonical_spherical basis
@ -59,16 +52,12 @@ let make_lowdin ~thresh ~overlap =
let u_vec' =
Mat.init_cols (Mat.dim1 u_vec) (Mat.dim2 u_vec) (fun i j -> u_vec.{i,j} *. u_val.{j})
in
let result =
gemm u_vec' ~transb:`T u_vec
in
Lowdin result
gemm u_vec' ~transb:`T u_vec
let make ~cartesian ?(thresh=1.e-12) ?basis overlap =
let make ?(thresh=1.e-12) ?basis ~cartesian overlap =
(*
make_lowdin ~thresh ~overlap
*)
make_canonical ~cartesian ~basis ~thresh ~overlap
make_canonical ~thresh ~basis ~cartesian ~overlap

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@ -0,0 +1,12 @@
(** Orthonormalization of the basis. *)
type t = Lacaml.D.Mat.t
val make: ?thresh:float -> ?basis:Basis.t -> cartesian:bool -> Overlap.t -> t
(** Returns a matrix or orthonormal vectors in the basis. The vectors are
linearly independent up to a threshold [thresh]. If [cartesian] is
[false], the [basis] argument needs to be given and the space spanned by
the vectors is the same as the space spanned by the basis in spherical
coordinates (5d,7f,...).
*)

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@ -17,10 +17,7 @@ let make ?guess:(guess=`Hcore) ?max_scf:(max_scf=64)
(* Orthogonalization matrix *)
let m_X =
match Lazy.force simulation.overlap_ortho with
| Lowdin x -> x
| Canonical x -> x
| Svd x -> x
Lazy.force simulation.overlap_ortho
in

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@ -169,13 +169,13 @@ let array_product a =
Array.fold_left ( *. ) 0. a
let diagonalize_symm h =
let v = lacpy h in
let w = Vec.create (Mat.dim1 h) in
let diagonalize_symm m_H =
let m_V = lacpy m_H in
let m_W = Vec.create (Mat.dim1 m_H) in
let result =
syevd ~vectors:true ~w v
syevd ~vectors:true ~w:m_W m_V
in
v, result
m_V, result
let xt_o_x ~o ~x =
gemm o x
@ -184,16 +184,19 @@ let xt_o_x ~o ~x =
let canonical_ortho ?thresh:(thresh=1.e-6) ~overlap c =
let d, u, _ = gesvd (lacpy overlap) in
let d0 = Vec.sqrt d in
let n = Vec.fold (fun accu x -> if x > thresh then accu + 1 else accu) 0 d in
let d = Vec.map (fun x ->
if x >= thresh then 1. /. x
else 0. ) ~y:d d0
let d_sqrt = Vec.sqrt d in
let n = (* Number of non-negligible singular vectors *)
Vec.fold (fun accu x -> if x > thresh then accu + 1 else accu) 0 d
in
if n < Vec.dim d0 then
let d_inv_sq = (* D^{-1/2} *)
Vec.map (fun x ->
if x >= thresh then 1. /. x
else 0. ) ~y:d d_sqrt
in
if n < Vec.dim d_sqrt then
Printf.printf "Removed linear dependencies below %f\n" (1. /. d.{n})
;
Mat.scal_cols u d ;
Mat.scal_cols u d_inv_sq ;
gemm c u

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@ -67,11 +67,19 @@ val diagonalize_symm : Lacaml.D.mat -> Lacaml.D.mat * Lacaml.D.vec
(** Diagonalize a symmetric matrix. Returns the eigenvectors and the eigenvalues. *)
val xt_o_x : o:Lacaml.D.mat -> x:Lacaml.D.mat -> Lacaml.D.mat
(** Computes X{^T}.O.X *)
(** Computes {% $\mathbf{X^\dag\, O\, X}$ %} *)
val canonical_ortho: ?thresh:float -> overlap:Lacaml.D.mat -> Lacaml.D.mat -> Lacaml.D.mat
(** Canonical orthogonalization. [overlap] is the overlap matrix, and the last argument
contains the vectors to orthogonalize. *)
(** Canonical orthogonalization. [overlap] is the overlap matrix {% $\mathbf{S}$ %},
and the last argument contains the vectors {% $\mathbf{C}$ %} to orthogonalize.
{%
\begin{align}
\mathbf{U\, D\, V^\dag} & = \mathbf{S} \\
\mathbf{C_\bot} & = \mathbf{C\, U\, D^{-1/2}}
\end{align}
%}
*)
val debug_matrix: string -> Lacaml.D.mat -> unit
(** Prints a matrix in stdout for debug *)