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mirror of https://gitlab.com/scemama/QCaml.git synced 2024-12-23 04:43:32 +01:00

Added exponential of matrix

This commit is contained in:
Anthony Scemama 2020-12-17 19:52:09 +01:00
parent 3c27ec0c10
commit 4146264c2e
3 changed files with 61 additions and 17 deletions

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@ -1,5 +1,5 @@
let integrals_cutoff = 1.e-15 let epsilon = 2.e-15
let epsilon = 1.e-20 let integrals_cutoff = epsilon
(** Constants *) (** Constants *)
let pi = acos (-1.) let pi = acos (-1.)

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@ -1,4 +1,5 @@
open Lacaml.D open Lacaml.D
open Common
type ('a, 'b) t = Mat.t type ('a, 'b) t = Mat.t
@ -352,6 +353,16 @@ let scale_cols a v =
a' a'
let scale_rows_inplace v a =
let v' = Vector.to_bigarray_inplace v in
Mat.scal_rows v' a
let scale_rows v a =
let a' = copy a in
let v' = Vector.to_bigarray_inplace v in
Mat.scal_rows v' a' ;
a'
let svd a = let svd a =
let d, u, vt = let d, u, vt =
gesvd (lacpy a) gesvd (lacpy a)
@ -382,24 +393,48 @@ let qr a =
q, r q, r
let exponential a = let exponential_iterative a =
assert (dim1 a = dim2 a); assert (dim1 a = dim2 a);
let a = to_bigarray_inplace a in let rec loop result accu n =
let n = Mat.dim1 a in let b = scale (1./.n) a in
let a2 = Lacaml.D.gemm a a in let new_accu = gemm accu b in
let (lv, wr, _wi, rv) = Lacaml.D.geev a2 in let residual =
let tau = Vec.map (fun x -> -. sqrt x) wr in sub new_accu accu
let cos_tau = |> amax
Mat.init_cols n n (fun i j -> |> abs_float
if i<>j then 0. else cos tau.{i})
in in
let sin_tau = let result = add result new_accu in
Mat.init_cols n n (fun i j -> if residual > Constants.epsilon then
if i<>j then 0. else (sin tau.{i}) /. tau.{i}) loop result new_accu (n+.1.)
else
result
in in
let g = Lacaml.D.gemm in let id = identity (dim1 a) in
Mat.add (g lv @@ g cos_tau rv) (g lv @@ g sin_tau @@ g rv a) loop id id 1.
|> of_bigarray_inplace
let exponential a =
let n = dim1 a in
assert (n = dim2 a);
let a2 = gemm a a in
let (u, w, vt) = svd a2 in
let tau = Vector.map (fun x -> -. sqrt x) w in
let cos_tau = Vector.cos tau in
let sin_tau_tau = Vector.mul (Vector.sin tau) (Vector.reci tau) in
let result =
add (gemm (scale_cols u cos_tau) vt) (gemm (scale_cols u sin_tau_tau) @@ gemm vt a)
in
(* Post-condition: Check if exp(-A) * exp(A) = I *)
let id = identity n in
let test =
gemm_tn ~beta:(-.1.0) ~c:id result result
|> amax
|> abs_float
in
assert (test < Constants.epsilon);
result
let to_file ~filename ?(sym=false) ?(cutoff=0.) t = let to_file ~filename ?(sym=false) ?(cutoff=0.) t =

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@ -171,6 +171,12 @@ val scale_cols: ('a,'b) t -> 'b Vector.t -> ('a,'b) t
val scale_cols_inplace: ('a,'b) t -> 'b Vector.t -> unit val scale_cols_inplace: ('a,'b) t -> 'b Vector.t -> unit
(** Multiplies the matrix by a constant *) (** Multiplies the matrix by a constant *)
val scale_rows: 'a Vector.t -> ('a,'b) t -> ('a,'b) t
(** Multiplies the matrix by a constant *)
val scale_rows_inplace: 'a Vector.t -> ('a,'b) t -> unit
(** Multiplies the matrix by a constant *)
val sycon: ('a,'b) t -> float val sycon: ('a,'b) t -> float
(** Returns the condition number of a matrix *) (** Returns the condition number of a matrix *)
@ -300,6 +306,9 @@ val diagonalize_symm : ('a,'a) t -> ('a,'a) t * 'a Vector.t
val exponential : ('a,'a) t -> ('a,'a) t val exponential : ('a,'a) t -> ('a,'a) t
(** Computes the exponential of a square matrix. *) (** Computes the exponential of a square matrix. *)
val exponential_iterative : ('a,'a) t -> ('a,'a) t
(** Computes the exponential of a square matrix with an iteratve algorithm. *)
val xt_o_x : o:('a,'a) t -> x:('a,'b) t -> ('b,'b) t val xt_o_x : o:('a,'a) t -> x:('a,'b) t -> ('b,'b) t
(** Computes {% $\mathbf{X^\dag\, O\, X}$ %} *) (** Computes {% $\mathbf{X^\dag\, O\, X}$ %} *)