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QCaml/linear_algebra/lib/orthonormalization.ml

30 lines
721 B
OCaml

let canonical_ortho ?thresh:(thresh=1.e-6) ~overlap c =
let u, d, _ = Matrix.svd overlap in
let d_sqrt = Vector.sqrt d in
let n = (* Number of non-negligible singular vectors *)
Vector.fold (fun accu x -> if x > thresh then accu + 1 else accu) 0 d
in
let d_inv_sq = (* D^{-1/2} *)
Vector.map (fun x ->
if x >= thresh then 1. /. x
else 0. ) d_sqrt
in
let dx = Vector.to_bigarray_inplace d in
if n < Vector.dim d_sqrt then
Printf.printf "Removed linear dependencies below %f\n" (1. /. dx.{n})
;
Matrix.scale_cols_inplace u d_inv_sq ;
Matrix.gemm_nn u c
let qr_ortho m =
(* Performed twice for precision *)
let q, _ = Matrix.qr m in
let q, _ = Matrix.qr q in
q