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module DLRA
USE prec_const
implicit none
PUBLIC :: filter_singular_value_ky_pj, test_SVD
CONTAINS
SUBROUTINE filter_singular_value_ky_pj(nsv,array_ky_pj)
IMPLICIT NONE
! ARGUMENTS
INTEGER, INTENT(IN) :: nsv ! number of singular values to keep
COMPLEX(xp), DIMENSION(:,:), INTENT(INOUT) :: array_ky_pj ! Array to filter
!
! Singular value decomposition
! CALL SVD(array_ky_pj,singular_values)
END SUBROUTINE
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SUBROUTINE test_SVD
! Program to perform Singular Value Decomposition (SVD)
! using LAPACK library
! Specify the dimensions of the input matrix A
INTEGER, PARAMETER :: m = 3, n = 2
INTEGER, PARAMETER :: lda = m
! Declare the input matrix A
REAL, DIMENSION(lda,n) :: A
! Specify the dimensions of the output matrices
INTEGER, PARAMETER :: ldu = m, ldvt = n
INTEGER, PARAMETER :: lwork = 5*n
REAL, DIMENSION(ldu,m) :: U
REAL, DIMENSION(n) :: S
REAL, DIMENSION(ldvt,n) :: VT
REAL, DIMENSION(lwork) :: work
INTEGER :: info, i,j
! Define the input matrix A
A = RESHAPE((/ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 /), SHAPE(A))
WRITE(*,*) 'Input matrix A = '
DO i = 1, m
WRITE(*,'(2X, 3F8.3)') (A(i,j), j=1,n)
END DO
! Compute the SVD of A using the LAPACK subroutine SGESVD
CALL SGESVD('A', 'A', m, n, A, lda, S, U, ldu, VT, ldvt, work, lwork, info)
! Print the results
WRITE(*,*) 'U = '
DO i = 1, m
WRITE(*,'(6F8.3)') (U(i,j), j=1,m)
END DO
WRITE(*,*)
WRITE(*,*) 'S = '
WRITE(*,'(2F8.3)') (S(i), i=1,n)
WRITE(*,*)
WRITE(*,*) 'VT = '
DO i = 1, n
WRITE(*,'(6F8.3)') (VT(i,j), j=1,n)
END DO
! Reconstruct A from its SVD
A = MATMUL(U, MATMUL(diagmat(S,m,n), TRANSPOSE(VT)))
! Print the reconstructed matrix A
WRITE(*,*) 'Reconstructed matrix A = '
DO i = 1, m
WRITE(*,'(2X, 3F8.3)') (A(i,j), j=1,n)
END DO
print*, "this was a test of the SVD using LAPACK. End run."
stop
END SUBROUTINE test_SVD
FUNCTION diagmat(v, m, n) RESULT(A)
REAL, DIMENSION(:), INTENT(IN) :: v
INTEGER, INTENT(IN) :: m, n
REAL, DIMENSION(m,n) :: A
INTEGER :: i, j
A = 0.0 ! Initialize A to a zero matrix
DO i = 1, MIN(m,n)
A(i,i) = v(i) ! Set the diagonal elements of A to the values in v
END DO
END FUNCTION diagmat