?lasdq

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?lasdq

Computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by ?bdsdc.

Syntax

call slasdq( uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info )

call dlasdq( uplo, sqre, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, work, info )

Include Files

mkl.fi

Description

The routine ?lasdq computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal d and off-diagonal e, accumulating the transformations if desired. If B is the input bidiagonal matrix, the algorithm computes orthogonal matrices Q and P such that B = Q*S*P^T. The singular values S are overwritten on d.

The input matrix U is changed to U*Q if desired.

The input matrix VT is changed to P^T*VT if desired.

The input matrix C is changed to Q^T*C if desired.

Input Parameters

uplo

CHARACTER*1. On entry, uplo specifies whether the input bidiagonal matrix is upper or lower bidiagonal.

If uplo = 'U' or 'u', B is upper bidiagonal;

If uplo = 'L' or 'l', B is lower bidiagonal.

sqre

INTEGER.

= 0: then the input matrix is n-by-n.

= 1: then the input matrix is n-by-(n+1) if uplu = 'U' and (n+1)-by-n if uplu

= 'L'. The bidiagonal matrix has n = nl + nr + 1 rows and m = n + sqre≥n columns.

n

INTEGER. On entry, n specifies the number of rows and columns in the matrix. n must be at least 0.

ncvt

INTEGER. On entry, ncvt specifies the number of columns of the matrix VT. ncvt must be at least 0.

nru

INTEGER. On entry, nru specifies the number of rows of the matrix U. nru must be at least 0.

ncc

INTEGER. On entry, ncc specifies the number of columns of the matrix C. ncc must be at least 0.

d

REAL for slasdq

DOUBLE PRECISION for dlasdq.

Array, DIMENSION (n). On entry, d contains the diagonal entries of the bidiagonal matrix.

e

REAL for slasdq

DOUBLE PRECISION for dlasdq.

Array, DIMENSION is (n-1) if sqre = 0 and n if sqre = 1. On entry, the entries of e contain the off-diagonal entries of the bidiagonal matrix.

vt

REAL for slasdq

DOUBLE PRECISION for dlasdq.

Array, DIMENSION (ldvt, ncvt). On entry, contains a matrix which on exit has been premultiplied by P^T, dimension n-by-ncvt if sqre = 0 and (n+1)-by-ncvt if sqre = 1 (not referenced if ncvt=0).

ldvt

INTEGER. On entry, ldvt specifies the leading dimension of vt as declared in the calling (sub) program. ldvt must be at least 1. If ncvt is nonzero, ldvt must also be at least n.

u

REAL for slasdq

DOUBLE PRECISION for dlasdq.

Array, DIMENSION (ldu, n). On entry, contains a matrix which on exit has been postmultiplied by Q, dimension nru-by-n if sqre = 0 and nru-by-(n+1) if sqre = 1 (not referenced if nru=0).

ldu

INTEGER. On entry, ldu specifies the leading dimension of u as declared in the calling (sub) program. ldu must be at least max(1, nru ) .

c

REAL for slasdq

DOUBLE PRECISION for dlasdq.

Array, DIMENSION (ldc, ncc). On entry, contains an n-by-ncc matrix which on exit has been premultiplied by Q', dimension n-by-ncc if sqre = 0 and (n+1)-by-ncc if sqre = 1 (not referenced if ncc=0).

ldc

INTEGER. On entry, ldc specifies the leading dimension of C as declared in the calling (sub) program. ldc must be at least 1. If ncc is non-zero, ldc must also be at least n.

work

REAL for slasdq

DOUBLE PRECISION for dlasdq.

Array, DIMENSION (4n). This is a workspace array. Only referenced if one of ncvt, nru, or ncc is nonzero, and if n is at least 2.

Output Parameters

d: On normal exit, d contains the singular values in ascending order.
e: On normal exit, e will contain 0. If the algorithm does not converge, d and e will contain the diagonal and superdiagonal entries of a bidiagonal matrix orthogonally equivalent to the one given as input.
vt: On exit, the matrix has been premultiplied by P'.
u: On exit, the matrix has been postmultiplied by Q.
c: On exit, the matrix has been premultiplied by Q'.
info: INTEGER. On exit, a value of 0 indicates a successful exit. If info < 0, argument number -info is illegal. If info > 0, the algorithm did not converge, and info specifies how many superdiagonals did not converge.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lasdq