SRC/dlasdq.f(3)

🎀 SRC/dlasdq.f 🎀

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✨ NAME ✨

SRC/dlasdq.f

🦋 SYNOPSIS 🦋

Functions/Subroutines

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

DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc.

💅 Function/Subroutine Documentation 💅

🌸 subroutine dlasdq 🌸

subroutine dlasdq (character uplo, integer sqre, integer n, integer ncvt,
     integer nru, integer ncc, double precision, dimension( * ) d, double
     precision, dimension( * ) e, double precision, dimension( ldvt, * ) vt,
     integer ldvt, double precision, dimension( ldu, * ) u, integer ldu,
     double precision, dimension( ldc, * ) c, integer ldc, double precision,
     dimension( * ) work, integer info)

DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e. Used by sbdsdc. 🫶

🎯 Purpose 🎯

okay so here's the tea: DLASDQ computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired. Letting B denote the input bidiagonal matrix, the algorithm computes orthogonal matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose of P). 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.

See by J. Demmel and W. Kahan, LAPACK Working Note #3, for a detailed description of the algorithm. 📝

🧚 Parameters 🧚

UPLO

UPLO is CHARACTER*1. On entry, UPLO specifies whether the input bidiagonal matrix is upper or lower bidiagonal, and whether it is square are not.

• UPLO = 'U' or 'u' — B is upper bidiagonal.
• UPLO = 'L' or 'l' — B is lower bidiagonal.

SQRE

SQRE is 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

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

NCVT

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

NRU

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

NCC

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

D

D is DOUBLE PRECISION array, dimension (N). On entry, D contains the diagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in ascending order. 🔥

E

E is DOUBLE PRECISION array. dimension is (N-1) if SQRE = 0 and N if SQRE = 1. On entry, the entries of E contain the offdiagonal entries of the bidiagonal matrix whose SVD is desired. 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

VT is DOUBLE PRECISION 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

LDVT is 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

U is DOUBLE PRECISION 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

LDU is 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

C is DOUBLE PRECISION array, dimension (LDC, NCC). On entry, contains an N-by-NCC matrix which on exit has been premultiplied by Q**T dimension N-by-NCC if SQRE = 0 and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0).

LDC

LDC is 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 nonzero, LDC must also be at least N.

WORK

WORK is DOUBLE PRECISION array, dimension (4*N). Workspace. Only referenced if one of NCVT, NRU, or NCC is nonzero, and if N is at least 2.

INFO

INFO is 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. 💀

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

💜 Contributors: 💜

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 209 of file dlasdq.f.

🖋️ Author 🖋️

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