slasdq(3)

NAME

SLASDQ - compute the singular value decomposition (SVD) of

a real (upper or lower) bidiagonal matrix with diagonal D and

offdiagonal E, accumulating the transformations if desired

SYNOPSIS

SUBROUTINE SLASDQ( UPLO, SQRE, N, NCVT, NRU,  NCC,  D,  E,
VT, LDVT, U, LDU, C, LDC, WORK, INFO )
    CHARACTER      UPLO
    INTEGER         INFO,  LDC,  LDU,  LDVT, N, NCC, NCVT,
NRU, SQRE
    REAL           C( LDC, * ), D( * ), E( * ), U( LDU,  *
), VT( LDVT, * ), WORK( * )

PURPOSE

SLASDQ 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. Let

ting B denote the input bidiagonal matrix, the algorithm computes

orthogonal matrices Q and P such that B = Q * S * P' (P' 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' * VT if desired.
The input matrix C is changed to Q' * C if desired.

See "Computing Small Singular Values of Bidiagonal Matri

ces With Guaranteed High Relative Accuracy," by J. Demmel and W.

Kahan, LAPACK Working Note #3, for a detailed description of the

algorithm.

ARGUMENTS

UPLO (input) CHARACTER*1

On entry, UPLO specifies whether the input bidiago

nal matrix is upper or lower bidiagonal, and wether it is square

are not. UPLO = 'U' or 'u' B is upper bidiagonal. UPLO = 'L'

or 'l' B is lower bidiagonal.

SQRE (input) 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 (input) INTEGER

On entry, N specifies the number of rows and columns

in the matrix. N must be at least 0.

NCVT (input) INTEGER

On entry, NCVT specifies the number of columns of

the matrix VT. NCVT must be at least 0.

NRU (input) INTEGER

On entry, NRU specifies the number of rows of the

matrix U. NRU must be at least 0.

NCC (input) INTEGER

On entry, NCC specifies the number of columns of the

matrix C. NCC must be at least 0.

D (input/output) REAL array, dimension (N)

On entry, D contains the diagonal entries of the

bidiagonal matrix whose SVD is desired. On normal exit, D con

tains the singular values in ascending order.

E (input/output) REAL 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 con

tain the diagonal and superdiagonal entries of a bidiagonal ma

trix orthogonally equivalent to the one given as input.

VT (input/output) REAL array, dimension (LDVT, NCVT)

On entry, contains a matrix which on exit has been

premultiplied by P', dimension N-by-NCVT if SQRE = 0 and

(N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).

LDVT (input) 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 (input/output) REAL 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 (input) 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 (input/output) REAL 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 (input) 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 (workspace) REAL array, dimension (4*N)

Workspace. Only referenced if one of NCVT, NRU, or

NCC is nonzero, and if N is at least 2.

INFO (output) 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 super

diagonals did not converge.

FURTHER DETAILS

Based on contributions by

Ming Gu and Huan Ren, Computer Science Division, Uni

versity of
California at Berkeley, USA

LAPACK version 3.0 15 June 2000

SLASDQ(3)