slasd0(3)

NAME

SLASD0 - a divide and conquer approach, SLASD0 computes

the singular value decomposition (SVD) of a real upper bidiagonal

N-by-M matrix B with diagonal D and offdiagonal E, where M = N +

SQRE

SYNOPSIS

SUBROUTINE  SLASD0(  N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, WORK, INFO )
    INTEGER        INFO, LDU, LDVT, N, SMLSIZ, SQRE
    INTEGER        IWORK( * )
    REAL           D( * ), E( * ), U( LDU, * ), VT(  LDVT,
* ), WORK( * )

PURPOSE

Using a divide and conquer approach, SLASD0 computes the

singular value decomposition (SVD) of a real upper bidiagonal N

by-M matrix B with diagonal D and offdiagonal E, where M = N +

SQRE. The algorithm computes orthogonal matrices U and VT such

that B = U * S * VT. The singular values S are overwritten on D.

A related subroutine, SLASDA, computes only the singular

values, and optionally, the singular vectors in compact form.

ARGUMENTS

N (input) INTEGER

On entry, the row dimension of the upper bidiagonal

matrix. This is also the dimension of the main diagonal array D.

SQRE (input) INTEGER

Specifies the column dimension of the bidiagonal

matrix. = 0: The bidiagonal matrix has column dimension M = N;
= 1: The bidiagonal matrix has column dimension M =

N+1;

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

On entry D contains the main diagonal of the bidi

agonal matrix. On exit D, if INFO = 0, contains its singular

values.

E (input) REAL array, dimension (M-1)

Contains the subdiagonal entries of the bidiagonal

matrix. On exit, E has been destroyed.

U (output) REAL array, dimension at least (LDQ, N)

On exit, U contains the left singular vectors.

LDU (input) INTEGER

On entry, leading dimension of U.

VT (output) REAL array, dimension at least (LDVT, M)

On exit, VT' contains the right singular vectors.

LDVT (input) INTEGER

On entry, leading dimension of VT.

SMLSIZ (input) INTEGER On entry, maximum size of

the subproblems at the bottom of the computation tree.

IWORK INTEGER work array.

Dimension must be at least (8 * N)

WORK REAL work array.

Dimension must be at least (3 * M**2 + 2 * M)

INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille

gal value.
> 0: if INFO = 1, an singular value did not con

verge

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

SLASD0(3)