.TH DLASD0 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) "
.SH NAME
DLASD0 - divide and conquer approach, DLASD0 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
.SH SYNOPSIS
.TP 19
SUBROUTINE DLASD0(
N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
WORK, INFO )
.TP 19
.ti +4
INTEGER
INFO, LDU, LDVT, N, SMLSIZ, SQRE
.TP 19
.ti +4
INTEGER
IWORK( * )
.TP 19
.ti +4
DOUBLE
PRECISION D( * ), E( * ), U( LDU, * ), VT( LDVT, * ),
WORK( * )
.SH PURPOSE
Using a divide and conquer approach, DLASD0 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, DLASDA, computes only the singular values,
and optionally, the singular vectors in compact form.
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.SH ARGUMENTS
.TP 7
N (input) INTEGER
On entry, the row dimension of the upper bidiagonal matrix.
This is also the dimension of the main diagonal array D.
.TP 7
SQRE (input) INTEGER
Specifies the column dimension of the bidiagonal matrix.
= 0: The bidiagonal matrix has column dimension M = N;
.br
= 1: The bidiagonal matrix has column dimension M = N+1;
.TP 7
D (input/output) DOUBLE PRECISION array, dimension (N)
On entry D contains the main diagonal of the bidiagonal
matrix.
On exit D, if INFO = 0, contains its singular values.
.TP 7
E (input) DOUBLE PRECISION array, dimension (M-1)
Contains the subdiagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.
.TP 7
U (output) DOUBLE PRECISION array, dimension at least (LDQ, N)
On exit, U contains the left singular vectors.
.TP 7
LDU (input) INTEGER
On entry, leading dimension of U.
.TP 7
VT (output) DOUBLE PRECISION array, dimension at least (LDVT, M)
On exit, VT\(aq contains the right singular vectors.
.TP 7
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.
.TP 7
IWORK (workspace) INTEGER work array.
Dimension must be at least (8 * N)
.TP 7
WORK (workspace) DOUBLE PRECISION work array.
Dimension must be at least (3 * M**2 + 2 * M)
.TP 7
INFO (output) INTEGER
= 0: successful exit.
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< 0: if INFO = -i, the i-th argument had an illegal value.
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> 0: if INFO = 1, an singular value did not converge
.SH FURTHER DETAILS
Based on contributions by
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Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA
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