NAME¶

DLASD0 - 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

SYNOPSIS¶

SUBROUTINE DLASD0(

N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, WORK, INFO )

INTEGER INFO, LDU, LDVT, N, SMLSIZ, SQRE INTEGER IWORK( * ) DOUBLE PRECISION D( * ), E( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

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.

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) 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.

E (input) DOUBLE PRECISION array, dimension (M-1)

Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed.

U (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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 (workspace) INTEGER work array.

Dimension must be at least (8 * N)

WORK (workspace) DOUBLE PRECISION 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 illegal value.
> 0: if INFO = 1, an singular value did not converge

FURTHER DETAILS¶

Based on contributions by
Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA