dlasd0 (l) - Linux Manuals

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

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, VTaq 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

Pages related to dlasd0

  • dlasd0 (3)
  • dlasd1 (l) - computes the SVD of an upper bidiagonal N-by-M matrix B,
  • dlasd2 (l) - merges the two sets of singular values together into a single sorted set
  • dlasd3 (l) - finds all the square roots of the roots of the secular equation, as defined by the values in D and Z
  • dlasd4 (l) - subroutine compute the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i < j and that RHO > 0
  • dlasd5 (l) - subroutine compute the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) * diag( D ) + RHO The diagonal entries in the array D are assumed to satisfy 0 <= D(i) < D(j) for i < j
  • dlasd6 (l) - computes the SVD of an updated upper bidiagonal matrix B obtained by merging two smaller ones by appending a row
  • dlasd7 (l) - merges the two sets of singular values together into a single sorted set
  • dlasd8 (l) - finds the square roots of the roots of the secular equation,
  • dlasd9 (l) - find the square roots of the roots of the secular equation,
  • dlasda (l) - a divide and conquer approach, DLASDA 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