slasda.f (3)  Linux Manuals
NAME
slasda.f 
SYNOPSIS
Functions/Subroutines
subroutine slasda (ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO)
SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and offdiagonal e. Used by sbdsdc.
Function/Subroutine Documentation
subroutine slasda (integerICOMPQ, integerSMLSIZ, integerN, integerSQRE, real, dimension( * )D, real, dimension( * )E, real, dimension( ldu, * )U, integerLDU, real, dimension( ldu, * )VT, integer, dimension( * )K, real, dimension( ldu, * )DIFL, real, dimension( ldu, * )DIFR, real, dimension( ldu, * )Z, real, dimension( ldu, * )POLES, integer, dimension( * )GIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL, integer, dimension( ldgcol, * )PERM, real, dimension( ldu, * )GIVNUM, real, dimension( * )C, real, dimension( * )S, real, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)
SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal matrix with diagonal d and offdiagonal e. Used by sbdsdc.
Purpose:

Using a divide and conquer approach, SLASDA computes the singular value decomposition (SVD) of a real upper bidiagonal NbyM matrix B with diagonal D and offdiagonal E, where M = N + SQRE. The algorithm computes the singular values in the SVD B = U * S * VT. The orthogonal matrices U and VT are optionally computed in compact form. A related subroutine, SLASD0, computes the singular values and the singular vectors in explicit form.
Parameters:

ICOMPQ
ICOMPQ is INTEGER Specifies whether singular vectors are to be computed in compact form, as follows = 0: Compute singular values only. = 1: Compute singular vectors of upper bidiagonal matrix in compact form.
SMLSIZSMLSIZ is INTEGER The maximum size of the subproblems at the bottom of the computation tree.
NN is INTEGER The row dimension of the upper bidiagonal matrix. This is also the dimension of the main diagonal array D.
SQRESQRE is 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.
DD is REAL array, dimension ( N ) On entry D contains the main diagonal of the bidiagonal matrix. On exit D, if INFO = 0, contains its singular values.
EE is REAL array, dimension ( M1 ) Contains the subdiagonal entries of the bidiagonal matrix. On exit, E has been destroyed.
UU is REAL array, dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left singular vector matrices of all subproblems at the bottom level.
LDULDU is INTEGER, LDU = > N. The leading dimension of arrays U, VT, DIFL, DIFR, POLES, GIVNUM, and Z.
VTVT is REAL array, dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right singular vector matrices of all subproblems at the bottom level.
KK is INTEGER array, dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1, on exit, K(I) is the dimension of the Ith secular equation on the computation tree.
DIFLDIFL is REAL array, dimension ( LDU, NLVL ), where NLVL = floor(log_2 (N/SMLSIZ))).
DIFRDIFR is REAL array, dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and dimension ( N ) if ICOMPQ = 0. If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I  1) record distances between singular values on the Ith level and singular values on the (I 1)th level, and DIFR(1:N, 2 * I ) contains the normalizing factors for the right singular vector matrix. See SLASD8 for details.
ZZ is REAL array, dimension ( LDU, NLVL ) if ICOMPQ = 1 and dimension ( N ) if ICOMPQ = 0. The first K elements of Z(1, I) contain the components of the deflationadjusted updating row vector for subproblems on the Ith level.
POLESPOLES is REAL array, dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I  1) and POLES(1, 2*I) contain the new and old singular values involved in the secular equations on the Ith level.
GIVPTRGIVPTR is INTEGER array, dimension ( N ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records the number of Givens rotations performed on the Ith problem on the computation tree.
GIVCOLGIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVCOL(1, 2 *I  1) and GIVCOL(1, 2 *I) record the locations of Givens rotations performed on the Ith level on the computation tree.
LDGCOLLDGCOL is INTEGER, LDGCOL = > N. The leading dimension of arrays GIVCOL and PERM.
PERMPERM is INTEGER array, dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records permutations done on the Ith level of the computation tree.
GIVNUMGIVNUM is REAL array, dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I, GIVNUM(1, 2 *I  1) and GIVNUM(1, 2 *I) record the C and S values of Givens rotations performed on the Ith level on the computation tree.
CC is REAL array, dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and the Ith subproblem is not square, on exit, C( I ) contains the Cvalue of a Givens rotation related to the right null space of the Ith subproblem.
SS is REAL array, dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and the Ith subproblem is not square, on exit, S( I ) contains the Svalue of a Givens rotation related to the right null space of the Ith subproblem.
WORKWORK is REAL array, dimension (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
IWORKIWORK is INTEGER array, dimension (7*N).
INFOINFO is INTEGER = 0: successful exit. < 0: if INFO = i, the ith argument had an illegal value. > 0: if INFO = 1, a singular value did not converge
Author:

Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
 September 2012
Contributors:
 Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA
Definition at line 272 of file slasda.f.
Author
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