
dlasda.f(3) LAPACK dlasda.f(3)
NAME
dlasda.f 
SYNOPSIS
Functions/Subroutines
subroutine dlasda (ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES,
GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO)
DLASDA 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 dlasda (integerICOMPQ, integerSMLSIZ, integerN, integerSQRE, double precision,
dimension( * )D, double precision, dimension( * )E, double precision, dimension( ldu, *
)U, integerLDU, double precision, dimension( ldu, * )VT, integer, dimension( * )K, double
precision, dimension( ldu, * )DIFL, double precision, dimension( ldu, * )DIFR, double
precision, dimension( ldu, * )Z, double precision, dimension( ldu, * )POLES, integer,
dimension( * )GIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL, integer,
dimension( ldgcol, * )PERM, double precision, dimension( ldu, * )GIVNUM, double precision,
dimension( * )C, double precision, dimension( * )S, double precision, dimension( * )WORK,
integer, dimension( * )IWORK, integerINFO)
DLASDA 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, DLASDA 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, DLASD0, 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.
SMLSIZ
SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.
N
N is INTEGER
The row dimension of the upper bidiagonal matrix. This is
also the dimension of the main diagonal array D.
SQRE
SQRE 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.
D
D is 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
E is DOUBLE PRECISION array, dimension ( M1 )
Contains the subdiagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.
U
U is DOUBLE PRECISION 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.
LDU
LDU is INTEGER, LDU = > N.
The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
GIVNUM, and Z.
VT
VT is DOUBLE PRECISION 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.
K
K 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.
DIFL
DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ),
where NLVL = floor(log_2 (N/SMLSIZ))).
DIFR
DIFR is DOUBLE PRECISION 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 DLASD8 for details.
Z
Z is DOUBLE PRECISION 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.
POLES
POLES is DOUBLE PRECISION 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.
GIVPTR
GIVPTR 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.
GIVCOL
GIVCOL 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.
LDGCOL
LDGCOL is INTEGER, LDGCOL = > N.
The leading dimension of arrays GIVCOL and PERM.
PERM
PERM 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.
GIVNUM
GIVNUM is DOUBLE PRECISION 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.
C
C is DOUBLE PRECISION 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.
S
S is DOUBLE PRECISION 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.
WORK
WORK is DOUBLE PRECISION array, dimension
(6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).
IWORK
IWORK is INTEGER array.
Dimension must be at least (7 * N).
INFO
INFO 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 273 of file dlasda.f.
Author
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Version 3.4.2 Tue Sep 25 2012 dlasda.f(3) 
