dlasda.f man page

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 off-diagonal 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 off-diagonal e. Used by sbdsdc.

Purpose:

Using 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. 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 ( M-1 )
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 I-th
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 I-th
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 deflation-adjusted updating row vector for subproblems
on the I-th 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 I-th 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 I-th
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 I-th 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 I-th 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 I-th 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 I-th subproblem is not square, on exit,
C( I ) contains the C-value of a Givens rotation related to
the right null space of the I-th subproblem.

S

 S is DOUBLE PRECISION array, dimension ( N ) if
ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
and the I-th subproblem is not square, on exit, S( I )
contains the S-value of a Givens rotation related to
the right null space of the I-th 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 i-th 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

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

dlasda(3) is an alias of dlasda.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK