DLASD9(3S)DLASD9(3S)NAME
DLASD9 - find the square roots of the roots of the secular equation,
SYNOPSIS
SUBROUTINE DLASD9( ICOMPQ, LDU, K, D, Z, VF, VL, DIFL, DIFR, DSIGMA,
WORK, INFO )
INTEGER ICOMPQ, INFO, K, LDU
DOUBLE PRECISION D( * ), DIFL( * ), DIFR( LDU, * ), DSIGMA( *
), VF( * ), VL( * ), WORK( * ), Z( * )
IMPLEMENTATION
These routines are part of the SCSL Scientific Library and can be loaded
using either the -lscs or the -lscs_mp option. The -lscs_mp option
directs the linker to use the multi-processor version of the library.
When linking to SCSL with -lscs or -lscs_mp, the default integer size is
4 bytes (32 bits). Another version of SCSL is available in which integers
are 8 bytes (64 bits). This version allows the user access to larger
memory sizes and helps when porting legacy Cray codes. It can be loaded
by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
only one of the two versions; 4-byte integer and 8-byte integer library
calls cannot be mixed.
PURPOSE
DLASD9 finds the square roots of the roots of the secular equation, as
defined by the values in DSIGMA and Z. It makes the
appropriate calls to DLASD4, and stores, for each element in D, the
distance to its two nearest poles (elements in DSIGMA). It also updates
the arrays VF and VL, the first and last components of all the right
singular vectors of the original bidiagonal matrix.
DLASD9 is called from DLASD7.
ARGUMENTS
ICOMPQ (input) INTEGER
Specifies whether singular vectors are to be computed in factored
form in the calling routine:
ICOMPQ = 0 Compute singular values only.
ICOMPQ = 1 Compute singular vector matrices in
factored form also.
K (input) INTEGER
The number of terms in the rational function to be solved by
DLASD4. K >= 1.
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DLASD9(3S)DLASD9(3S)
D (output) DOUBLE PRECISION array, dimension(K)D(I) contains the updated singular values.
DSIGMA (input) DOUBLE PRECISION array, dimension(K)
The first K elements of this array contain the old roots of the
deflated updating problem. These are the poles of the secular
equation.
Z (input) DOUBLE PRECISION array, dimension (K)
The first K elements of this array contain the components of the
deflation-adjusted updating row vector.
VF (input/output) DOUBLE PRECISION array, dimension(K)
On entry, VF contains information passed through SBEDE8.f On
exit, VF contains the first K components of the first components
of all right singular vectors of the bidiagonal matrix.
VL (input/output) DOUBLE PRECISION array, dimension(K)
On entry, VL contains information passed through SBEDE8.f On
exit, VL contains the first K components of the last components
of all right singular vectors of the bidiagonal matrix.
DIFL (output) DOUBLE PRECISION array, dimension (K).
On exit, DIFL(I) = D(I) - DSIGMA(I).
DIFR (output) DOUBLE PRECISION array,
dimension (LDU, 2) if ICOMPQ =1 and dimension (K) if ICOMPQ = 0.
On exit, DIFR(I, 1) = D(I) - DSIGMA(I+1), DIFR(K, 1) is not
defined and will not be referenced.
If ICOMPQ = 1, DIFR(1:K, 2) is an array containing the
normalizing factors for the right singular vector matrix.
LDU (input) INTEGER
The leading dimension of DIFR if ICOMPQ = 1. LDU >= 1.
WORK (workspace) DOUBLE PRECISION array,
dimension at least (3 * K) Workspace.
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
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DLASD9(3S)DLASD9(3S)SEE ALSOINTRO_LAPACK(3S), INTRO_SCSL(3S)
This man page is available only online.
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