SLASD8(l) ) SLASD8(l)NAME
SLASD8 - find the square roots of the roots of the secular equation,
SYNOPSIS
SUBROUTINE SLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA,
WORK, INFO )
INTEGER ICOMPQ, INFO, K, LDDIFR
REAL D( * ), DIFL( * ), DIFR( LDDIFR, * ), DSIGMA( * ),
VF( * ), VL( * ), WORK( * ), Z( * )
PURPOSE
SLASD8 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 SLASD4, 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.
SLASD8 is called from SLASD6.
ARGUMENTS
ICOMPQ (input) INTEGER
Specifies whether singular vectors are to be computed in fac‐
tored form in the calling routine:
= 0: Compute singular values only.
= 1: Compute singular vectors in factored form as well.
K (input) INTEGER
The number of terms in the rational function to be solved by
SLASD4. K >= 1.
D (output) REAL array, dimension ( K )
On output, D contains the updated singular values.
Z (input) REAL array, dimension ( K )
The first K elements of this array contain the components of
the deflation-adjusted updating row vector.
VF (input/output) REAL array, dimension ( K )
On entry, VF contains information passed through DBEDE8. On
exit, VF contains the first K components of the first compo‐
nents of all right singular vectors of the bidiagonal matrix.
VL (input/output) REAL array, dimension ( K )
On entry, VL contains information passed through DBEDE8. On
exit, VL contains the first K components of the last components
of all right singular vectors of the bidiagonal matrix.
DIFL (output) REAL array, dimension ( K )
On exit, DIFL(I) = D(I) - DSIGMA(I).
DIFR (output) REAL array,
dimension ( LDDIFR, 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 normaliz‐
ing factors for the right singular vector matrix.
LDDIFR (input) INTEGER
The leading dimension of DIFR, must be at least K.
DSIGMA (input) REAL 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.
WORK (workspace) REAL array, dimension at least 3 * K
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
LAPACK version 3.0 15 June 2000 SLASD8(l)
