
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 val
ues in DSIGMA and Z. It makes the appropriate calls to SLASD4, and stores, for each ele
ment 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 factored 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 components 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 refer
enced.
If ICOMPQ = 1, DIFR(1:K,2) is an array containing the normalizing 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 ith 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) 
