.TH  DLASD8 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " 
.SH NAME
DLASD8 - the square roots of the roots of the secular equation,
.SH SYNOPSIS
.TP 19
SUBROUTINE DLASD8(
ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR,
DSIGMA, WORK, INFO )
.TP 19
.ti +4
INTEGER
ICOMPQ, INFO, K, LDDIFR
.TP 19
.ti +4
DOUBLE
PRECISION D( * ), DIFL( * ), DIFR( LDDIFR, * ),
DSIGMA( * ), VF( * ), VL( * ), WORK( * ),
Z( * )
.SH PURPOSE
DLASD8 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.

DLASD8 is called from DLASD6.
.br

.SH ARGUMENTS
.TP 8
ICOMPQ  (input) INTEGER
Specifies whether singular vectors are to be computed in
factored form in the calling routine:
.br
= 0: Compute singular values only.
.br
= 1: Compute singular vectors in factored form as well.
.TP 8
K       (input) INTEGER
The number of terms in the rational function to be solved
by DLASD4.  K >= 1.
.TP 8
D       (output) DOUBLE PRECISION array, dimension ( K )
On output, D contains the updated singular values.
.TP 8
Z       (input) DOUBLE PRECISION array, dimension ( K )
The first K elements of this array contain the components
of the deflation-adjusted updating row vector.
.TP 8
VF      (input/output) DOUBLE PRECISION 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.
.TP 8
VL      (input/output) DOUBLE PRECISION 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.
.TP 8
DIFL    (output) DOUBLE PRECISION array, dimension ( K )
On exit, DIFL(I) = D(I) - DSIGMA(I).
.TP 8
DIFR    (output) DOUBLE PRECISION 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
normalizing factors for the right singular vector matrix.
.TP 8
LDDIFR  (input) INTEGER
The leading dimension of DIFR, must be at least K.
.TP 8
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.
.TP 8
WORK    (workspace) DOUBLE PRECISION array, dimension at least 3 * K
.TP 8
INFO    (output) INTEGER
= 0:  successful exit.
.br
< 0:  if INFO = -i, the i-th argument had an illegal value.
.br
> 0:  if INFO = 1, an singular value did not converge
.SH FURTHER DETAILS
Based on contributions by
.br
   Ming Gu and Huan Ren, Computer Science Division, University of
   California at Berkeley, USA
.br

