# dlasd8.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlasd8.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlasd8 (ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA, WORK, INFO)
DLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc.

## Function/Subroutine Documentation

### subroutine dlasd8 (integer ICOMPQ, integer K, double precision, dimension( * ) D, double precision, dimension( * ) Z, double precision, dimension( * ) VF, double precision, dimension( * ) VL, double precision, dimension( * ) DIFL, double precision, dimension( lddifr, * ) DIFR, integer LDDIFR, double precision, dimension( * ) DSIGMA, double precision, dimension( * ) WORK, integer INFO)

DLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc.

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.

Parameters:

ICOMPQ

ICOMPQ is 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

K is INTEGER
The number of terms in the rational function to be solved
by DLASD4.  K >= 1.

D

D is DOUBLE PRECISION array, dimension ( K )
On output, D contains the updated singular values.

Z

Z is DOUBLE PRECISION array, dimension ( K )
On entry, the first K elements of this array contain the
components of the deflation-adjusted updating row vector.
On exit, Z is updated.

VF

VF is 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.

VL

VL is 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.

DIFL

DIFL is DOUBLE PRECISION array, dimension ( K )
On exit, DIFL(I) = D(I) - DSIGMA(I).

DIFR

DIFR is 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.

LDDIFR

LDDIFR is INTEGER
The leading dimension of DIFR, must be at least K.

DSIGMA

DSIGMA is DOUBLE PRECISION array, dimension ( K )
On entry, the first K elements of this array contain the old
roots of the deflated updating problem.  These are the poles
of the secular equation.
On exit, the elements of DSIGMA may be very slightly altered
in value.

WORK

WORK is DOUBLE PRECISION array, dimension (3*K)

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

NAG Ltd.

Date:

June 2017

Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Definition at line 168 of file dlasd8.f.

## Author

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