dlasd8(3)

NAME

DLASD8 - find the square roots of the roots of the secular

equation,

SYNOPSIS

SUBROUTINE  DLASD8(  ICOMPQ,  K, D, Z, VF, VL, DIFL, DIFR,
LDDIFR, DSIGMA, WORK, INFO )
    INTEGER        ICOMPQ, INFO, K, LDDIFR
    DOUBLE         PRECISION D( * ), DIFL( * ), DIFR(  LDDIFR, * ), DSIGMA( * ), VF( * ), VL( * ), WORK( * ), Z( * )

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 ma

trix.

DLASD8 is called from DLASD6.

ARGUMENTS

ICOMPQ (input) INTEGER

Specifies whether singular vectors are to be com

puted 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 DLASD4. K >= 1.

D (output) DOUBLE PRECISION array, dimension ( K )

On output, D contains the updated singular values.

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

DBEDE8. On exit, VF contains the first K components of the first

components of all right singular vectors of the bidiagonal ma

trix.

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 ma

trix.

DIFL (output) DOUBLE PRECISION array, dimension ( K )

On exit, DIFL(I) = D(I) - DSIGMA(I).

DIFR (output) DOUBLE PRECISION array,

dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and dimen

sion ( K ) if ICOMPQ = 0. On exit, DIFR(I,1) = D(I) - DSIG

MA(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 (input) INTEGER

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

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.

WORK (workspace) DOUBLE PRECISION array, dimension at

least 3 * K

INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an ille

gal value.
> 0: if INFO = 1, an singular value did not con

verge

FURTHER DETAILS

Based on contributions by

Ming Gu and Huan Ren, Computer Science Division, Uni

versity of
California at Berkeley, USA

LAPACK version 3.0 15 June 2000

DLASD8(3)