slasd8(3)

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 ma

trix.

SLASD8 is called from SLASD6.

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 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 ma

trix.

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 ma

trix.

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 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) 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 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

SLASD8(3)