slasd9(3)

NAME

SLASD9 - find the square roots of the roots of the secular

equation,

SYNOPSIS

SUBROUTINE  SLASD9(  ICOMPQ,  LDU,  K, D, Z, VF, VL, DIFL,
DIFR, DSIGMA, WORK, INFO )
    INTEGER        ICOMPQ, INFO, K, LDU
    REAL           D( * ), DIFL( *  ),  DIFR(  LDU,  *  ),
DSIGMA( * ), VF( * ), VL( * ), WORK( * ), Z( * )

PURPOSE

SLASD9 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 compo

nents of all the right singular vectors of the original bidiago

nal matrix.

SLASD9 is called from SLASD7.

ARGUMENTS

ICOMPQ (input) INTEGER

Specifies whether singular vectors are to be com

puted in factored form in the calling routine:

ICOMPQ = 0 Compute singular values on

ly.

ICOMPQ = 1 Compute singular vector ma

trices in factored form also. K (input) INTEGER The number

of terms in the rational function to be solved by SLASD4. K >=

1.

D (output) REAL array, dimension(K)

D(I) contains the updated singular values.

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.

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

SBEDE8.f 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

SBEDE8.f 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 (LDU, 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.

WORK (workspace) REAL array,

dimension at least (3 * K) Workspace.

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

SLASD9(3)