dlasd9(3)

NAME

DLASD9 - find the square roots of the roots of the secular

equation,

SYNOPSIS

SUBROUTINE  DLASD9(  ICOMPQ,  LDU,  K, D, Z, VF, VL, DIFL,
DIFR, DSIGMA, WORK, INFO )
    INTEGER        ICOMPQ, INFO, K, LDU
    DOUBLE         PRECISION D( * ), DIFL( * ), DIFR( LDU,
* ), DSIGMA( * ), VF( * ), VL( * ), WORK( * ), Z( * )

PURPOSE

DLASD9 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 compo

nents of all the right singular vectors of the original bidiago

nal matrix.

DLASD9 is called from DLASD7.

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 DLASD4. K >=

1.

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

D(I) contains the updated singular values.

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.

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, dimen

sion(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) DOUBLE PRECISION array, dimen

sion(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) DOUBLE PRECISION array, dimension (K).

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

DIFR (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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

DLASD9(3)