DLASD8(3) finds 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 matrix. DLASD8 is called from DLASD6.

## ARGUMENTS

ICOMPQ (input) 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 (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/output) 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 (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 matrix.
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 matrix.
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 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 (input) INTEGER
The leading dimension of DIFR, must be at least K.
DSIGMA (input/output) 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 (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 illegal value.
> 0: if INFO = 1, an singular value did not converge

## FURTHER DETAILS

Based on contributions by

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