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 singu
lar vectors of the original bidiagonal matrix.
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 compo
nents of the first components of all right singu
lar vectors of the bidiagonal matrix.
K )
On entry, VL contains information passed through
DBEDE8. On exit, VL contains the first K compo
nents 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 dimen
sion ( 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) 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
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