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 components of all the right singular vectors of
the original bidiagonal 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
only.
ICOMPQ = 1 Compute singular vector
matrices in factored form also. K (input)
INTEGER The number of terms in the rational func
tion 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.
sion(K)
On entry, VF contains information passed through
SBEDE8.f On exit, VF contains the first K compo
nents of the first components of all right singu
lar vectors of the bidiagonal matrix.
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 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 (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
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