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 components of all the right singular vectors of
the original bidiagonal 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
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 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.
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) REAL array, dimension(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) 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
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