DLASD9(l) ) DLASD9(l)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 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 computed in fac‐
tored form in the calling routine:
ICOMPQ = 0 Compute singular values only.
ICOMPQ = 1 Compute singular vector matrices in fac‐
tored 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, dimension(K)
On entry, VF contains information passed through SBEDE8.f On
exit, VF contains the first K components of the first compo‐
nents of all right singular vectors of the bidiagonal matrix.
VL (input/output) DOUBLE PRECISION array, dimension(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 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 normal‐
izing 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 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
LAPACK version 3.0 15 June 2000 DLASD9(l)
