
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 val
ues 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 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 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 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 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 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 ith 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) 
