2. EL 6 ELS
  3. lapack
  4. dlasd8(l)

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DLASD8(1) LAPACK auxiliary routine (version 3.2) DLASD8(1)

NAME

DLASD8 - finds the square roots of the roots of the secular equation,

SYNOPSIS

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 singular vectors of the original bidiagonal matrix. DLASD8 is called from DLASD6.

ARGUMENTS

Specifies whether singular vectors are to be computed in factored form in the calling routine:
= 0: Compute singular values only.
= 1: Compute singular vectors in factored form as well.
The number of terms in the rational function to be solved by DLASD4. K >= 1.
On output, D contains the updated singular values.
On entry, the first K elements of this array contain the components of the deflation-adjusted updating row vector. On exit, Z is updated.
On entry, VF contains information passed through DBEDE8. On exit, VF contains the first K components of the first components of all right singular vectors of the bidiagonal matrix.
On entry, VL contains information passed through DBEDE8. On exit, VL contains the first K components of the last components of all right singular vectors of the bidiagonal matrix.
On exit, DIFL(I) = D(I) - DSIGMA(I).
dimension ( LDDIFR, 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.
The leading dimension of DIFR, must be at least K.
On entry, the first K elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation. On exit, the elements of DSIGMA may be very slightly altered in value.
= 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

November 2008 LAPACK auxiliary routine (version 3.2)