# ?lasd8

Finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by ?bdsdc.

## Syntax

call slasd8( icompq, k, d, z, vf, vl, difl, difr, lddifr, dsigma, work, info )

call dlasd8( icompq, k, d, z, vf, vl, difl, difr, lddifr, dsigma, work, info )

## Description

The routine ?lasd8 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 ?lasd4, 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. ?lasd8 is called from ?lasd6.

## Input Parameters

icompq

  INTEGER. 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.

k

  INTEGER. The number of terms in the rational function to be solved by ?lasd4. `k ≥ 1`.

z

  REAL for slasd8

  DOUBLE PRECISION for dlasd8.

  Array, DIMENSION ( k ).

  The first k elements of this array contain the components of the deflation-adjusted updating row vector.

vf

  REAL for slasd8

  DOUBLE PRECISION for dlasd8.

  Array, DIMENSION ( k ).

  On entry, vf contains information passed through dbede8.

vl

  REAL for slasd8

  DOUBLE PRECISION for dlasd8.

  Array, DIMENSION ( k ). On entry, vl contains information passed through dbede8.

lddifr

  INTEGER. The leading dimension of the output array difr, must be at least k.

dsigma

  REAL for slasd8

  DOUBLE PRECISION for dlasd8.

  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.

work

  REAL for slasd8

  DOUBLE PRECISION for dlasd8.

  Workspace array, DIMENSION at least (3k).

## Output Parameters

d

  REAL for slasd8

  DOUBLE PRECISION for dlasd8.

  Array, DIMENSION ( k ).

  On output, D contains the updated singular values.

vf

  On exit, vf contains the first k components of the first components of all right singular vectors of the bidiagonal matrix.

vl

  On exit, vl contains the first k components of the last components of all right singular vectors of the bidiagonal matrix.

difl

  REAL for slasd8

  DOUBLE PRECISION for dlasd8.

  Array, DIMENSION ( k ). On exit, `difl(i) = d(i) - dsigma(i)`.

difr

  REAL for slasd8

  DOUBLE PRECISION for dlasd8.

  Array,

  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.

info

  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.

Parent topic: Auxiliary Routines