?lasd9

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?lasd9

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 slasd9( icompq, ldu, k, d, z, vf, vl, difl, difr, dsigma, work, info )

call dlasd9( icompq, ldu, k, d, z, vf, vl, difl, difr, dsigma, work, info )

Include Files

mkl.fi

Description

The routine ?lasd9 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. ?lasd9 is called from ?lasd7.

Input Parameters

icompq

INTEGER. Specifies whether singular vectors are to be computed in factored form in the calling routine:

If icompq = 0, compute singular values only;

If icompq = 1, compute singular vector matrices in factored form also.

k

INTEGER. The number of terms in the rational function to be solved by slasd4. k≥ 1.

dsigma

REAL for slasd9

DOUBLE PRECISION for dlasd9.

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

REAL for slasd9

DOUBLE PRECISION for dlasd9.

Array, DIMENSION (k). The first k elements of this array contain the components of the deflation-adjusted updating row vector.

vf

REAL for slasd9

DOUBLE PRECISION for dlasd9.

Array, DIMENSION(k). On entry, vf contains information passed through sbede8.

vl

REAL for slasd9

DOUBLE PRECISION for dlasd9.

Array, DIMENSION(k). On entry, vl contains information passed through sbede8.

work

REAL for slasd9

DOUBLE PRECISION for dlasd9.

Workspace array, DIMENSION at least (3k).

Output Parameters

d

REAL for slasd9

DOUBLE PRECISION for dlasd9.

Array, DIMENSION(k). d(i) 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 slasd9

DOUBLE PRECISION for dlasd9.

Array, DIMENSION (k).

On exit, difl(i) = d(i) - dsigma(i).

difr

REAL for slasd9

DOUBLE PRECISION for dlasd9.

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.

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: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?lasd9