?lasd9

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

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

void slasd9( lapack_int *icompq, lapack_int *k, float *d, float *z, float *vf, float *vl, float *difl, float *difr, float *dsigma, float *work, lapack_int *info );

void dlasd9( lapack_int *icompq, lapack_int *k, double *d, double *z, double *vf, double *vl, double *difl, double *difr, double *dsigma, double *work, lapack_int *info );

Include Files

mkl.h

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

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

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

dsigma

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

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

vf

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

vl

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

work

Workspace array, DIMENSION at least (3k).

Output Parameters

d

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

Array, DIMENSION (k).

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

difr

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

= 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 C

?lasd9