lasd8#

Functions

void slasd8(
    const INT           icompq,
    const INT           k,
          f32* restrict D,
          f32* restrict Z,
          f32* restrict VF,
          f32* restrict VL,
          f32* restrict DIFL,
          f32* restrict DIFR,
    const INT           lddifr,
    const f32* restrict DSIGMA,
          f32* restrict work,
          INT*          info
);
void slasd8(const INT icompq, const INT k, f32 *restrict D, f32 *restrict Z, f32 *restrict VF, f32 *restrict VL, f32 *restrict DIFL, f32 *restrict DIFR, const INT lddifr, const f32 *restrict DSIGMA, f32 *restrict work, INT *info)#

SLASD8 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 SLASD4, 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.

SLASD8 is called from SLASD6.

Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Parameters

in
icompq

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 vectors in factored form as well.

in
k

The number of terms in the rational function to be solved by SLASD4. k>=1.

out
D

Array of dimension (k). On output, D contains the updated singular values.

inout
Z

Array of dimension (k). On entry, the first k elements of this array contain the components of the deflation-adjusted updating row vector. On exit, Z is updated.

inout
VF

Array of dimension (k). On entry, VF contains information passed through SBEDE8. On exit, VF contains the first k components of the first components of all right singular vectors of the bidiagonal matrix.

inout
VL

Array of dimension (k). On entry, VL contains information passed through SBEDE8. On exit, VL contains the first k components of the last components of all right singular vectors of the bidiagonal matrix.

out
DIFL

Array of dimension (k). On exit, DIFL[i] = D[i] - DSIGMA[i].

out
DIFR

Array of dimension (lddifr, 2) if icompq=1 and dimension (k) if icompq=0. On exit, DIFR[i,0] = D[i] - DSIGMA[i+1], DIFR[k-1,0] is not defined and will not be referenced. If icompq=1, DIFR[0:k-1,1] is an array containing the normalizing factors for the right singular vector matrix.

in
lddifr

The leading dimension of DIFR, must be at least k.

in
DSIGMA

Array of dimension (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.

out
work

Array of dimension (3*k).

out
info

info=0: successful exit. info<0: if info=-i, the i-th argument had an illegal value. info>0: if info=1, a singular value did not converge.

Functions

void dlasd8(
    const INT           icompq,
    const INT           k,
          f64* restrict D,
          f64* restrict Z,
          f64* restrict VF,
          f64* restrict VL,
          f64* restrict DIFL,
          f64* restrict DIFR,
    const INT           lddifr,
    const f64* restrict DSIGMA,
          f64* restrict work,
          INT*          info
);
void dlasd8(const INT icompq, const INT k, f64 *restrict D, f64 *restrict Z, f64 *restrict VF, f64 *restrict VL, f64 *restrict DIFL, f64 *restrict DIFR, const INT lddifr, const f64 *restrict DSIGMA, f64 *restrict work, INT *info)#

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.

Contributors:

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Parameters

in
icompq

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 vectors in factored form as well.

in
k

The number of terms in the rational function to be solved by DLASD4. k>=1.

out
D

Array of dimension (k). On output, D contains the updated singular values.

inout
Z

Array of dimension (k). On entry, the first k elements of this array contain the components of the deflation-adjusted updating row vector. On exit, Z is updated.

inout
VF

Array of dimension (k). 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.

inout
VL

Array of dimension (k). 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.

out
DIFL

Array of dimension (k). On exit, DIFL[i] = D[i] - DSIGMA[i].

out
DIFR

Array of dimension (lddifr, 2) if icompq=1 and dimension (k) if icompq=0. On exit, DIFR[i,0] = D[i] - DSIGMA[i+1], DIFR[k-1,0] is not defined and will not be referenced. If icompq=1, DIFR[0:k-1,1] is an array containing the normalizing factors for the right singular vector matrix.

in
lddifr

The leading dimension of DIFR, must be at least k.

in
DSIGMA

Array of dimension (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.

out
work

Array of dimension (3*k).

out
info

info=0: successful exit. info<0: if info=-i, the i-th argument had an illegal value. info>0: if info=1, a singular value did not converge.