laed9#

Functions

void slaed9(
    const INT  k,
    const INT  kstart,
    const INT  kstop,
    const INT  n,
          f32* D,
          f32* Q,
    const INT  ldq,
    const f32  rho,
    const f32* dlambda,
          f32* W,
          f32* S,
    const INT  lds,
          INT* info
);
void slaed9(const INT k, const INT kstart, const INT kstop, const INT n, f32 *D, f32 *Q, const INT ldq, const f32 rho, const f32 *dlambda, f32 *W, f32 *S, const INT lds, INT *info)#

SLAED9 finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP.

It makes the appropriate calls to SLAED4 and then stores the new matrix of eigenvectors for use in calculating the next level of Z vectors.

Parameters

in
k

The number of terms in the rational function to be solved by SLAED4. k >= 0.

in
kstart

The starting index (0-based) of eigenvalues to compute.

in
kstop

The stopping index (0-based, exclusive). The updated eigenvalues D(i), kstart <= i < kstop, are computed. 0 <= kstart < kstop <= k.

in
n

The number of rows and columns in the Q matrix. n >= k (deflation may result in n > k).

out
D

Double precision array, dimension (n). D(i) contains the updated eigenvalues for kstart <= i < kstop.

out
Q

Double precision array, dimension (ldq, n).

in
ldq

The leading dimension of the array Q. ldq >= max(1, k).

in
rho

The value of the parameter in the rank one update equation. rho >= 0 required.

in
dlambda

Double precision array, dimension (k). The first k elements contain the old roots of the deflated updating problem. These are the poles of the secular equation.

in
W

Double precision array, dimension (k). The first k elements contain the components of the deflation-adjusted updating vector.

out
S

Double precision array, dimension (lds, k). Will contain the eigenvectors of the repaired matrix which will be stored for subsequent Z vector calculation and multiplied by the previously accumulated eigenvectors to update the system.

in
lds

The leading dimension of S. lds >= max(1, k).

out
info

  • = 0: successful exit.

  • < 0: if info = -i, the i-th argument had an illegal value.

  • > 0: if info = 1, an eigenvalue did not converge.

Functions

void dlaed9(
    const INT  k,
    const INT  kstart,
    const INT  kstop,
    const INT  n,
          f64* D,
          f64* Q,
    const INT  ldq,
    const f64  rho,
    const f64* dlambda,
          f64* W,
          f64* S,
    const INT  lds,
          INT* info
);
void dlaed9(const INT k, const INT kstart, const INT kstop, const INT n, f64 *D, f64 *Q, const INT ldq, const f64 rho, const f64 *dlambda, f64 *W, f64 *S, const INT lds, INT *info)#

DLAED9 finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP.

It makes the appropriate calls to DLAED4 and then stores the new matrix of eigenvectors for use in calculating the next level of Z vectors.

Parameters

in
k

The number of terms in the rational function to be solved by DLAED4. k >= 0.

in
kstart

The starting index (0-based) of eigenvalues to compute.

in
kstop

The stopping index (0-based, exclusive). The updated eigenvalues D(i), kstart <= i < kstop, are computed. 0 <= kstart < kstop <= k.

in
n

The number of rows and columns in the Q matrix. n >= k (deflation may result in n > k).

out
D

Double precision array, dimension (n). D(i) contains the updated eigenvalues for kstart <= i < kstop.

out
Q

Double precision array, dimension (ldq, n).

in
ldq

The leading dimension of the array Q. ldq >= max(1, k).

in
rho

The value of the parameter in the rank one update equation. rho >= 0 required.

in
dlambda

Double precision array, dimension (k). The first k elements contain the old roots of the deflated updating problem. These are the poles of the secular equation.

in
W

Double precision array, dimension (k). The first k elements contain the components of the deflation-adjusted updating vector.

out
S

Double precision array, dimension (lds, k). Will contain the eigenvectors of the repaired matrix which will be stored for subsequent Z vector calculation and multiplied by the previously accumulated eigenvectors to update the system.

in
lds

The leading dimension of S. lds >= max(1, k).

out
info

  • = 0: successful exit.

  • < 0: if info = -i, the i-th argument had an illegal value.

  • > 0: if info = 1, an eigenvalue did not converge.

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