spevx#

Functions

void sspevx(
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
          f32*  restrict AP,
    const f32            vl,
    const f32            vu,
    const INT            il,
    const INT            iu,
    const f32            abstol,
          INT*           m,
          f32*  restrict W,
          f32*  restrict Z,
    const INT            ldz,
          f32*  restrict work,
          INT*  restrict iwork,
          INT*  restrict ifail,
          INT*           info
);
void sspevx(const char *jobz, const char *range, const char *uplo, const INT n, f32 *restrict AP, const f32 vl, const f32 vu, const INT il, const INT iu, const f32 abstol, INT *m, f32 *restrict W, f32 *restrict Z, const INT ldz, f32 *restrict work, INT *restrict iwork, INT *restrict ifail, INT *info)#

SSPEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage.

Eigenvalues/vectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters

in
jobz

= ‘N’: Compute eigenvalues only; = ‘V’: Compute eigenvalues and eigenvectors.

in
range

= ‘A’: all eigenvalues will be found; = ‘V’: all eigenvalues in the half-open interval (VL,VU] will be found; = ‘I’: the IL-th through IU-th eigenvalues will be found.

in
uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in
n

The order of the matrix A. n >= 0.

inout
AP

Double precision array, dimension (n*(n+1)/2). On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. On exit, AP is overwritten by values generated during the reduction to tridiagonal form.

in
vl

If range=’V’, the lower bound of the interval to be searched for eigenvalues. vl < vu. Not referenced if range = ‘A’ or ‘I’.

in
vu

If range=’V’, the upper bound of the interval to be searched for eigenvalues. vl < vu. Not referenced if range = ‘A’ or ‘I’.

in
il

If range=’I’, the index of the smallest eigenvalue to be returned (0-based). 0 <= il <= iu <= n-1, if n > 0. Not referenced if range = ‘A’ or ‘V’.

in
iu

If range=’I’, the index of the largest eigenvalue to be returned (0-based). 0 <= il <= iu <= n-1, if n > 0. Not referenced if range = ‘A’ or ‘V’.

in
abstol

The absolute error tolerance for the eigenvalues.

out
m

The total number of eigenvalues found. 0 <= m <= n.

out
W

Double precision array, dimension (n). If info = 0, the selected eigenvalues in ascending order.

out
Z

Double precision array, dimension (ldz, max(1,m)). If jobz = ‘V’, contains the orthonormal eigenvectors. If jobz = ‘N’, Z is not referenced.

in
ldz

The leading dimension of the array Z. ldz >= 1, and if jobz = ‘V’, ldz >= max(1,n).

out
work

Double precision array, dimension (8*n).

out
iwork

Integer array, dimension (5*n).

out
ifail

Integer array, dimension (n). If jobz = ‘V’, then if info = 0, the first m elements of ifail are zero. If info > 0, then ifail contains the indices of the eigenvectors that failed to converge. If jobz = ‘N’, then ifail is not referenced.

out
info

  • = 0: successful exit

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

  • > 0: if info = i, then i eigenvectors failed to converge.

Functions

void dspevx(
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
          f64*  restrict AP,
    const f64            vl,
    const f64            vu,
    const INT            il,
    const INT            iu,
    const f64            abstol,
          INT*           m,
          f64*  restrict W,
          f64*  restrict Z,
    const INT            ldz,
          f64*  restrict work,
          INT*  restrict iwork,
          INT*  restrict ifail,
          INT*           info
);
void dspevx(const char *jobz, const char *range, const char *uplo, const INT n, f64 *restrict AP, const f64 vl, const f64 vu, const INT il, const INT iu, const f64 abstol, INT *m, f64 *restrict W, f64 *restrict Z, const INT ldz, f64 *restrict work, INT *restrict iwork, INT *restrict ifail, INT *info)#

DSPEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed storage.

Eigenvalues/vectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.

Parameters

in
jobz

= ‘N’: Compute eigenvalues only; = ‘V’: Compute eigenvalues and eigenvectors.

in
range

= ‘A’: all eigenvalues will be found; = ‘V’: all eigenvalues in the half-open interval (VL,VU] will be found; = ‘I’: the IL-th through IU-th eigenvalues will be found.

in
uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in
n

The order of the matrix A. n >= 0.

inout
AP

Double precision array, dimension (n*(n+1)/2). On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. On exit, AP is overwritten by values generated during the reduction to tridiagonal form.

in
vl

If range=’V’, the lower bound of the interval to be searched for eigenvalues. vl < vu. Not referenced if range = ‘A’ or ‘I’.

in
vu

If range=’V’, the upper bound of the interval to be searched for eigenvalues. vl < vu. Not referenced if range = ‘A’ or ‘I’.

in
il

If range=’I’, the index of the smallest eigenvalue to be returned (0-based). 0 <= il <= iu <= n-1, if n > 0. Not referenced if range = ‘A’ or ‘V’.

in
iu

If range=’I’, the index of the largest eigenvalue to be returned (0-based). 0 <= il <= iu <= n-1, if n > 0. Not referenced if range = ‘A’ or ‘V’.

in
abstol

The absolute error tolerance for the eigenvalues.

out
m

The total number of eigenvalues found. 0 <= m <= n.

out
W

Double precision array, dimension (n). If info = 0, the selected eigenvalues in ascending order.

out
Z

Double precision array, dimension (ldz, max(1,m)). If jobz = ‘V’, contains the orthonormal eigenvectors. If jobz = ‘N’, Z is not referenced.

in
ldz

The leading dimension of the array Z. ldz >= 1, and if jobz = ‘V’, ldz >= max(1,n).

out
work

Double precision array, dimension (8*n).

out
iwork

Integer array, dimension (5*n).

out
ifail

Integer array, dimension (n). If jobz = ‘V’, then if info = 0, the first m elements of ifail are zero. If info > 0, then ifail contains the indices of the eigenvectors that failed to converge. If jobz = ‘N’, then ifail is not referenced.

out
info

  • = 0: successful exit

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

  • > 0: if info = i, then i eigenvectors failed to converge.

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