syevr#

Functions

void ssyevr(
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
          f32*  restrict A,
    const INT            lda,
    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,
          INT*  restrict isuppz,
          f32*  restrict work,
    const INT            lwork,
          INT*  restrict iwork,
    const INT            liwork,
          INT*           info
);
void ssyevr(const char *jobz, const char *range, const char *uplo, const INT n, f32 *restrict A, const INT lda, 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, INT *restrict isuppz, f32 *restrict work, const INT lwork, INT *restrict iwork, const INT liwork, INT *info)#

SSYEVR computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

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

SSYEVR first reduces the matrix A to tridiagonal form T with a call to SSYTRD. Then, whenever possible, SSYEVR calls SSTEMR to compute the eigenspectrum using Relatively Robust Representations.

Parameters

in
jobz

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

in
range

= ‘A’: all eigenvalues will be found. = ‘V’: all eigenvalues in (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
A

On entry, the symmetric matrix A. On exit, the triangle is destroyed.

in
lda

The leading dimension of A. lda >= max(1, n).

in
vl

If RANGE=’V’, lower bound of interval. Not referenced otherwise.

in
vu

If RANGE=’V’, upper bound of interval. VL < VU. Not referenced otherwise.

in
il

If RANGE=’I’, index of smallest eigenvalue (0-based). Not referenced otherwise.

in
iu

If RANGE=’I’, index of largest eigenvalue (0-based). Not referenced otherwise.

in
abstol

Absolute error tolerance for eigenvalues.

out
m

The total number of eigenvalues found.

out
W

Array of dimension (n). The first M elements contain the selected eigenvalues in ascending order.

out
Z

If JOBZ = ‘V’, the first M columns contain the orthonormal eigenvectors. If JOBZ = ‘N’, Z is not referenced.

in
ldz

Leading dimension of Z. LDZ >= 1, and if JOBZ = ‘V’, LDZ >= N.

out
isuppz

Support of eigenvectors in Z. Dimension (2*max(1,M)).

out
work

Workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The dimension of work. If N <= 1, LWORK >= 1, else LWORK >= 26*N. If lwork = -1, workspace query only.

out
iwork

Integer workspace array, dimension (max(1, liwork)). On exit, if info = 0, iwork[0] returns the optimal liwork.

in
liwork

The dimension of iwork. If N <= 1, LIWORK >= 1, else LIWORK >= 10*N. If liwork = -1, workspace query only.

out
info

  • = 0: successful exit

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

  • > 0: Internal error

Functions

void dsyevr(
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
          f64*  restrict A,
    const INT            lda,
    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,
          INT*  restrict isuppz,
          f64*  restrict work,
    const INT            lwork,
          INT*  restrict iwork,
    const INT            liwork,
          INT*           info
);
void dsyevr(const char *jobz, const char *range, const char *uplo, const INT n, f64 *restrict A, const INT lda, 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, INT *restrict isuppz, f64 *restrict work, const INT lwork, INT *restrict iwork, const INT liwork, INT *info)#

DSYEVR computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A.

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

DSYEVR first reduces the matrix A to tridiagonal form T with a call to DSYTRD. Then, whenever possible, DSYEVR calls DSTEMR to compute the eigenspectrum using Relatively Robust Representations.

Parameters

in
jobz

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

in
range

= ‘A’: all eigenvalues will be found. = ‘V’: all eigenvalues in (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
A

On entry, the symmetric matrix A. On exit, the triangle is destroyed.

in
lda

The leading dimension of A. lda >= max(1, n).

in
vl

If RANGE=’V’, lower bound of interval. Not referenced otherwise.

in
vu

If RANGE=’V’, upper bound of interval. VL < VU. Not referenced otherwise.

in
il

If RANGE=’I’, index of smallest eigenvalue (0-based). Not referenced otherwise.

in
iu

If RANGE=’I’, index of largest eigenvalue (0-based). Not referenced otherwise.

in
abstol

Absolute error tolerance for eigenvalues.

out
m

The total number of eigenvalues found.

out
W

Array of dimension (n). The first M elements contain the selected eigenvalues in ascending order.

out
Z

If JOBZ = ‘V’, the first M columns contain the orthonormal eigenvectors. If JOBZ = ‘N’, Z is not referenced.

in
ldz

Leading dimension of Z. LDZ >= 1, and if JOBZ = ‘V’, LDZ >= N.

out
isuppz

Support of eigenvectors in Z. Dimension (2*max(1,M)).

out
work

Workspace array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The dimension of work. If N <= 1, LWORK >= 1, else LWORK >= 26*N. If lwork = -1, workspace query only.

out
iwork

Integer workspace array, dimension (max(1, liwork)). On exit, if info = 0, iwork[0] returns the optimal liwork.

in
liwork

The dimension of iwork. If N <= 1, LIWORK >= 1, else LIWORK >= 10*N. If liwork = -1, workspace query only.

out
info

  • = 0: successful exit

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

  • > 0: Internal error

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