heevx#

Functions

void cheevx(
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
          c64*  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,
          c64*  restrict Z,
    const INT            ldz,
          c64*  restrict work,
    const INT            lwork,
          f32*  restrict rwork,
          INT*  restrict iwork,
          INT*  restrict ifail,
          INT*           info
);
void cheevx(const char *jobz, const char *range, const char *uplo, const INT n, c64 *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, c64 *restrict Z, const INT ldz, c64 *restrict work, const INT lwork, f32 *restrict rwork, INT *restrict iwork, INT *restrict ifail, INT *info)#

CHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.

Eigenvalues and eigenvectors 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
A

Single complex array, dimension (LDA, N). On entry, the Hermitian matrix A. If UPLO = ‘U’, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = ‘L’, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=’L’) or the upper triangle (if UPLO=’U’) of A, including the diagonal, is destroyed.

in
lda

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

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). Not referenced if RANGE = ‘A’ or ‘V’.

in
iu

If RANGE=’I’, the index of the largest eigenvalue to be returned (0-based). 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

Single precision array, dimension (N). On normal exit, the first M elements contain the selected eigenvalues in ascending order.

out
Z

Single complex array, dimension (LDZ, max(1,M)). 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
work

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

in
lwork

The dimension of work. LWORK >= 1 when N <= 1, otherwise 2*N. For optimal efficiency, LWORK >= (NB+1)*N. If lwork = -1, workspace query only.

out
rwork

Single precision workspace array, dimension (7*N).

out
iwork

Integer workspace array, dimension (5*N).

out
ifail

Integer array, dimension (N). If JOBZ = ‘V’, indices of eigenvectors that failed to converge. If JOBZ = ‘N’, 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. Their indices are stored in array IFAIL.

Functions

void zheevx(
    const char*          jobz,
    const char*          range,
    const char*          uplo,
    const INT            n,
          c128* 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,
          c128* restrict Z,
    const INT            ldz,
          c128* restrict work,
    const INT            lwork,
          f64*  restrict rwork,
          INT*  restrict iwork,
          INT*  restrict ifail,
          INT*           info
);
void zheevx(const char *jobz, const char *range, const char *uplo, const INT n, c128 *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, c128 *restrict Z, const INT ldz, c128 *restrict work, const INT lwork, f64 *restrict rwork, INT *restrict iwork, INT *restrict ifail, INT *info)#

ZHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A.

Eigenvalues and eigenvectors 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
A

Double complex array, dimension (LDA, N). On entry, the Hermitian matrix A. If UPLO = ‘U’, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = ‘L’, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, the lower triangle (if UPLO=’L’) or the upper triangle (if UPLO=’U’) of A, including the diagonal, is destroyed.

in
lda

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

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). Not referenced if RANGE = ‘A’ or ‘V’.

in
iu

If RANGE=’I’, the index of the largest eigenvalue to be returned (0-based). 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). On normal exit, the first M elements contain the selected eigenvalues in ascending order.

out
Z

Double complex array, dimension (LDZ, max(1,M)). 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
work

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

in
lwork

The dimension of work. LWORK >= 1 when N <= 1, otherwise 2*N. For optimal efficiency, LWORK >= (NB+1)*N. If lwork = -1, workspace query only.

out
rwork

Double precision workspace array, dimension (7*N).

out
iwork

Integer workspace array, dimension (5*N).

out
ifail

Integer array, dimension (N). If JOBZ = ‘V’, indices of eigenvectors that failed to converge. If JOBZ = ‘N’, 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. Their indices are stored in array IFAIL.

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