hbevd_2stage#

Functions

void chbevd_2stage(
    const char*          jobz,
    const char*          uplo,
    const INT            n,
    const INT            kd,
          c64*  restrict AB,
    const INT            ldab,
          f32*  restrict W,
          c64*  restrict Z,
    const INT            ldz,
          c64*  restrict work,
    const INT            lwork,
          f32*  restrict rwork,
    const INT            lrwork,
          INT*  restrict iwork,
    const INT            liwork,
          INT*           info
);
void chbevd_2stage(const char *jobz, const char *uplo, const INT n, const INT kd, c64 *restrict AB, const INT ldab, f32 *restrict W, c64 *restrict Z, const INT ldz, c64 *restrict work, const INT lwork, f32 *restrict rwork, const INT lrwork, INT *restrict iwork, const INT liwork, INT *info)#

CHBEVD_2STAGE computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A using the 2stage technique for the reduction to tridiagonal.

If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

in
jobz

= ‘N’: Compute eigenvalues only; = ‘V’: Compute eigenvalues and eigenvectors. Not available in this release.

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.

in
kd

The number of superdiagonals of the matrix A if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KD >= 0.

inout
AB

Complex*16 array, dimension (ldab, n). On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. On exit, AB is overwritten by values generated during the reduction to tridiagonal form.

in
ldab

The leading dimension of the array AB. LDAB >= KD + 1.

out
W

Single precision array, dimension (n). If INFO = 0, the eigenvalues in ascending order.

out
Z

Complex*16 array, dimension (ldz, n). If JOBZ = ‘V’, then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A. If JOBZ = ‘N’, then 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

Complex*16 array, dimension (max(1,lwork)). On exit, if INFO = 0, WORK(0) returns the optimal LWORK.

in
lwork

The length of the array WORK.

out
rwork

Single precision array, dimension (lrwork). On exit, if INFO = 0, RWORK(0) returns the optimal LRWORK.

in
lrwork

The dimension of array RWORK.

out
iwork

Integer array, dimension (max(1,liwork)). On exit, if INFO = 0, IWORK(0) returns the optimal LIWORK.

in
liwork

The dimension of array IWORK.

out
info

= 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

Functions

void zhbevd_2stage(
    const char*          jobz,
    const char*          uplo,
    const INT            n,
    const INT            kd,
          c128* restrict AB,
    const INT            ldab,
          f64*  restrict W,
          c128* restrict Z,
    const INT            ldz,
          c128* restrict work,
    const INT            lwork,
          f64*  restrict rwork,
    const INT            lrwork,
          INT*  restrict iwork,
    const INT            liwork,
          INT*           info
);
void zhbevd_2stage(const char *jobz, const char *uplo, const INT n, const INT kd, c128 *restrict AB, const INT ldab, f64 *restrict W, c128 *restrict Z, const INT ldz, c128 *restrict work, const INT lwork, f64 *restrict rwork, const INT lrwork, INT *restrict iwork, const INT liwork, INT *info)#

ZHBEVD_2STAGE computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A using the 2stage technique for the reduction to tridiagonal.

If eigenvectors are desired, it uses a divide and conquer algorithm.

Parameters

in
jobz

= ‘N’: Compute eigenvalues only; = ‘V’: Compute eigenvalues and eigenvectors. Not available in this release.

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.

in
kd

The number of superdiagonals of the matrix A if UPLO = ‘U’, or the number of subdiagonals if UPLO = ‘L’. KD >= 0.

inout
AB

Complex*16 array, dimension (ldab, n). On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. On exit, AB is overwritten by values generated during the reduction to tridiagonal form.

in
ldab

The leading dimension of the array AB. LDAB >= KD + 1.

out
W

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

out
Z

Complex*16 array, dimension (ldz, n). If JOBZ = ‘V’, then if INFO = 0, Z contains the orthonormal eigenvectors of the matrix A. If JOBZ = ‘N’, then 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

Complex*16 array, dimension (max(1,lwork)). On exit, if INFO = 0, WORK(0) returns the optimal LWORK.

in
lwork

The length of the array WORK.

out
rwork

Double precision array, dimension (lrwork). On exit, if INFO = 0, RWORK(0) returns the optimal LRWORK.

in
lrwork

The dimension of array RWORK.

out
iwork

Integer array, dimension (max(1,liwork)). On exit, if INFO = 0, IWORK(0) returns the optimal LIWORK.

in
liwork

The dimension of array IWORK.

out
info

= 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.