?hbev

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/22/2024

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?hbev

Computes all eigenvalues and, optionally, eigenvectors of a Hermitian band matrix.

Syntax

call chbev(jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info)

call zhbev(jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, rwork, info)

call hbev(ab, w [,uplo] [,z] [,info])

Include Files

mkl.fi, lapack.f90

Description

The routine computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian band matrix A.

Input Parameters

jobz

CHARACTER*1. Must be 'N' or 'V'.

If jobz = 'N', then only eigenvalues are computed.

If jobz = 'V', then eigenvalues and eigenvectors are computed.

uplo

CHARACTER*1. Must be 'U' or 'L'.

If uplo = 'U', ab stores the upper triangular part of A.

If uplo = 'L', ab stores the lower triangular part of A.

n

INTEGER. The order of the matrix A (n≥ 0).

kd

INTEGER. The number of super- or sub-diagonals in A

(kd≥ 0).

ab, work

COMPLEX for chbev

DOUBLE COMPLEX for zhbev.

Arrays:

ab(lda,*) is an array containing either upper or lower triangular part of the Hermitian matrix A (as specified by uplo) in band storage format.

The second dimension of ab must be at least max(1, n).

work (*) is a workspace array.

The dimension of work must be at least max(1, n).

ldab

INTEGER. The leading dimension of ab; must be at least kd +1.

ldz

INTEGER. The leading dimension of the output array z.

Constraints:

if jobz = 'N', then ldz≥ 1;

if jobz = 'V', then ldz≥ max(1, n) .

rwork

REAL for chbev

DOUBLE PRECISION for zhbev

Workspace array, size at least max(1, 3n-2).

Output Parameters

w

REAL for chbev

DOUBLE PRECISION for zhbev

Array, size at least max(1, n).

If info = 0, contains the eigenvalues in ascending order.

z

COMPLEX for chbev

DOUBLE COMPLEX for zhbev.

Array z(ldz,*).

The second dimension of z must be at least max(1, n).

If jobz = 'V', then if info = 0, z contains the orthonormal eigenvectors of the matrix A, with the i-th column of z holding the eigenvector associated with w(i).

If jobz = 'N', then z is not referenced.

ab

On exit, this array is overwritten by the values generated during the reduction to tridiagonal form(see the description of hbtrd).

info

INTEGER.

If info = 0, the execution is successful.

If info = -i, the ith parameter had an illegal value.

If info = i, then the algorithm failed to converge;

i indicates the number of elements of an intermediate tridiagonal form which did not converge to zero.

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine hbev interface are the following:

ab

Holds the array A of size (kd+1,n).

w

Holds the vector with the number of elements n.

z

Holds the matrix Z of size (n, n).

uplo

Must be 'U' or 'L'. The default value is 'U'.

jobz

Restored based on the presence of the argument z as follows:

jobz = 'V', if z is present,

jobz = 'N', if z is omitted.

Parent topic: Symmetric Eigenvalue Problems: LAPACK Driver Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?hbev

Syntax

Include Files

Description

Input Parameters

Output Parameters

LAPACK 95 Interface Notes