?hbev

Syntax

FORTRAN 77:

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)

Fortran 95:

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

C:

lapack_int LAPACKE_chbev( int matrix_order, char jobz, char uplo, lapack_int n, lapack_int kd, lapack_complex_float* ab, lapack_int ldab, float* w, lapack_complex_float* z, lapack_int ldz );

lapack_int LAPACKE_zhbev( int matrix_order, char jobz, char uplo, lapack_int n, lapack_int kd, lapack_complex_double* ab, lapack_int ldab, double* w, lapack_complex_double* z, lapack_int ldz );

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi and mkl_lapack.h include files, the Fortran 95 interfaces are specified in the lapack.f90 include file, and the C interfaces are specified in the mkl_lapacke.h include file.

Description

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

Input Parameters

The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.

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 (ldab,*) 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, DIMENSION at least max(1, 3n-2).

Output Parameters

w

REAL for chbev

DOUBLE PRECISION for zhbev

Array, DIMENSION 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.

If uplo = 'U', the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows kd and kd+1 of ab, and if uplo = 'L', the diagonal and first subdiagonal of T are returned in the first two rows of ab.

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.

Fortran 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 Fortran 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.