# ?hbev

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

## Syntax

lapack_int LAPACKE_chbev( int matrix_layout, 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_layout, 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 );

• mkl.h

## Description

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

## Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

jobz

Must be 'N' or 'V'.

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

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

uplo

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

The order of the matrix A (n 0).

kd

The number of super- or sub-diagonals in A

(kd 0).

ab

ab (size at least max(1, ldab*n) for column major layout and at least max(1, ldab*(kd + 1)) for row major layout) is an array containing either upper or lower triangular part of the Hermitian matrix A (as specified by uplo) in band storage format.

ldab

The leading dimension of ab; must be at least kd +1 for column major layout and n for row major layout.

ldz

The leading dimension of the output array z.

Constraints:

if jobz = 'N', then ldz 1;

if jobz = 'V', then ldz max(1, n) .

## Output Parameters

w

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

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

z

Array z(size max(1, ldz*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 - 1].

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).

## Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, the i-th 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.

For more complete information about compiler optimizations, see our Optimization Notice.