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.

Para obtener información más completa sobre las optimizaciones del compilador, consulte nuestro Aviso de optimización.