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

## Syntax

lapack_int LAPACKE_cheev( int matrix_layout, char jobz, char uplo, lapack_int n, lapack_complex_float* a, lapack_int lda, float* w );

lapack_int LAPACKE_zheev( int matrix_layout, char jobz, char uplo, lapack_int n, lapack_complex_double* a, lapack_int lda, double* w );

• mkl.h

## Description

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

Note that for most cases of complex Hermitian eigenvalue problems the default choice should be heevr function as its underlying algorithm is faster and uses less workspace.

## 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', a stores the upper triangular part of A.

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

n

The order of the matrix A (n 0).

a

a (size max(1, lda*n)) is an array containing either upper or lower triangular part of the Hermitian matrix A, as specified by uplo.

lda

The leading dimension of the array a. Must be at least max(1, n).

## Output Parameters

a

On exit, if jobz = 'V', then if info = 0, array a contains the orthonormal eigenvectors of the matrix A.

If jobz = 'N', then on exit the lower triangle

(if uplo = 'L') or the upper triangle (if uplo = 'U') of A, including the diagonal, is overwritten.

w

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

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

## 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.

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