# man cheev (Fonctions bibliothèques) - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

## NAME

CHEEV - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

## SYNOPSIS

SUBROUTINE CHEEV(
JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDA, LWORK, N
REAL RWORK( * ), W( * )
COMPLEX A( LDA, * ), WORK( * )

## PURPOSE

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

## ARGUMENTS

JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;

= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1

= 'U': Upper triangle of A is stored;

= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) COMPLEX array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, 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 destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. LWORK >= max(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where NB is the blocksize for CHETRD returned by ILAENV.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

RWORK (workspace) REAL array, dimension (max(1, 3*N-2))
INFO (output) INTEGER
= 0: successful exit

< 0: if INFO = -i, the i-th argument had an illegal value

> 0: if INFO = i, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.