NAME¶

ZHEEV - computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

SYNOPSIS¶

SUBROUTINE ZHEEV(

JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )

CHARACTER JOBZ, UPLO INTEGER INFO, LDA, LWORK, N DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 A( LDA, * ), WORK( * )

PURPOSE¶

ZHEEV 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*16 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) DOUBLE PRECISION array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,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 ZHETRD 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) DOUBLE PRECISION 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.