NAME

ZHEEV - compute 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 (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.

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.

  —  LAPACK version 2.0  —  08 October 1994