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# zheev

```
NAME
ZHEEV - compute all eigenvalues and, optionally, eigenvec-
tors 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 con-
tains 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 des-
troyed.

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) 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.

3*N-2))
RWORK   (workspace) DOUBLE PRECISION array, dimension (max(1,

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 tridiago-
nal form did not converge to zero.
```