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# chpev

```
NAME
CHPEV - compute all the eigenvalues and, optionally, eigen-
vectors of a complex Hermitian matrix in packed storage

SYNOPSIS
SUBROUTINE CHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
INFO )

CHARACTER     JOBZ, UPLO

INTEGER       INFO, LDZ, N

REAL          RWORK( * ), W( * )

COMPLEX       AP( * ), WORK( * ), Z( LDZ, * )

PURPOSE
CHPEV computes all the eigenvalues and, optionally, eigen-
vectors of a complex Hermitian matrix in packed storage.

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.

AP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermi-
tian matrix A, packed columnwise in a linear array.
The j-th column of A is stored in the array AP as
follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j)
for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2)
= A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated dur-
ing the reduction to tridiagonal form.  If UPLO =
'U', the diagonal and first superdiagonal of the
tridiagonal matrix T overwrite the corresponding
elements of A, and if UPLO = 'L', the diagonal and
first subdiagonal of T overwrite the corresponding
elements of A.

W       (output) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.

Z       (output) COMPLEX array, dimension (LDZ, N)
If JOBZ = 'V', then if INFO = 0, Z contains the
orthonormal eigenvectors of the matrix A, with the
i-th column of Z holding the eigenvector associated
with W(i).  If JOBZ = 'N', then Z is not referenced.

LDZ     (input) INTEGER
The leading dimension of the array Z.  LDZ >= 1, and
if JOBZ = 'V', LDZ >= max(1,N).

WORK    (workspace) COMPLEX array, dimension (max(1, 2*N-1))

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