Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian
matrix A

```

#### SYNOPSIS

```       SUBROUTINE CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,  LRWORK,  IWORK,  LIWORK,
INFO )

CHARACTER      JOBZ, UPLO

INTEGER        INFO, LDA, LIWORK, LRWORK, LWORK, N

INTEGER        IWORK( * )

REAL           RWORK( * ), W( * )

COMPLEX        A( LDA, * ), WORK( * )

```

#### PURPOSE

```       CHEEVD  computes  all  eigenvalues  and,  optionally,  eigenvectors of a complex Hermitian
matrix A.  If eigenvectors are desired, it uses a
divide and conquer algorithm.
The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.

```

#### 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 (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK   (input) INTEGER
The length of the array WORK.
If N <= 1,                LWORK must be at least 1.
If JOBZ  = 'N' and N > 1, LWORK must be at least N + 1.
If JOBZ  = 'V' and N > 1, LWORK must be at least 2*N + N**2.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal sizes of the WORK, RWORK and
IWORK arrays, returns these values as the first entries of
the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK   (workspace/output) REAL array,
dimension (LRWORK)
On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK  (input) INTEGER
The dimension of the array RWORK.
If N <= 1,                LRWORK must be at least 1.
If JOBZ  = 'N' and N > 1, LRWORK must be at least N.
If JOBZ  = 'V' and N > 1, LRWORK must be at least
1 + 5*N + 2*N**2.
If LRWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK  (input) INTEGER
The dimension of the array IWORK.
If N <= 1,                LIWORK must be at least 1.
If JOBZ  = 'N' and N > 1, LIWORK must be at least 1.
If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
If LIWORK = -1, then a workspace query is assumed; the
routine only calculates the optimal sizes of the WORK, RWORK
and IWORK arrays, returns these values as the first entries
of the WORK, RWORK and IWORK arrays, and no error message
related to LWORK or LRWORK or LIWORK is issued by XERBLA.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i and JOBZ = 'N', then the algorithm failed
to converge; i off-diagonal elements of an intermediate
tridiagonal form did not converge to zero;
if INFO = i and JOBZ = 'V', then the algorithm failed
to compute an eigenvalue while working on the submatrix
lying in rows and columns INFO/(N+1) through
mod(INFO,N+1).

```

#### FURTHERDETAILS

```        Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
Modified description of INFO. Sven, 16 Feb 05.

LAPACK driver routine (version 3.2)        April 2011                            CHEEVD(3lapack)
```