NAME

CHEEVD - compute 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 (LWORK)
On exit, if LWORK > 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.

RWORK   (workspace/output) REAL array,
dimension (LRWORK) On exit, if LRWORK > 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 + 4∗N + 2∗N∗lg N + 3∗N∗∗2 , where lg( N ) = smallest integer k such that 2∗∗k >= N .

IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if LIWORK > 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 2 + 5∗N.

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