CHEEVD - compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A

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( * )

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.

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 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 size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK 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 size of the RWORK array, returns this value as the first entry of the RWORK array, and no error message related to LRWORK is issued by XERBLA.

IWORK (workspace/output) INTEGER array, dimension (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 size of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to 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, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

Based on contributions by

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA