CHEEVD(3f)

NAME
CHEEVD - 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).

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