cheev(3)

NAME

CHEEV - compute all eigenvalues and, optionally, eigenvec

tors of a complex Hermitian matrix A

SYNOPSIS

SUBROUTINE  CHEEV(  JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
RWORK, INFO )
    CHARACTER     JOBZ, UPLO
    INTEGER       INFO, LDA, LWORK, N
    REAL          RWORK( * ), W( * )
    COMPLEX       A( LDA, * ), WORK( * )

PURPOSE

CHEEV computes all eigenvalues and, optionally, eigenvec

tors of a complex Hermitian matrix A.

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 de

stroyed.

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. LWORK >=

max(1,2*N-1). For optimal efficiency, LWORK >= (NB+1)*N, where

NB is the blocksize for CHETRD returned by ILAENV.

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) REAL array, dimension (max(1, 3*N-2))

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value
> 0: if INFO = i, the algorithm failed to con

verge; i off-diagonal elements of an intermediate tridiagonal

form did not converge to zero.

LAPACK version 3.0 15 June 2000

CHEEV(3)