zheev(3)

NAME

ZHEEV - compute all eigenvalues and, optionally, eigenvec

tors of a complex Hermitian matrix A

SYNOPSIS

SUBROUTINE  ZHEEV(  JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
RWORK, INFO )
    CHARACTER     JOBZ, UPLO
    INTEGER       INFO, LDA, LWORK, N
    DOUBLE        PRECISION RWORK( * ), W( * )
    COMPLEX*16    A( LDA, * ), WORK( * )

PURPOSE

ZHEEV 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*16 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) DOUBLE PRECISION array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

WORK (workspace/output) COMPLEX*16 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 ZHETRD 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) DOUBLE PRECISION 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

ZHEEV(3)