chpev(3)

NAME

CHPEV - compute all the eigenvalues and, optionally,

eigenvectors of a complex Hermitian matrix in packed storage

SYNOPSIS

SUBROUTINE  CHPEV(  JOBZ,  UPLO,  N,  AP, W, Z, LDZ, WORK,
RWORK, INFO )
    CHARACTER     JOBZ, UPLO
    INTEGER       INFO, LDZ, N
    REAL          RWORK( * ), W( * )
    COMPLEX       AP( * ), WORK( * ), Z( LDZ, * )

PURPOSE

CHPEV computes all the eigenvalues and, optionally, eigen

vectors of a complex Hermitian matrix in packed storage.

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.

AP (input/output) COMPLEX array, dimension

(N*(N+1)/2)

On entry, the upper or lower triangle of the Her

mitian matrix A, packed columnwise in a linear array. The j-th

column of A is stored in the array AP as follows: if UPLO = 'U',

AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +

(j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

On exit, AP is overwritten by values generated

during the reduction to tridiagonal form. If UPLO = 'U', the di

agonal and first superdiagonal of the tridiagonal matrix T over

write the corresponding elements of A, and if UPLO = 'L', the di

agonal and first subdiagonal of T overwrite the corresponding el

ements of A.

W (output) REAL array, dimension (N)

If INFO = 0, the eigenvalues in ascending order.

Z (output) COMPLEX array, dimension (LDZ, N)

If JOBZ = 'V', then if INFO = 0, Z contains the

orthonormal eigenvectors of the matrix A, with the i-th column of

Z holding the eigenvector associated with W(i). If JOBZ = 'N',

then Z is not referenced.

LDZ (input) INTEGER

The leading dimension of the array Z. LDZ >= 1,

and if JOBZ = 'V', LDZ >= max(1,N).

WORK (workspace) COMPLEX array, dimension (max(1,

2*N-1))

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

CHPEV(3)