CHPEV(3f)

NAME
CHPEV - 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, eigenvectors 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 Hermitian 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 diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements 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 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.