man chpev (Fonctions bibliothèques) - compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage

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, 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.