# zhpev (l) - Linux Man Pages

## NAME

ZHPEV - computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage

## SYNOPSIS

SUBROUTINE ZHPEV(
JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, INFO )

CHARACTER JOBZ, UPLO

INTEGER INFO, LDZ, N

DOUBLE PRECISION RWORK( * ), W( * )

COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )

## PURPOSE

ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage.

## ARGUMENTS

JOBZ (input) CHARACTER*1
= aqNaq: Compute eigenvalues only;
= aqVaq: Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1

= aqUaq: Upper triangle of A is stored;
= aqLaq: Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) COMPLEX*16 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 = aqUaq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = aqLaq, 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 = aqUaq, the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = aqLaq, the diagonal and first subdiagonal of T overwrite the corresponding elements of A.
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
Z (output) COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = aqVaq, 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 = aqNaq, then Z is not referenced.
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if JOBZ = aqVaq, LDZ >= max(1,N).
WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
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 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.