.TH ZHPEV 1 "November 2006" " LAPACK driver routine (version 3.1) " " LAPACK driver routine (version 3.1) "
.SH NAME
ZHPEV - all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage
.SH SYNOPSIS
.TP 18
SUBROUTINE ZHPEV(
JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
INFO )
.TP 18
.ti +4
CHARACTER
JOBZ, UPLO
.TP 18
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INTEGER
INFO, LDZ, N
.TP 18
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DOUBLE
PRECISION RWORK( * ), W( * )
.TP 18
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COMPLEX*16
AP( * ), WORK( * ), Z( LDZ, * )
.SH PURPOSE
ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix in packed storage.
.SH ARGUMENTS
.TP 8
JOBZ (input) CHARACTER*1
= \(aqN\(aq: Compute eigenvalues only;
.br
= \(aqV\(aq: Compute eigenvalues and eigenvectors.
.TP 8
UPLO (input) CHARACTER*1
.br
= \(aqU\(aq: Upper triangle of A is stored;
.br
= \(aqL\(aq: Lower triangle of A is stored.
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
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 = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = \(aqL\(aq, 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 = \(aqU\(aq, the diagonal
and first superdiagonal of the tridiagonal matrix T overwrite
the corresponding elements of A, and if UPLO = \(aqL\(aq, the
diagonal and first subdiagonal of T overwrite the
corresponding elements of A.
.TP 8
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
.TP 8
Z (output) COMPLEX*16 array, dimension (LDZ, N)
If JOBZ = \(aqV\(aq, 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 = \(aqN\(aq, then Z is not referenced.
.TP 8
LDZ (input) INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = \(aqV\(aq, LDZ >= max(1,N).
.TP 8
WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1))
.TP 8
RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
.TP 8
INFO (output) INTEGER
= 0: successful exit.
.br
< 0: if INFO = -i, the i-th argument had an illegal value.
.br
> 0: if INFO = i, the algorithm failed to converge; i
off-diagonal elements of an intermediate tridiagonal
form did not converge to zero.