
ZHPEVD(l) ) ZHPEVD(l)
NAME
ZHPEVD  compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian
matrix A in packed storage
SYNOPSIS
SUBROUTINE ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
LIWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
PURPOSE
ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian
matrix A in packed storage. If eigenvectors are desired, it uses a divide and conquer
algorithm.
The divide and conquer algorithm makes very mild assumptions about floating point arith
metic. It will work on machines with a guard digit in add/subtract, or on those binary
machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C90, or
Cray2. It could conceivably fail on hexadecimal or decimal machines without guard digits,
but we know of none.
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*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 jth column of A is stored in the array AP as follows: if
UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
(j1)*(2*nj)/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 diago
nal 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 = 'V', then if INFO = 0, Z contains the orthonormal eigenvectors of the
matrix A, with the ith 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/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of array WORK. If N <= 1, LWORK must be at least 1.
If JOBZ = 'N' and N > 1, LWORK must be at least N. If JOBZ = 'V' and N > 1, LWORK
must be at least 2*N.
If LWORK = 1, then a workspace query is assumed; the routine only calculates the
optimal size of the WORK array, returns this value as the first entry of the WORK
array, and no error message related to LWORK is issued by XERBLA.
RWORK (workspace/output) DOUBLE PRECISION array,
dimension (LRWORK) On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
LRWORK (input) INTEGER
The dimension of array RWORK. If N <= 1, LRWORK must be at least 1.
If JOBZ = 'N' and N > 1, LRWORK must be at least N. If JOBZ = 'V' and N > 1,
LRWORK must be at least 1 + 5*N + 2*N**2.
If LRWORK = 1, then a workspace query is assumed; the routine only calculates the
optimal size of the RWORK array, returns this value as the first entry of the
RWORK array, and no error message related to LRWORK is issued by XERBLA.
IWORK (workspace/output) INTEGER array, dimension (LIWORK)
On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
LIWORK (input) INTEGER
The dimension of array IWORK. If JOBZ = 'N' or N <= 1, LIWORK must be at least
1. If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
If LIWORK = 1, then a workspace query is assumed; the routine only calculates the
optimal size of the IWORK array, returns this value as the first entry of the
IWORK array, and no error message related to LIWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value.
> 0: if INFO = i, the algorithm failed to converge; i offdiagonal elements of an
intermediate tridiagonal form did not converge to zero.
LAPACK version 3.0 15 June 2000 ZHPEVD(l) 
