
ZHEEVD(l) ) ZHEEVD(l)
NAME
ZHEEVD  compute all eigenvalues and, optionally, eigenvectors of a complex Hermitian
matrix A
SYNOPSIS
SUBROUTINE ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK,
INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
INTEGER IWORK( * )
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 A( LDA, * ), WORK( * )
PURPOSE
ZHEEVD computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian
matrix A. 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.
A (input/output) COMPLEX*16 array, dimension (LDA, N)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading NbyN upper trian
gular part of A contains the upper triangular part of the matrix A. If UPLO =
'L', the leading NbyN lower triangular part of A contains the lower triangular
part of the matrix A. On exit, if JOBZ = 'V', then if INFO = 0, A contains the
orthonormal eigenvectors of the matrix A. If JOBZ = 'N', then on exit the lower
triangle (if UPLO='L') or the upper triangle (if UPLO='U') of A, including the
diagonal, is destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
W (output) DOUBLE PRECISION array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The length of the array WORK. If N <= 1, LWORK must be at least 1.
If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. If JOBZ = 'V' and N > 1,
LWORK must be at least 2*N + N**2.
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 the 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 the array IWORK. If N <= 1, LIWORK must be at
least 1. If JOBZ = 'N' and 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.
FURTHER DETAILS
Based on contributions by
Jeff Rutter, Computer Science Division, University of California
at Berkeley, USA
LAPACK version 3.0 15 June 2000 ZHEEVD(l) 
