zheevd(3)

NAME

ZHEEVD - compute all eigenvalues and, optionally, eigen

vectors 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, eigenvec

tors of a complex Hermitian matrix A. If eigenvectors are de

sired, it uses a divide and conquer algorithm.

The divide and conquer algorithm makes very mild assump

tions about floating point arithmetic. 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 X-MP, Cray Y

MP, Cray C-90, or Cray-2. It could conceivably fail on hexadeci

mal 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 N-by-N upper triangular part of A contains the upper

triangular part of the matrix A. If UPLO = 'L', the leading N

by-N 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 de

stroyed.

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 (LI

WORK)

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 i-th argument had an ille

gal value
> 0: if INFO = i, the algorithm failed to con

verge; i off-diagonal 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(3)