
ZHEGV(l) ) ZHEGV(l)
NAME
ZHEGV  compute all the eigenvalues, and optionally, the eigenvectors of a complex gener
alized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
SYNOPSIS
SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
PURPOSE
ZHEGV computes all the eigenvalues, and optionally, the eigenvectors of a complex general
ized Hermitiandefinite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x. Here A and B are assumed to be Hermitian and B is also
positive definite.
ARGUMENTS
ITYPE (input) INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
JOBZ (input) CHARACTER*1
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
UPLO (input) CHARACTER*1
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) INTEGER
The order of the matrices A and B. 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 matrix Z of eigenvectors.
The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**H*B*Z = I; if
ITYPE = 3, Z**H*inv(B)*Z = I. If JOBZ = 'N', then on exit the upper triangle (if
UPLO='U') or the lower triangle (if UPLO='L') of A, including the diagonal, is
destroyed.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input/output) COMPLEX*16 array, dimension (LDB, N)
On entry, the Hermitian positive definite matrix B. If UPLO = 'U', the leading N
byN upper triangular part of B contains the upper triangular part of the matrix
B. If UPLO = 'L', the leading NbyN lower triangular part of B contains the
lower triangular part of the matrix B.
On exit, if INFO <= N, the part of B containing the matrix is overwritten by the
triangular factor U or L from the Cholesky factorization B = U**H*U or B = L*L**H.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= 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. LWORK >= max(1,2*N1). For optimal efficiency,
LWORK >= (NB+1)*N, where NB is the blocksize for ZHETRD returned by ILAENV.
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) DOUBLE PRECISION array, dimension (max(1, 3*N2))
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: ZPOTRF or ZHEEV returned an error code:
<= N: if INFO = i, ZHEEV failed to converge; i offdiagonal elements of an inter
mediate tridiagonal form did not converge to zero; > N: if INFO = N + i, for 1
<= i <= N, then the leading minor of order i of B is not positive definite. The
factorization of B could not be completed and no eigenvalues or eigenvectors were
computed.
LAPACK version 3.0 15 June 2000 ZHEGV(l) 
