ZHEGV(1) LAPACK driver routine (version 3.2) ZHEGV(1)NAME
ZHEGV - computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite 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 generalized Hermitian-definite 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
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 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 tri‐
angle (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-by-N upper triangular part of B contains the
upper triangular part of the matrix B. If UPLO = 'L', the
leading N-by-N 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 triangu‐
lar 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 (MAX(1,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*N-1). For
optimal efficiency, LWORK >= (NB+1)*N, where NB is the block‐
size 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*N-2))
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: ZPOTRF or ZHEEV returned an error code:
<= N: if INFO = i, ZHEEV failed to converge; i off-diagonal
elements of an intermediate 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 driver routine (version 3November 2008 ZHEGV(1)
