ZHEGV - compute 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 con
tains 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.
tains the matrix Z of eigenvectors. The eigenvec
tors 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-by-N upper trian
gular 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 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*N-1). 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*N-2))
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
> 0: ZPOTRF or ZHEEV returned an error code:
<= N: if INFO = i, ZHEEV failed to converge; i
off-diagonal elements of an intermediate tridiago
nal 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.
Man(1) output converted with
man2html