CHEGV - 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 CHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
WORK, LWORK, RWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
REAL RWORK( * ), W( * )
COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
PURPOSE
CHEGV 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 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.
On exit, if JOBZ = 'V', then if INFO = 0, A
vectors 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 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) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) COMPLEX 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 CHETRD
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) REAL array, dimension (max(1, 3*N-2))
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
<= N: if INFO = i, CHEEV 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.
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