DSYGV - compute all the eigenvalues, and optionally, the
eigenvectors of a real generalized symmetric-definite
eigenproblem, of the form A*x=(lambda)*B*x,
A*Bx=(lambda)*x, or B*A*x=(lambda)*x
SYNOPSIS
SUBROUTINE DSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
WORK, LWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( *
), WORK( * )
PURPOSE
DSYGV computes all the eigenvalues, and optionally, the
eigenvectors of a real generalized symmetric-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 symmetric 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) DOUBLE PRECISION array, dimension
(LDA, N)
On entry, the symmetric 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**T*B*Z = I; if ITYPE = 3, Z**T*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) DOUBLE PRECISION array, dimension
(LDB, N)
On entry, the symmetric 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**T*U
or B = L*L**T.
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) DOUBLE PRECISION 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(1,3*N-1). For optimal efficiency, LWORK >=
(NB+2)*N, where NB is the blocksize for DSYTRD
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.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille
gal value
> 0: DPOTRF or DSYEV returned an error code:
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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