SSYGV - 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 SSYGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
WORK, LWORK, INFO )
CHARACTER JOBZ, UPLO
INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
REAL A( LDA, * ), B( LDB, * ), W( * ), WORK(
* )
PURPOSE
SSYGV 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) REAL 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 con
tains the matrix Z of eigenvectors. The
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 trian
gle (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) REAL 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) REAL array, dimension (N)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace/output) REAL 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 SSYTRD
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: SPOTRF or SSYEV returned an error code:
<= N: if INFO = i, SSYEV failed to converge; i
off-diagonal elements of an intermediate
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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