Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  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

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 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**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 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 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 (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(1,3*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 illegal value
                > 0:  DPOTRF or DSYEV returned an error code:
                <= N:  if INFO = i, DSYEV 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 3.3.1)      April 2011                             DSYGV(3lapack)