NAME

       dsygv.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dsygv (ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, INFO)
           DSYGST

Function/Subroutine Documentation

   subroutine dsygv (integerITYPE, characterJOBZ, characterUPLO, integerN, double precision,
       dimension( lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB,
       double precision, dimension( * )W, double precision, dimension( * )WORK, integerLWORK,
       integerINFO)
       DSYGST

       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.

       Parameters:
           ITYPE

                     ITYPE is 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

                     JOBZ is CHARACTER*1
                     = 'N':  Compute eigenvalues only;
                     = 'V':  Compute eigenvalues and eigenvectors.

           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangles of A and B are stored;
                     = 'L':  Lower triangles of A and B are stored.

           N

                     N is INTEGER
                     The order of the matrices A and B.  N >= 0.

           A

                     A is 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

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

           B

                     B is 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

                     LDB is INTEGER
                     The leading dimension of the array B.  LDB >= max(1,N).

           W

                     W is DOUBLE PRECISION array, dimension (N)
                     If INFO = 0, the eigenvalues in ascending order.

           WORK

                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is 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

                     INFO is 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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Definition at line 175 of file dsygv.f.

Author

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