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dsygv

 NAME
      DSYGV - compute all the eigenvalues, and optionally, the
      eigenvectors of a real generalized symmetric-definite eigen-
      problem, 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 eigen-
      problem, 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 matrix A.  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 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 matrix B.  If UPLO = 'U',
              the leading N-by-N upper triangular part of B con-
              tains 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) 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.

      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.