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dsygs2

 NAME
      DSYGS2 - reduce a real symmetric-definite generalized eigen-
      problem to standard form

 SYNOPSIS
      SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )

          CHARACTER      UPLO

          INTEGER        INFO, ITYPE, LDA, LDB, N

          DOUBLE         PRECISION A( LDA, * ), B( LDB, * )

 PURPOSE
      DSYGS2 reduces a real symmetric-definite generalized eigen-
      problem to standard form.

      If ITYPE = 1, the problem is A*x = lambda*B*x,
      and A is overwritten by inv(U')*A*inv(U) or inv(L)*A*inv(L')

      If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
      B*A*x = lambda*x, and A is overwritten by U*A*U` or L'*A*L.

      B must have been previously factorized as U'*U or L*L' by
      DPOTRF.

 ARGUMENTS
      ITYPE   (input) INTEGER
              = 1: compute inv(U')*A*inv(U) or inv(L)*A*inv(L');
              = 2 or 3: compute U*A*U' or L'*A*L.

      UPLO    (input) CHARACTER
              Specifies whether the upper or lower triangular part
              of the symmetric matrix A is stored, and how B has
              been factorized.  = 'U':  Upper triangular
              = 'L':  Lower triangular

      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, and
              the strictly lower triangular part of A is not
              referenced.  If UPLO = 'L', the leading n by n lower
              triangular part of A contains the lower triangular
              part of the matrix A, and the strictly upper tri-
              angular part of A is not referenced.

              On exit, if INFO = 0, the transformed matrix, stored

              in the same format as A.

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

      B       (input) DOUBLE PRECISION array, dimension (LDB,N)
              The triangular factor from the Cholesky factoriza-
              tion of B, as returned by DPOTRF.

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

      INFO    (output) INTEGER
              = 0:  successful exit.
              < 0:  if INFO = -i, the i-th argument had an illegal
              value.