DSYGS2 (3lapack)

reduce a real symmetric-definite generalized eigenproblem 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 eigenproblem 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 contains 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 triangular 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 factorization 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.