DSYGS2(3f)               LAPACK routine (version 3.1)               DSYGS2(3f)



NAME
       DSYGS2 - 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*1
               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.



 LAPACK routine (version 3.1)    November 2006                      DSYGS2(3f)
