DGESC2  -  solve  a  system  of  linear equations  A * X =
       scale* RHS  with a general N-by-N matrix A  using  the  LU
       factorization with complete pivoting computed by DGETC2


SYNOPSIS

       SUBROUTINE DGESC2( N, A, LDA, RHS, IPIV, JPIV, SCALE )

           INTEGER        LDA, N

           DOUBLE         PRECISION SCALE

           INTEGER        IPIV( * ), JPIV( * )

           DOUBLE         PRECISION A( LDA, * ), RHS( * )


PURPOSE

       DGESC2  solves a system of linear equations A * X = scale*
       RHS with a general N-by-N matrix A using the LU factoriza­
       tion with complete pivoting computed by DGETC2.


ARGUMENTS

       N       (input) INTEGER
               The order of the matrix A.

       A       (input) DOUBLE PRECISION array, dimension (LDA,N)
               On entry, the  LU part of the factorization of the
               n-by-n matrix A computed by DGETC2:  A = P * L * U
               * Q

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

       RHS     (input/output) DOUBLE PRECISION array, dimension
               (N).
               On  entry, the right hand side vector b.  On exit,
               the solution vector X.

       IPIV    (iput) INTEGER array, dimension (N).
               The pivot indices; for 1 <= i <= N, row i  of  the
               matrix has been interchanged with row IPIV(i).

       JPIV    (iput) INTEGER array, dimension (N).
               The  pivot  indices;  for 1 <= j <= N, column j of
               the  matrix  has  been  interchanged  with  column
               JPIV(j).

       SCALE    (output) DOUBLE PRECISION
                On  exit,  SCALE contains the scale factor. SCALE
                is chosen 0 <= SCALE <= 1 to prevent owerflow  in
                the solution.

       Based on contributions by
          Bo  Kagstrom and Peter Poromaa, Department of Computing
       Science,
          Umea University, S-901 87 Umea, Sweden.


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