DGETC2  - compute an LU factorization with complete pivot­
       ing of the n-by-n matrix A


SYNOPSIS

       SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )

           INTEGER        INFO, LDA, N

           INTEGER        IPIV( * ), JPIV( * )

           DOUBLE         PRECISION A( LDA, * )


PURPOSE

       DGETC2 computes an LU factorization with complete pivoting
       of the n-by-n matrix A. The factorization has the form A =
       P * L * U * Q, where P and Q are permutation  matrices,  L
       is  lower  triangular with unit diagonal elements and U is
       upper triangular.

       This is the Level 2 BLAS algorithm.


ARGUMENTS

       N       (input) INTEGER
               The order of the matrix A. N >= 0.

       A       (input/output) DOUBLE PRECISION array, dimension
               (LDA, N)
               On entry, the n-by-n matrix A to be factored.   On
               exit, the factors L and U from the factorization A
               = P*L*U*Q; the unit diagonal elements of L are not
               stored.   If U(k, k) appears to be less than SMIN,
               U(k, k) is given the value of SMIN, i.e., giving a
               nonsingular perturbed system.

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

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

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

       INFO    (output) INTEGER
               = 0: successful exit
               >  0:  if  INFO  = k, U(k, k) is likely to produce
               owerflow if we try to solve for x in Ax = b. So  U
               is perturbed to avoid the overflow.

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


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