ZGETC2  - compute an LU factorization, using complete piv­
       oting, of the n-by-n matrix A


SYNOPSIS

       SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )

           INTEGER        INFO, LDA, N

           INTEGER        IPIV( * ), JPIV( * )

           COMPLEX*16     A( LDA, * )


PURPOSE

       ZGETC2 computes an LU factorization, using complete pivot­
       ing,  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 ele­
       ments and U is upper triangular.

       This is a level 1 BLAS version of the algorithm.


ARGUMENTS

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

       A       (input/output) COMPLEX*16 array, dimension (LDA,
               N)
               On  entry,  the  n-by-n matrix 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, giving a non­
               singular 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
               overflow if one tries 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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