ZGETRF  -  compute an LU factorization of a general M-by-N
       matrix A using partial pivoting with row interchanges


SYNOPSIS

       SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO )

           INTEGER        INFO, LDA, M, N

           INTEGER        IPIV( * )

           COMPLEX*16     A( LDA, * )


PURPOSE

       ZGETRF computes an LU factorization of  a  general  M-by-N
       matrix  A  using  partial  pivoting with row interchanges.
       The factorization has the form
          A = P * L * U
       where P is a permutation matrix,  L  is  lower  triangular
       with  unit diagonal elements (lower trapezoidal if m > n),
       and U is upper triangular (upper trapezoidal if m < n).

       This is the right-looking Level  3  BLAS  version  of  the
       algorithm.


ARGUMENTS

       M       (input) INTEGER
               The number of rows of the matrix A.  M >= 0.

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

       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
               On entry, the M-by-N matrix to  be  factored.   On
               exit, the factors L and U from the factorization A
               = P*L*U; the unit diagonal elements of L  are  not
               stored.

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

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

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value
               > 0:  if INFO = i, U(i,i)  is  exactly  zero.  The
               factorization has been completed, but the factor U
               is exactly singular, and  division  by  zero  will

               tions.


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