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


SYNOPSIS

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

           INTEGER        INFO, LDA, M, N

           INTEGER        IPIV( * )

           REAL           A( LDA, * )


PURPOSE

       SGETRF 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) REAL 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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