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sgetrf

 NAME
      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 algo-
      rithm.

 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 illegal
              value

              > 0:  if INFO = i, U(i,i) is exactly zero. The fac-
              torization has been completed, but the factor U is
              exactly singular, and division by zero will occur if
              it is used to solve a system of equations.