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LAPACK version 3.0
sgetrf(3)

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

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

      INTEGER	     INFO, LDA, M, N

      INTEGER	     IPIV( * )

      REAL	     A( LDA, * )

DESCRIPTION
  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 illegal 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 occur if it is used to solve a system of equations.