sgetrf.f

          SUBROUTINE SGETRF( M, N, A, LDA, IPIV, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          INTEGER            INFO, LDA, M, N
    *     ..
    *     .. Array Arguments ..
          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 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.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ONE
          PARAMETER          ( ONE = 1.0E+0 )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, IINFO, J, JB, NB
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SGEMM, SGETF2, SLASWP, STRSM, XERBLA
    *     ..
    *     .. External Functions ..
          INTEGER            ILAENV
          EXTERNAL           ILAENV
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          IF( M.LT.0 ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
             INFO = -4
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'SGETRF', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( M.EQ.0 .OR. N.EQ.0 )
         $   RETURN
    *
    *     Determine the block size for this environment.
    *
          NB = ILAENV( 1, 'SGETRF', ' ', M, N, -1, -1 )
          IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
    *
    *        Use unblocked code.
    *
             CALL SGETF2( M, N, A, LDA, IPIV, INFO )
          ELSE
    *
    *        Use blocked code.
    *
             DO 20 J = 1, MIN( M, N ), NB
                JB = MIN( MIN( M, N )-J+1, NB )
    *
    *           Factor diagonal and subdiagonal blocks and test for exact
    *           singularity.
    *
                CALL SGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
    *
    *           Adjust INFO and the pivot indices.
    *
                IF( INFO.EQ.0 .AND. IINFO.GT.0 )
         $         INFO = IINFO + J - 1
                DO 10 I = J, MIN( M, J+JB-1 )
                   IPIV( I ) = J - 1 + IPIV( I )
       10       CONTINUE
    *
    *           Apply interchanges to columns 1:J-1.
    *
                CALL SLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
    *
                IF( J+JB.LE.N ) THEN
    *
    *              Apply interchanges to columns J+JB:N.
    *
                   CALL SLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
         $                      IPIV, 1 )
    *
    *              Compute block row of U.
    *
                   CALL STRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,
         $                     N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ),
         $                     LDA )
                   IF( J+JB.LE.M ) THEN
    *
    *                 Update trailing submatrix.
    *
                      CALL SGEMM( 'No transpose', 'No transpose', M-J-JB+1,
         $                        N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA,
         $                        A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ),
         $                        LDA )
                   END IF
                END IF
       20    CONTINUE
          END IF
          RETURN
    *
    *     End of SGETRF
    *
          END