dgetrf.f

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      SUBROUTINE DGETRF ( M, N, A, LDA, IPIV, INFO)
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     March 2008
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, M, N
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * )
*     ..
*
*  Purpose
*  =======
*
*  DGETRF 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 left-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) DOUBLE PRECISION 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 ..
      DOUBLE PRECISION   ONE
      PARAMETER          ( ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, IINFO, J, JB, K, NB
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEMM, DGETF2, DLASWP, DTRSM, 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( 'DGETRF', -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, 'DGETRF', ' ', M, N, -1, -1 )
      IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
*
*        Use unblocked code.
*
         CALL DGETF2( 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 )
*
*           Update before factoring the current panel
*
            DO 30 K = 1, J-NB, NB
*            
*              Apply interchanges to rows K:K+NB-1.
* 
               CALL DLASWP( JB, A(1, J), LDA, K, K+NB-1, IPIV, 1 )
*
*              Compute block row of U.
*
               CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
     $                    NB, JB, ONE, A( K, K ), LDA, 
     $                    A( K, J ), LDA )
*
*              Update trailing submatrix.
*
               CALL DGEMM( 'No transpose', 'No transpose', 
     $                    M-K-NB+1, JB, NB, -ONE, 
     $                    A( K+NB, K ), LDA, A( K, J ), LDA, ONE,
     $                    A( K+NB, J ), LDA )
   30       CONTINUE
*
*           Factor diagonal and subdiagonal blocks and test for exact
*           singularity.
*
            CALL DGETF2( 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
*
   20    CONTINUE

*
*        Apply interchanges to the left-overs
*
         DO 40 K = 1, MIN( M, N ), NB
            CALL DLASWP( K-1, A( 1, 1 ), LDA, K, 
     $                  MIN (K+NB-1, MIN ( M, N )), IPIV, 1 )
   40    CONTINUE 
*
*        Apply update to the M+1:N columns when N > M
*
         IF ( N.GT.M ) THEN

            CALL DLASWP( N-M, A(1, M+1), LDA, 1, M, IPIV, 1 )

            DO 50 K = 1, M, NB

               JB = MIN( M-K+1, NB )
*
               CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
     $                    JB, N-M, ONE, A( K, K ), LDA, 
     $                    A( K, M+1 ), LDA )

*     
               IF ( K+NB.LE.M ) THEN
                    CALL DGEMM( 'No transpose', 'No transpose', 
     $                         M-K-NB+1, N-M, NB, -ONE, 
     $                         A( K+NB, K ), LDA, A( K, M+1 ), LDA, ONE,
     $                        A( K+NB, M+1 ), LDA )
               END IF
   50       CONTINUE  
         END IF
*
      END IF
      RETURN
*
*     End of DGETRF
*
      END