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    1:       SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
    2: *
    3: *  -- LAPACK routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       INTEGER            INFO, LDA, M, N
   10: *     ..
   11: *     .. Array Arguments ..
   12:       INTEGER            IPIV( * )
   13:       DOUBLE PRECISION   A( LDA, * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  DGETRF computes an LU factorization of a general M-by-N matrix A
   20: *  using partial pivoting with row interchanges.
   21: *
   22: *  The factorization has the form
   23: *     A = P * L * U
   24: *  where P is a permutation matrix, L is lower triangular with unit
   25: *  diagonal elements (lower trapezoidal if m > n), and U is upper
   26: *  triangular (upper trapezoidal if m < n).
   27: *
   28: *  This is the right-looking Level 3 BLAS version of the algorithm.
   29: *
   30: *  Arguments
   31: *  =========
   32: *
   33: *  M       (input) INTEGER
   34: *          The number of rows of the matrix A.  M >= 0.
   35: *
   36: *  N       (input) INTEGER
   37: *          The number of columns of the matrix A.  N >= 0.
   38: *
   39: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
   40: *          On entry, the M-by-N matrix to be factored.
   41: *          On exit, the factors L and U from the factorization
   42: *          A = P*L*U; the unit diagonal elements of L are not stored.
   43: *
   44: *  LDA     (input) INTEGER
   45: *          The leading dimension of the array A.  LDA >= max(1,M).
   46: *
   47: *  IPIV    (output) INTEGER array, dimension (min(M,N))
   48: *          The pivot indices; for 1 <= i <= min(M,N), row i of the
   49: *          matrix was interchanged with row IPIV(i).
   50: *
   51: *  INFO    (output) INTEGER
   52: *          = 0:  successful exit
   53: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   54: *          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization
   55: *                has been completed, but the factor U is exactly
   56: *                singular, and division by zero will occur if it is used
   57: *                to solve a system of equations.
   58: *
   59: *  =====================================================================
   60: *
   61: *     .. Parameters ..
   62:       DOUBLE PRECISION   ONE
   63:       PARAMETER          ( ONE = 1.0D+0 )
   64: *     ..
   65: *     .. Local Scalars ..
   66:       INTEGER            I, IINFO, J, JB, NB
   67: *     ..
   68: *     .. External Subroutines ..
   69:       EXTERNAL           DGEMM, DGETF2, DLASWP, DTRSM, XERBLA
   70: *     ..
   71: *     .. External Functions ..
   72:       INTEGER            ILAENV
   73:       EXTERNAL           ILAENV
   74: *     ..
   75: *     .. Intrinsic Functions ..
   76:       INTRINSIC          MAX, MIN
   77: *     ..
   78: *     .. Executable Statements ..
   79: *
   80: *     Test the input parameters.
   81: *
   82:       INFO = 0
   83:       IF( M.LT.0 ) THEN
   84:          INFO = -1
   85:       ELSE IF( N.LT.0 ) THEN
   86:          INFO = -2
   87:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
   88:          INFO = -4
   89:       END IF
   90:       IF( INFO.NE.0 ) THEN
   91:          CALL XERBLA( 'DGETRF', -INFO )
   92:          RETURN
   93:       END IF
   94: *
   95: *     Quick return if possible
   96: *
   97:       IF( M.EQ.0 .OR. N.EQ.0 )
   98:      $   RETURN
   99: *
  100: *     Determine the block size for this environment.
  101: *
  102:       NB = ILAENV( 1, 'DGETRF', ' ', M, N, -1, -1 )
  103:       IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
  104: *
  105: *        Use unblocked code.
  106: *
  107:          CALL DGETF2( M, N, A, LDA, IPIV, INFO )
  108:       ELSE
  109: *
  110: *        Use blocked code.
  111: *
  112:          DO 20 J = 1, MIN( M, N ), NB
  113:             JB = MIN( MIN( M, N )-J+1, NB )
  114: *
  115: *           Factor diagonal and subdiagonal blocks and test for exact
  116: *           singularity.
  117: *
  118:             CALL DGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
  119: *
  120: *           Adjust INFO and the pivot indices.
  121: *
  122:             IF( INFO.EQ.0 .AND. IINFO.GT.0 )
  123:      $         INFO = IINFO + J - 1
  124:             DO 10 I = J, MIN( M, J+JB-1 )
  125:                IPIV( I ) = J - 1 + IPIV( I )
  126:    10       CONTINUE
  127: *
  128: *           Apply interchanges to columns 1:J-1.
  129: *
  130:             CALL DLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
  131: *
  132:             IF( J+JB.LE.N ) THEN
  133: *
  134: *              Apply interchanges to columns J+JB:N.
  135: *
  136:                CALL DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
  137:      $                      IPIV, 1 )
  138: *
  139: *              Compute block row of U.
  140: *
  141:                CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,
  142:      $                     N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ),
  143:      $                     LDA )
  144:                IF( J+JB.LE.M ) THEN
  145: *
  146: *                 Update trailing submatrix.
  147: *
  148:                   CALL DGEMM( 'No transpose', 'No transpose', M-J-JB+1,
  149:      $                        N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA,
  150:      $                        A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ),
  151:      $                        LDA )
  152:                END IF
  153:             END IF
  154:    20    CONTINUE
  155:       END IF
  156:       RETURN
  157: *
  158: *     End of DGETRF
  159: *
  160:       END