LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
dgetrf.f
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00001 *> \brief \b DGETRF
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *> \htmlonly
00009 *> Download DGETRF + dependencies 
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00011 *> [TGZ]</a> 
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00013 *> [ZIP]</a> 
00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetrf.f"> 
00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
00022 * 
00023 *       .. Scalar Arguments ..
00024 *       INTEGER            INFO, LDA, M, N
00025 *       ..
00026 *       .. Array Arguments ..
00027 *       INTEGER            IPIV( * )
00028 *       DOUBLE PRECISION   A( LDA, * )
00029 *       ..
00030 *  
00031 *
00032 *> \par Purpose:
00033 *  =============
00034 *>
00035 *> \verbatim
00036 *>
00037 *> DGETRF computes an LU factorization of a general M-by-N matrix A
00038 *> using partial pivoting with row interchanges.
00039 *>
00040 *> The factorization has the form
00041 *>    A = P * L * U
00042 *> where P is a permutation matrix, L is lower triangular with unit
00043 *> diagonal elements (lower trapezoidal if m > n), and U is upper
00044 *> triangular (upper trapezoidal if m < n).
00045 *>
00046 *> This is the right-looking Level 3 BLAS version of the algorithm.
00047 *> \endverbatim
00048 *
00049 *  Arguments:
00050 *  ==========
00051 *
00052 *> \param[in] M
00053 *> \verbatim
00054 *>          M is INTEGER
00055 *>          The number of rows of the matrix A.  M >= 0.
00056 *> \endverbatim
00057 *>
00058 *> \param[in] N
00059 *> \verbatim
00060 *>          N is INTEGER
00061 *>          The number of columns of the matrix A.  N >= 0.
00062 *> \endverbatim
00063 *>
00064 *> \param[in,out] A
00065 *> \verbatim
00066 *>          A is DOUBLE PRECISION array, dimension (LDA,N)
00067 *>          On entry, the M-by-N matrix to be factored.
00068 *>          On exit, the factors L and U from the factorization
00069 *>          A = P*L*U; the unit diagonal elements of L are not stored.
00070 *> \endverbatim
00071 *>
00072 *> \param[in] LDA
00073 *> \verbatim
00074 *>          LDA is INTEGER
00075 *>          The leading dimension of the array A.  LDA >= max(1,M).
00076 *> \endverbatim
00077 *>
00078 *> \param[out] IPIV
00079 *> \verbatim
00080 *>          IPIV is INTEGER array, dimension (min(M,N))
00081 *>          The pivot indices; for 1 <= i <= min(M,N), row i of the
00082 *>          matrix was interchanged with row IPIV(i).
00083 *> \endverbatim
00084 *>
00085 *> \param[out] INFO
00086 *> \verbatim
00087 *>          INFO is INTEGER
00088 *>          = 0:  successful exit
00089 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
00090 *>          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization
00091 *>                has been completed, but the factor U is exactly
00092 *>                singular, and division by zero will occur if it is used
00093 *>                to solve a system of equations.
00094 *> \endverbatim
00095 *
00096 *  Authors:
00097 *  ========
00098 *
00099 *> \author Univ. of Tennessee 
00100 *> \author Univ. of California Berkeley 
00101 *> \author Univ. of Colorado Denver 
00102 *> \author NAG Ltd. 
00103 *
00104 *> \date November 2011
00105 *
00106 *> \ingroup doubleGEcomputational
00107 *
00108 *  =====================================================================
00109       SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO )
00110 *
00111 *  -- LAPACK computational routine (version 3.4.0) --
00112 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00113 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00114 *     November 2011
00115 *
00116 *     .. Scalar Arguments ..
00117       INTEGER            INFO, LDA, M, N
00118 *     ..
00119 *     .. Array Arguments ..
00120       INTEGER            IPIV( * )
00121       DOUBLE PRECISION   A( LDA, * )
00122 *     ..
00123 *
00124 *  =====================================================================
00125 *
00126 *     .. Parameters ..
00127       DOUBLE PRECISION   ONE
00128       PARAMETER          ( ONE = 1.0D+0 )
00129 *     ..
00130 *     .. Local Scalars ..
00131       INTEGER            I, IINFO, J, JB, NB
00132 *     ..
00133 *     .. External Subroutines ..
00134       EXTERNAL           DGEMM, DGETF2, DLASWP, DTRSM, XERBLA
00135 *     ..
00136 *     .. External Functions ..
00137       INTEGER            ILAENV
00138       EXTERNAL           ILAENV
00139 *     ..
00140 *     .. Intrinsic Functions ..
00141       INTRINSIC          MAX, MIN
00142 *     ..
00143 *     .. Executable Statements ..
00144 *
00145 *     Test the input parameters.
00146 *
00147       INFO = 0
00148       IF( M.LT.0 ) THEN
00149          INFO = -1
00150       ELSE IF( N.LT.0 ) THEN
00151          INFO = -2
00152       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00153          INFO = -4
00154       END IF
00155       IF( INFO.NE.0 ) THEN
00156          CALL XERBLA( 'DGETRF', -INFO )
00157          RETURN
00158       END IF
00159 *
00160 *     Quick return if possible
00161 *
00162       IF( M.EQ.0 .OR. N.EQ.0 )
00163      $   RETURN
00164 *
00165 *     Determine the block size for this environment.
00166 *
00167       NB = ILAENV( 1, 'DGETRF', ' ', M, N, -1, -1 )
00168       IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
00169 *
00170 *        Use unblocked code.
00171 *
00172          CALL DGETF2( M, N, A, LDA, IPIV, INFO )
00173       ELSE
00174 *
00175 *        Use blocked code.
00176 *
00177          DO 20 J = 1, MIN( M, N ), NB
00178             JB = MIN( MIN( M, N )-J+1, NB )
00179 *
00180 *           Factor diagonal and subdiagonal blocks and test for exact
00181 *           singularity.
00182 *
00183             CALL DGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
00184 *
00185 *           Adjust INFO and the pivot indices.
00186 *
00187             IF( INFO.EQ.0 .AND. IINFO.GT.0 )
00188      $         INFO = IINFO + J - 1
00189             DO 10 I = J, MIN( M, J+JB-1 )
00190                IPIV( I ) = J - 1 + IPIV( I )
00191    10       CONTINUE
00192 *
00193 *           Apply interchanges to columns 1:J-1.
00194 *
00195             CALL DLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
00196 *
00197             IF( J+JB.LE.N ) THEN
00198 *
00199 *              Apply interchanges to columns J+JB:N.
00200 *
00201                CALL DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
00202      $                      IPIV, 1 )
00203 *
00204 *              Compute block row of U.
00205 *
00206                CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,
00207      $                     N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ),
00208      $                     LDA )
00209                IF( J+JB.LE.M ) THEN
00210 *
00211 *                 Update trailing submatrix.
00212 *
00213                   CALL DGEMM( 'No transpose', 'No transpose', M-J-JB+1,
00214      $                        N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA,
00215      $                        A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ),
00216      $                        LDA )
00217                END IF
00218             END IF
00219    20    CONTINUE
00220       END IF
00221       RETURN
00222 *
00223 *     End of DGETRF
00224 *
00225       END
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