LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
cgetrf.f
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00001 C> \brief \b CGETRF VARIANT: Crout Level 3 BLAS version of the algorithm.
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
00008 *  Definition:
00009 *  ===========
00010 *
00011 *       SUBROUTINE CGETRF ( M, N, A, LDA, IPIV, INFO)
00012 * 
00013 *       .. Scalar Arguments ..
00014 *       INTEGER            INFO, LDA, M, N
00015 *       ..
00016 *       .. Array Arguments ..
00017 *       INTEGER            IPIV( * )
00018 *       COMPLEX            A( LDA, * )
00019 *       ..
00020 *  
00021 *  Purpose
00022 *  =======
00023 *
00024 C>\details \b Purpose:
00025 C>\verbatim
00026 C>
00027 C> CGETRF computes an LU factorization of a general M-by-N matrix A
00028 C> using partial pivoting with row interchanges.
00029 C>
00030 C> The factorization has the form
00031 C>    A = P * L * U
00032 C> where P is a permutation matrix, L is lower triangular with unit
00033 C> diagonal elements (lower trapezoidal if m > n), and U is upper
00034 C> triangular (upper trapezoidal if m < n).
00035 C>
00036 C> This is the Crout Level 3 BLAS version of the algorithm.
00037 C>
00038 C>\endverbatim
00039 *
00040 *  Arguments:
00041 *  ==========
00042 *
00043 C> \param[in] M
00044 C> \verbatim
00045 C>          M is INTEGER
00046 C>          The number of rows of the matrix A.  M >= 0.
00047 C> \endverbatim
00048 C>
00049 C> \param[in] N
00050 C> \verbatim
00051 C>          N is INTEGER
00052 C>          The number of columns of the matrix A.  N >= 0.
00053 C> \endverbatim
00054 C>
00055 C> \param[in,out] A
00056 C> \verbatim
00057 C>          A is COMPLEX array, dimension (LDA,N)
00058 C>          On entry, the M-by-N matrix to be factored.
00059 C>          On exit, the factors L and U from the factorization
00060 C>          A = P*L*U; the unit diagonal elements of L are not stored.
00061 C> \endverbatim
00062 C>
00063 C> \param[in] LDA
00064 C> \verbatim
00065 C>          LDA is INTEGER
00066 C>          The leading dimension of the array A.  LDA >= max(1,M).
00067 C> \endverbatim
00068 C>
00069 C> \param[out] IPIV
00070 C> \verbatim
00071 C>          IPIV is INTEGER array, dimension (min(M,N))
00072 C>          The pivot indices; for 1 <= i <= min(M,N), row i of the
00073 C>          matrix was interchanged with row IPIV(i).
00074 C> \endverbatim
00075 C>
00076 C> \param[out] INFO
00077 C> \verbatim
00078 C>          INFO is INTEGER
00079 C>          = 0:  successful exit
00080 C>          < 0:  if INFO = -i, the i-th argument had an illegal value
00081 C>          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization
00082 C>                has been completed, but the factor U is exactly
00083 C>                singular, and division by zero will occur if it is used
00084 C>                to solve a system of equations.
00085 C> \endverbatim
00086 C>
00087 *
00088 *  Authors:
00089 *  ========
00090 *
00091 C> \author Univ. of Tennessee 
00092 C> \author Univ. of California Berkeley 
00093 C> \author Univ. of Colorado Denver 
00094 C> \author NAG Ltd. 
00095 *
00096 C> \date November 2011
00097 *
00098 C> \ingroup variantsGEcomputational
00099 *
00100 *  =====================================================================
00101       SUBROUTINE CGETRF ( M, N, A, LDA, IPIV, INFO)
00102 *
00103 *  -- LAPACK computational routine (version 3.1) --
00104 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00105 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00106 *     November 2011
00107 *
00108 *     .. Scalar Arguments ..
00109       INTEGER            INFO, LDA, M, N
00110 *     ..
00111 *     .. Array Arguments ..
00112       INTEGER            IPIV( * )
00113       COMPLEX            A( LDA, * )
00114 *     ..
00115 *
00116 *  =====================================================================
00117 *
00118 *     .. Parameters ..
00119       COMPLEX            ONE
00120       PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ) )
00121 *     ..
00122 *     .. Local Scalars ..
00123       INTEGER            I, IINFO, J, JB, NB
00124 *     ..
00125 *     .. External Subroutines ..
00126       EXTERNAL           CGEMM, CGETF2, CLASWP, CTRSM, XERBLA
00127 *     ..
00128 *     .. External Functions ..
00129       INTEGER            ILAENV
00130       EXTERNAL           ILAENV
00131 *     ..
00132 *     .. Intrinsic Functions ..
00133       INTRINSIC          MAX, MIN
00134 *     ..
00135 *     .. Executable Statements ..
00136 *
00137 *     Test the input parameters.
00138 *
00139       INFO = 0
00140       IF( M.LT.0 ) THEN
00141          INFO = -1
00142       ELSE IF( N.LT.0 ) THEN
00143          INFO = -2
00144       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00145          INFO = -4
00146       END IF
00147       IF( INFO.NE.0 ) THEN
00148          CALL XERBLA( 'CGETRF', -INFO )
00149          RETURN
00150       END IF
00151 *
00152 *     Quick return if possible
00153 *
00154       IF( M.EQ.0 .OR. N.EQ.0 )
00155      $   RETURN
00156 *
00157 *     Determine the block size for this environment.
00158 *
00159       NB = ILAENV( 1, 'CGETRF', ' ', M, N, -1, -1 )
00160       IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
00161 *
00162 *        Use unblocked code.
00163 *
00164          CALL CGETF2( M, N, A, LDA, IPIV, INFO )
00165       ELSE
00166 *
00167 *        Use blocked code.
00168 *
00169          DO 20 J = 1, MIN( M, N ), NB
00170             JB = MIN( MIN( M, N )-J+1, NB )
00171 *
00172 *           Update current block.
00173 *
00174             CALL CGEMM( 'No transpose', 'No transpose', 
00175      $                 M-J+1, JB, J-1, -ONE, 
00176      $                 A( J, 1 ), LDA, A( 1, J ), LDA, ONE,
00177      $                 A( J, J ), LDA )
00178             
00179 *
00180 *           Factor diagonal and subdiagonal blocks and test for exact
00181 *           singularity.
00182 *
00183             CALL CGETF2( 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 column 1:J-1            
00194 *
00195             CALL CLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
00196 *
00197             IF ( J+JB.LE.N ) THEN
00198 *            
00199 *              Apply interchanges to column J+JB:N            
00200 *
00201                CALL CLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, 
00202      $                     IPIV, 1 )
00203 *               
00204                CALL CGEMM( 'No transpose', 'No transpose', 
00205      $                    JB, N-J-JB+1, J-1, -ONE, 
00206      $                    A( J, 1 ), LDA, A( 1, J+JB ), LDA, ONE,
00207      $                    A( J, J+JB ), LDA )
00208 *
00209 *              Compute block row of U.
00210 *
00211                CALL CTRSM( 'Left', 'Lower', 'No transpose', 'Unit',
00212      $                    JB, N-J-JB+1, ONE, A( J, J ), LDA, 
00213      $                    A( J, J+JB ), LDA )
00214             END IF
00215 
00216    20    CONTINUE
00217 
00218       END IF
00219       RETURN
00220 *
00221 *     End of CGETRF
00222 *
00223       END
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