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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DGETF2 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DGETF2 + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetf2.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetf2.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetf2.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE DGETF2( 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 *> DGETF2 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 2 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 = -k, the k-th argument had an illegal value 00090 *> > 0: if INFO = k, U(k,k) 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 DGETF2( 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, ZERO 00128 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00129 * .. 00130 * .. Local Scalars .. 00131 DOUBLE PRECISION SFMIN 00132 INTEGER I, J, JP 00133 * .. 00134 * .. External Functions .. 00135 DOUBLE PRECISION DLAMCH 00136 INTEGER IDAMAX 00137 EXTERNAL DLAMCH, IDAMAX 00138 * .. 00139 * .. External Subroutines .. 00140 EXTERNAL DGER, DSCAL, DSWAP, XERBLA 00141 * .. 00142 * .. Intrinsic Functions .. 00143 INTRINSIC MAX, MIN 00144 * .. 00145 * .. Executable Statements .. 00146 * 00147 * Test the input parameters. 00148 * 00149 INFO = 0 00150 IF( M.LT.0 ) THEN 00151 INFO = -1 00152 ELSE IF( N.LT.0 ) THEN 00153 INFO = -2 00154 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 00155 INFO = -4 00156 END IF 00157 IF( INFO.NE.0 ) THEN 00158 CALL XERBLA( 'DGETF2', -INFO ) 00159 RETURN 00160 END IF 00161 * 00162 * Quick return if possible 00163 * 00164 IF( M.EQ.0 .OR. N.EQ.0 ) 00165 $ RETURN 00166 * 00167 * Compute machine safe minimum 00168 * 00169 SFMIN = DLAMCH('S') 00170 * 00171 DO 10 J = 1, MIN( M, N ) 00172 * 00173 * Find pivot and test for singularity. 00174 * 00175 JP = J - 1 + IDAMAX( M-J+1, A( J, J ), 1 ) 00176 IPIV( J ) = JP 00177 IF( A( JP, J ).NE.ZERO ) THEN 00178 * 00179 * Apply the interchange to columns 1:N. 00180 * 00181 IF( JP.NE.J ) 00182 $ CALL DSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA ) 00183 * 00184 * Compute elements J+1:M of J-th column. 00185 * 00186 IF( J.LT.M ) THEN 00187 IF( ABS(A( J, J )) .GE. SFMIN ) THEN 00188 CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 ) 00189 ELSE 00190 DO 20 I = 1, M-J 00191 A( J+I, J ) = A( J+I, J ) / A( J, J ) 00192 20 CONTINUE 00193 END IF 00194 END IF 00195 * 00196 ELSE IF( INFO.EQ.0 ) THEN 00197 * 00198 INFO = J 00199 END IF 00200 * 00201 IF( J.LT.MIN( M, N ) ) THEN 00202 * 00203 * Update trailing submatrix. 00204 * 00205 CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA, 00206 $ A( J+1, J+1 ), LDA ) 00207 END IF 00208 10 CONTINUE 00209 RETURN 00210 * 00211 * End of DGETF2 00212 * 00213 END