1*> \brief \b ZGETRF 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8*> \htmlonly 9*> Download ZGETRF + dependencies 10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgetrf.f"> 11*> [TGZ]</a> 12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgetrf.f"> 13*> [ZIP]</a> 14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgetrf.f"> 15*> [TXT]</a> 16*> \endhtmlonly 17* 18* Definition: 19* =========== 20* 21* SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO ) 22* 23* .. Scalar Arguments .. 24* INTEGER INFO, LDA, M, N 25* .. 26* .. Array Arguments .. 27* INTEGER IPIV( * ) 28* COMPLEX*16 A( LDA, * ) 29* .. 30* 31* 32*> \par Purpose: 33* ============= 34*> 35*> \verbatim 36*> 37*> ZGETRF computes an LU factorization of a general M-by-N matrix A 38*> using partial pivoting with row interchanges. 39*> 40*> The factorization has the form 41*> A = P * L * U 42*> where P is a permutation matrix, L is lower triangular with unit 43*> diagonal elements (lower trapezoidal if m > n), and U is upper 44*> triangular (upper trapezoidal if m < n). 45*> 46*> This is the right-looking Level 3 BLAS version of the algorithm. 47*> \endverbatim 48* 49* Arguments: 50* ========== 51* 52*> \param[in] M 53*> \verbatim 54*> M is INTEGER 55*> The number of rows of the matrix A. M >= 0. 56*> \endverbatim 57*> 58*> \param[in] N 59*> \verbatim 60*> N is INTEGER 61*> The number of columns of the matrix A. N >= 0. 62*> \endverbatim 63*> 64*> \param[in,out] A 65*> \verbatim 66*> A is COMPLEX*16 array, dimension (LDA,N) 67*> On entry, the M-by-N matrix to be factored. 68*> On exit, the factors L and U from the factorization 69*> A = P*L*U; the unit diagonal elements of L are not stored. 70*> \endverbatim 71*> 72*> \param[in] LDA 73*> \verbatim 74*> LDA is INTEGER 75*> The leading dimension of the array A. LDA >= max(1,M). 76*> \endverbatim 77*> 78*> \param[out] IPIV 79*> \verbatim 80*> IPIV is INTEGER array, dimension (min(M,N)) 81*> The pivot indices; for 1 <= i <= min(M,N), row i of the 82*> matrix was interchanged with row IPIV(i). 83*> \endverbatim 84*> 85*> \param[out] INFO 86*> \verbatim 87*> INFO is INTEGER 88*> = 0: successful exit 89*> < 0: if INFO = -i, the i-th argument had an illegal value 90*> > 0: if INFO = i, U(i,i) is exactly zero. The factorization 91*> has been completed, but the factor U is exactly 92*> singular, and division by zero will occur if it is used 93*> to solve a system of equations. 94*> \endverbatim 95* 96* Authors: 97* ======== 98* 99*> \author Univ. of Tennessee 100*> \author Univ. of California Berkeley 101*> \author Univ. of Colorado Denver 102*> \author NAG Ltd. 103* 104*> \ingroup complex16GEcomputational 105* 106* ===================================================================== 107 SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO ) 108* 109* -- LAPACK computational routine -- 110* -- LAPACK is a software package provided by Univ. of Tennessee, -- 111* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 112* 113* .. Scalar Arguments .. 114 INTEGER INFO, LDA, M, N 115* .. 116* .. Array Arguments .. 117 INTEGER IPIV( * ) 118 COMPLEX*16 A( LDA, * ) 119* .. 120* 121* ===================================================================== 122* 123* .. Parameters .. 124 COMPLEX*16 ONE 125 PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) 126* .. 127* .. Local Scalars .. 128 INTEGER I, IINFO, J, JB, NB 129* .. 130* .. External Subroutines .. 131 EXTERNAL XERBLA, ZGEMM, ZGETRF2, ZLASWP, ZTRSM 132* .. 133* .. External Functions .. 134 INTEGER ILAENV 135 EXTERNAL ILAENV 136* .. 137* .. Intrinsic Functions .. 138 INTRINSIC MAX, MIN 139* .. 140* .. Executable Statements .. 141* 142* Test the input parameters. 143* 144 INFO = 0 145 IF( M.LT.0 ) THEN 146 INFO = -1 147 ELSE IF( N.LT.0 ) THEN 148 INFO = -2 149 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 150 INFO = -4 151 END IF 152 IF( INFO.NE.0 ) THEN 153 CALL XERBLA( 'ZGETRF', -INFO ) 154 RETURN 155 END IF 156* 157* Quick return if possible 158* 159 IF( M.EQ.0 .OR. N.EQ.0 ) 160 $ RETURN 161* 162* Determine the block size for this environment. 163* 164 NB = ILAENV( 1, 'ZGETRF', ' ', M, N, -1, -1 ) 165 IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN 166* 167* Use unblocked code. 168* 169 CALL ZGETRF2( M, N, A, LDA, IPIV, INFO ) 170 ELSE 171* 172* Use blocked code. 173* 174 DO 20 J = 1, MIN( M, N ), NB 175 JB = MIN( MIN( M, N )-J+1, NB ) 176* 177* Factor diagonal and subdiagonal blocks and test for exact 178* singularity. 179* 180 CALL ZGETRF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO ) 181* 182* Adjust INFO and the pivot indices. 183* 184 IF( INFO.EQ.0 .AND. IINFO.GT.0 ) 185 $ INFO = IINFO + J - 1 186 DO 10 I = J, MIN( M, J+JB-1 ) 187 IPIV( I ) = J - 1 + IPIV( I ) 188 10 CONTINUE 189* 190* Apply interchanges to columns 1:J-1. 191* 192 CALL ZLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 ) 193* 194 IF( J+JB.LE.N ) THEN 195* 196* Apply interchanges to columns J+JB:N. 197* 198 CALL ZLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, 199 $ IPIV, 1 ) 200* 201* Compute block row of U. 202* 203 CALL ZTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB, 204 $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ), 205 $ LDA ) 206 IF( J+JB.LE.M ) THEN 207* 208* Update trailing submatrix. 209* 210 CALL ZGEMM( 'No transpose', 'No transpose', M-J-JB+1, 211 $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA, 212 $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ), 213 $ LDA ) 214 END IF 215 END IF 216 20 CONTINUE 217 END IF 218 RETURN 219* 220* End of ZGETRF 221* 222 END 223