1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2012 Dsir Nuentsa-Wakam <desire.nuentsa_wakam (at) inria.fr> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 /* 11 12 * NOTE: This file is the modified version of xpivotL.c file in SuperLU 13 14 * -- SuperLU routine (version 3.0) -- 15 * Univ. of California Berkeley, Xerox Palo Alto Research Center, 16 * and Lawrence Berkeley National Lab. 17 * October 15, 2003 18 * 19 * Copyright (c) 1994 by Xerox Corporation. All rights reserved. 20 * 21 * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY 22 * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. 23 * 24 * Permission is hereby granted to use or copy this program for any 25 * purpose, provided the above notices are retained on all copies. 26 * Permission to modify the code and to distribute modified code is 27 * granted, provided the above notices are retained, and a notice that 28 * the code was modified is included with the above copyright notice. 29 */ 30 #ifndef SPARSELU_PIVOTL_H 31 #define SPARSELU_PIVOTL_H 32 33 namespace Eigen { 34 namespace internal { 35 36 /** 37 * \brief Performs the numerical pivotin on the current column of L, and the CDIV operation. 38 * 39 * Pivot policy : 40 * (1) Compute thresh = u * max_(i>=j) abs(A_ij); 41 * (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN 42 * pivot row = k; 43 * ELSE IF abs(A_jj) >= thresh THEN 44 * pivot row = j; 45 * ELSE 46 * pivot row = m; 47 * 48 * Note: If you absolutely want to use a given pivot order, then set u=0.0. 49 * 50 * \param jcol The current column of L 51 * \param diagpivotthresh diagonal pivoting threshold 52 * \param[in,out] perm_r Row permutation (threshold pivoting) 53 * \param[in] iperm_c column permutation - used to finf diagonal of Pc*A*Pc' 54 * \param[out] pivrow The pivot row 55 * \param glu Global LU data 56 * \return 0 if success, i > 0 if U(i,i) is exactly zero 57 * 58 */ 59 template <typename Scalar, typename StorageIndex> 60 Index SparseLUImpl<Scalar,StorageIndex>::pivotL(const Index jcol, const RealScalar& diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, Index& pivrow, GlobalLU_t& glu) 61 { 62 63 Index fsupc = (glu.xsup)((glu.supno)(jcol)); // First column in the supernode containing the column jcol 64 Index nsupc = jcol - fsupc; // Number of columns in the supernode portion, excluding jcol; nsupc >=0 65 Index lptr = glu.xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion 66 Index nsupr = glu.xlsub(fsupc+1) - lptr; // Number of rows in the supernode 67 Index lda = glu.xlusup(fsupc+1) - glu.xlusup(fsupc); // leading dimension 68 Scalar* lu_sup_ptr = &(glu.lusup.data()[glu.xlusup(fsupc)]); // Start of the current supernode 69 Scalar* lu_col_ptr = &(glu.lusup.data()[glu.xlusup(jcol)]); // Start of jcol in the supernode 70 StorageIndex* lsub_ptr = &(glu.lsub.data()[lptr]); // Start of row indices of the supernode 71 72 // Determine the largest abs numerical value for partial pivoting 73 Index diagind = iperm_c(jcol); // diagonal index 74 RealScalar pivmax(-1.0); 75 Index pivptr = nsupc; 76 Index diag = emptyIdxLU; 77 RealScalar rtemp; 78 Index isub, icol, itemp, k; 79 for (isub = nsupc; isub < nsupr; ++isub) { 80 using std::abs; 81 rtemp = abs(lu_col_ptr[isub]); 82 if (rtemp > pivmax) { 83 pivmax = rtemp; 84 pivptr = isub; 85 } 86 if (lsub_ptr[isub] == diagind) diag = isub; 87 } 88 89 // Test for singularity 90 if ( pivmax <= RealScalar(0.0) ) { 91 // if pivmax == -1, the column is structurally empty, otherwise it is only numerically zero 92 pivrow = pivmax < RealScalar(0.0) ? diagind : lsub_ptr[pivptr]; 93 perm_r(pivrow) = StorageIndex(jcol); 94 return (jcol+1); 95 } 96 97 RealScalar thresh = diagpivotthresh * pivmax; 98 99 // Choose appropriate pivotal element 100 101 { 102 // Test if the diagonal element can be used as a pivot (given the threshold value) 103 if (diag >= 0 ) 104 { 105 // Diagonal element exists 106 using std::abs; 107 rtemp = abs(lu_col_ptr[diag]); 108 if (rtemp != RealScalar(0.0) && rtemp >= thresh) pivptr = diag; 109 } 110 pivrow = lsub_ptr[pivptr]; 111 } 112 113 // Record pivot row 114 perm_r(pivrow) = StorageIndex(jcol); 115 // Interchange row subscripts 116 if (pivptr != nsupc ) 117 { 118 std::swap( lsub_ptr[pivptr], lsub_ptr[nsupc] ); 119 // Interchange numerical values as well, for the two rows in the whole snode 120 // such that L is indexed the same way as A 121 for (icol = 0; icol <= nsupc; icol++) 122 { 123 itemp = pivptr + icol * lda; 124 std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]); 125 } 126 } 127 // cdiv operations 128 Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc]; 129 for (k = nsupc+1; k < nsupr; k++) 130 lu_col_ptr[k] *= temp; 131 return 0; 132 } 133 134 } // end namespace internal 135 } // end namespace Eigen 136 137 #endif // SPARSELU_PIVOTL_H 138
