1// This file is part of Eigen, a lightweight C++ template library 2// for linear algebra. 3// 4// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@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 33namespace Eigen { 34namespace 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 */ 59template <typename Scalar, typename Index> 60Index SparseLUImpl<Scalar,Index>::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 Index* 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 = 0.0; 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 rtemp = std::abs(lu_col_ptr[isub]); 81 if (rtemp > pivmax) { 82 pivmax = rtemp; 83 pivptr = isub; 84 } 85 if (lsub_ptr[isub] == diagind) diag = isub; 86 } 87 88 // Test for singularity 89 if ( pivmax == 0.0 ) { 90 pivrow = lsub_ptr[pivptr]; 91 perm_r(pivrow) = jcol; 92 return (jcol+1); 93 } 94 95 RealScalar thresh = diagpivotthresh * pivmax; 96 97 // Choose appropriate pivotal element 98 99 { 100 // Test if the diagonal element can be used as a pivot (given the threshold value) 101 if (diag >= 0 ) 102 { 103 // Diagonal element exists 104 rtemp = std::abs(lu_col_ptr[diag]); 105 if (rtemp != 0.0 && rtemp >= thresh) pivptr = diag; 106 } 107 pivrow = lsub_ptr[pivptr]; 108 } 109 110 // Record pivot row 111 perm_r(pivrow) = jcol; 112 // Interchange row subscripts 113 if (pivptr != nsupc ) 114 { 115 std::swap( lsub_ptr[pivptr], lsub_ptr[nsupc] ); 116 // Interchange numerical values as well, for the two rows in the whole snode 117 // such that L is indexed the same way as A 118 for (icol = 0; icol <= nsupc; icol++) 119 { 120 itemp = pivptr + icol * lda; 121 std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * lda]); 122 } 123 } 124 // cdiv operations 125 Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc]; 126 for (k = nsupc+1; k < nsupr; k++) 127 lu_col_ptr[k] *= temp; 128 return 0; 129} 130 131} // end namespace internal 132} // end namespace Eigen 133 134#endif // SPARSELU_PIVOTL_H 135