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