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 [s,d,c,z]column_dfs.c file in SuperLU
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13 |
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14 | * -- SuperLU routine (version 2.0) --
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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 | * November 15, 1997
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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_COLUMN_DFS_H
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31 | #define SPARSELU_COLUMN_DFS_H
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32 |
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33 | template <typename Scalar, typename Index> class SparseLUImpl;
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34 | namespace Eigen {
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35 |
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36 | namespace internal {
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37 |
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38 | template<typename IndexVector, typename ScalarVector>
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39 | struct column_dfs_traits : no_assignment_operator
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40 | {
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41 | typedef typename ScalarVector::Scalar Scalar;
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42 | typedef typename IndexVector::Scalar Index;
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43 | column_dfs_traits(Index jcol, Index& jsuper, typename SparseLUImpl<Scalar, Index>::GlobalLU_t& glu, SparseLUImpl<Scalar, Index>& luImpl)
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44 | : m_jcol(jcol), m_jsuper_ref(jsuper), m_glu(glu), m_luImpl(luImpl)
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45 | {}
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46 | bool update_segrep(Index /*krep*/, Index /*jj*/)
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47 | {
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48 | return true;
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49 | }
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50 | void mem_expand(IndexVector& lsub, Index& nextl, Index chmark)
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51 | {
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52 | if (nextl >= m_glu.nzlmax)
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53 | m_luImpl.memXpand(lsub, m_glu.nzlmax, nextl, LSUB, m_glu.num_expansions);
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54 | if (chmark != (m_jcol-1)) m_jsuper_ref = emptyIdxLU;
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55 | }
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56 | enum { ExpandMem = true };
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57 |
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58 | Index m_jcol;
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59 | Index& m_jsuper_ref;
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60 | typename SparseLUImpl<Scalar, Index>::GlobalLU_t& m_glu;
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61 | SparseLUImpl<Scalar, Index>& m_luImpl;
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62 | };
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63 |
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64 |
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65 | /**
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66 | * \brief Performs a symbolic factorization on column jcol and decide the supernode boundary
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67 | *
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68 | * A supernode representative is the last column of a supernode.
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69 | * The nonzeros in U[*,j] are segments that end at supernodes representatives.
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70 | * The routine returns a list of the supernodal representatives
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71 | * in topological order of the dfs that generates them.
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72 | * The location of the first nonzero in each supernodal segment
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73 | * (supernodal entry location) is also returned.
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74 | *
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75 | * \param m number of rows in the matrix
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76 | * \param jcol Current column
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77 | * \param perm_r Row permutation
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78 | * \param maxsuper Maximum number of column allowed in a supernode
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79 | * \param [in,out] nseg Number of segments in current U[*,j] - new segments appended
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80 | * \param lsub_col defines the rhs vector to start the dfs
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81 | * \param [in,out] segrep Segment representatives - new segments appended
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82 | * \param repfnz First nonzero location in each row
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83 | * \param xprune
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84 | * \param marker marker[i] == jj, if i was visited during dfs of current column jj;
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85 | * \param parent
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86 | * \param xplore working array
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87 | * \param glu global LU data
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88 | * \return 0 success
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89 | * > 0 number of bytes allocated when run out of space
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90 | *
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91 | */
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92 | template <typename Scalar, typename Index>
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93 | Index SparseLUImpl<Scalar,Index>::column_dfs(const Index m, const Index jcol, IndexVector& perm_r, Index maxsuper, Index& nseg, BlockIndexVector lsub_col, IndexVector& segrep, BlockIndexVector repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu)
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94 | {
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95 |
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96 | Index jsuper = glu.supno(jcol);
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97 | Index nextl = glu.xlsub(jcol);
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98 | VectorBlock<IndexVector> marker2(marker, 2*m, m);
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99 |
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100 |
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101 | column_dfs_traits<IndexVector, ScalarVector> traits(jcol, jsuper, glu, *this);
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102 |
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103 | // For each nonzero in A(*,jcol) do dfs
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104 | for (Index k = 0; ((k < m) ? lsub_col[k] != emptyIdxLU : false) ; k++)
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105 | {
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106 | Index krow = lsub_col(k);
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107 | lsub_col(k) = emptyIdxLU;
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108 | Index kmark = marker2(krow);
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109 |
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110 | // krow was visited before, go to the next nonz;
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111 | if (kmark == jcol) continue;
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112 |
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113 | dfs_kernel(jcol, perm_r, nseg, glu.lsub, segrep, repfnz, xprune, marker2, parent,
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114 | xplore, glu, nextl, krow, traits);
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115 | } // for each nonzero ...
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116 |
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117 | Index fsupc, jptr, jm1ptr, ito, ifrom, istop;
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118 | Index nsuper = glu.supno(jcol);
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119 | Index jcolp1 = jcol + 1;
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120 | Index jcolm1 = jcol - 1;
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121 |
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122 | // check to see if j belongs in the same supernode as j-1
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123 | if ( jcol == 0 )
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124 | { // Do nothing for column 0
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125 | nsuper = glu.supno(0) = 0 ;
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126 | }
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127 | else
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128 | {
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129 | fsupc = glu.xsup(nsuper);
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130 | jptr = glu.xlsub(jcol); // Not yet compressed
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131 | jm1ptr = glu.xlsub(jcolm1);
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132 |
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133 | // Use supernodes of type T2 : see SuperLU paper
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134 | if ( (nextl-jptr != jptr-jm1ptr-1) ) jsuper = emptyIdxLU;
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135 |
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136 | // Make sure the number of columns in a supernode doesn't
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137 | // exceed threshold
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138 | if ( (jcol - fsupc) >= maxsuper) jsuper = emptyIdxLU;
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139 |
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140 | /* If jcol starts a new supernode, reclaim storage space in
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141 | * glu.lsub from previous supernode. Note we only store
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142 | * the subscript set of the first and last columns of
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143 | * a supernode. (first for num values, last for pruning)
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144 | */
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145 | if (jsuper == emptyIdxLU)
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146 | { // starts a new supernode
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147 | if ( (fsupc < jcolm1-1) )
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148 | { // >= 3 columns in nsuper
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149 | ito = glu.xlsub(fsupc+1);
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150 | glu.xlsub(jcolm1) = ito;
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151 | istop = ito + jptr - jm1ptr;
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152 | xprune(jcolm1) = istop; // intialize xprune(jcol-1)
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153 | glu.xlsub(jcol) = istop;
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154 |
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155 | for (ifrom = jm1ptr; ifrom < nextl; ++ifrom, ++ito)
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156 | glu.lsub(ito) = glu.lsub(ifrom);
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157 | nextl = ito; // = istop + length(jcol)
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158 | }
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159 | nsuper++;
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160 | glu.supno(jcol) = nsuper;
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161 | } // if a new supernode
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162 | } // end else: jcol > 0
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163 |
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164 | // Tidy up the pointers before exit
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165 | glu.xsup(nsuper+1) = jcolp1;
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166 | glu.supno(jcolp1) = nsuper;
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167 | xprune(jcol) = nextl; // Intialize upper bound for pruning
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168 | glu.xlsub(jcolp1) = nextl;
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169 |
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170 | return 0;
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171 | }
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172 |
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173 | } // end namespace internal
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174 |
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175 | } // end namespace Eigen
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176 |
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177 | #endif
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