1 | /*************************************************************** |
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2 | * |
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3 | * File: gitfan.cc |
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4 | * Purpose: Computationally intensive procedures for gitfan.lib, |
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5 | * outsourced to improve the performance. |
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6 | * Authors: Janko Boehm boehm@mathematik.uni-kl.de |
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7 | * Simon Keicher keicher@mail.mathematik.uni-tuebingen.de |
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8 | * Yue Ren ren@mathematik.uni-kl.de |
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9 | * |
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10 | ***************************************************************/ |
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11 | |
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12 | #include "kernel/mod2.h" |
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13 | |
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14 | #if HAVE_GFANLIB |
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15 | |
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16 | #include "Singular/dyn_modules/gfanlib/callgfanlib_conversion.h" |
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17 | #include "Singular/dyn_modules/gfanlib/bbcone.h" |
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18 | #include "Singular/dyn_modules/gfanlib/bbfan.h" |
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19 | #include "Singular/mod_lib.h" |
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20 | |
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21 | #include "gitfan.h" |
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22 | |
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23 | |
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24 | |
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25 | namespace gitfan |
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26 | { |
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27 | |
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28 | facet::facet(): |
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29 | eta(gfan::ZCone()), |
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30 | interiorPoint(gfan::ZVector()), |
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31 | facetNormal(gfan::ZVector()) |
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32 | { |
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33 | } |
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34 | |
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35 | facet::facet(const gitfan::facet &f): |
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36 | eta(f.eta), |
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37 | interiorPoint(f.interiorPoint), |
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38 | facetNormal(f.facetNormal) |
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39 | { |
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40 | #ifndef SING_NDEBUG |
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41 | gfan::ZCone c = f.eta; |
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42 | gfan::ZVector v = f.interiorPoint; |
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43 | gfan::ZVector w = f.facetNormal; |
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44 | assume(c.ambientDimension() == (int)v.size()); |
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45 | assume(c.ambientDimension() == (int)w.size()); |
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46 | assume(c.contains(v)); |
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47 | assume(!c.contains(w)); |
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48 | #endif |
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49 | } |
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50 | |
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51 | facet::facet(const gfan::ZCone &c, const gfan::ZVector &v, const gfan::ZVector &w): |
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52 | eta(c), |
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53 | interiorPoint(v), |
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54 | facetNormal(w) |
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55 | { |
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56 | #ifndef SING_NDEBUG |
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57 | assume(c.ambientDimension() == (int)v.size()); |
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58 | assume(c.ambientDimension() == (int)w.size()); |
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59 | assume(c.contains(v)); |
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60 | assume(!c.contains(w)); |
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61 | #endif |
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62 | } |
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63 | |
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64 | facet::~facet() |
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65 | { |
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66 | #ifndef SING_NDEBUG |
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67 | gfan::ZCone c = this->eta; |
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68 | gfan::ZVector v = this->interiorPoint; |
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69 | gfan::ZVector w = this->facetNormal; |
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70 | assume(c.ambientDimension() == (int)v.size()); |
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71 | assume(c.ambientDimension() == (int)w.size()); |
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72 | assume(c.contains(v)); |
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73 | assume(!c.contains(w)); |
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74 | #endif |
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75 | } |
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76 | |
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77 | void mergeFacets(facets &F, const facets &newFacets) |
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78 | { |
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79 | std::pair<facets::iterator,bool> check(newFacets.begin(),false); |
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80 | for(facets::iterator p=newFacets.begin(); p!=newFacets.end(); p++) |
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81 | { |
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82 | check = F.insert(*p); |
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83 | if(!check.second) |
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84 | F.erase(check.first); |
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85 | } |
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86 | } |
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87 | |
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88 | } |
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89 | |
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90 | |
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91 | static gfan::ZCone subcone(const lists &cones, const gfan::ZVector &point) |
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92 | { |
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93 | gfan::ZCone sigma = gfan::ZCone(gfan::ZMatrix(1,point.size()), gfan::ZMatrix(1,point.size())); |
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94 | gfan::ZCone* zc; |
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95 | for (int i=0; i<=cones->nr; i++) |
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96 | { |
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97 | zc = (gfan::ZCone*) cones->m[i].Data(); |
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98 | if (zc->contains(point)) |
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99 | sigma = gfan::intersection(sigma,*zc); |
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100 | } |
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101 | return(sigma); |
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102 | } |
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103 | |
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104 | static gitfan::facets interiorFacets(const gfan::ZCone &zc, const gfan::ZCone &bound) |
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105 | { |
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106 | gfan::ZMatrix inequalities = zc.getFacets(); |
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107 | gfan::ZMatrix equations = zc.getImpliedEquations(); |
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108 | int r = inequalities.getHeight(); |
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109 | int c = inequalities.getWidth(); |
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110 | gitfan::facets F; |
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111 | if (r*c == 0) |
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112 | /*** |
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113 | * this is the trivial case where either we are in a zerodimensional ambient space, |
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114 | * or the cone has no facets. |
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115 | **/ |
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116 | return F; |
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117 | |
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118 | // int index = 0; |
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119 | /* next we iterate over each of the r facets, build the respective cone and add it to the list */ |
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120 | /* this is the i=0 case */ |
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121 | gfan::ZMatrix newInequalities = inequalities.submatrix(1,0,r,c); |
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122 | gfan::ZMatrix newEquations = equations; |
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123 | newEquations.appendRow(inequalities[0]); |
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124 | gfan::ZCone eta = gfan::ZCone(newInequalities,newEquations); |
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125 | eta.canonicalize(); |
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126 | gfan::ZVector v = eta.getRelativeInteriorPoint(); |
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127 | gfan::ZVector w = inequalities[0]; |
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128 | |
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129 | if (bound.containsRelatively(v)) |
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130 | F.insert(gitfan::facet(eta,v,w)); |
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131 | |
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132 | /* these are the cases i=1,...,r-2 */ |
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133 | for (int i=1; i<r-1; i++) |
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134 | { |
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135 | newInequalities = inequalities.submatrix(0,0,i,c); |
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136 | newInequalities.append(inequalities.submatrix(i+1,0,r,c)); |
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137 | newEquations = equations; |
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138 | newEquations.appendRow(inequalities[i]); |
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139 | eta = gfan::ZCone(newInequalities,newEquations); |
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140 | eta.canonicalize(); |
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141 | v = eta.getRelativeInteriorPoint(); |
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142 | w = inequalities[i]; |
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143 | if (bound.containsRelatively(v)) |
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144 | F.insert(gitfan::facet(eta,v,w)); |
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145 | } |
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146 | |
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147 | /* this is the i=r-1 case */ |
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148 | newInequalities = inequalities.submatrix(0,0,r-1,c); |
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149 | newEquations = equations; |
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150 | newEquations.appendRow(inequalities[r-1]); |
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151 | eta = gfan::ZCone(newInequalities,newEquations); |
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152 | eta.canonicalize(); |
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153 | |
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154 | v = eta.getRelativeInteriorPoint(); |
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155 | w = inequalities[r-1]; |
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156 | if (bound.containsRelatively(v)) |
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157 | F.insert(gitfan::facet(eta,v,w)); |
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158 | |
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159 | return F; |
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160 | } |
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161 | |
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162 | BOOLEAN refineCones(leftv res, leftv args) |
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163 | { |
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164 | leftv u=args; |
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165 | if ((u != NULL) && (u->Typ() == LIST_CMD)) |
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166 | { |
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167 | leftv v=u->next; |
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168 | if ((v != NULL) && (v->Typ() == BIGINTMAT_CMD)) |
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169 | { |
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170 | lists cones = (lists) u->Data(); |
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171 | bigintmat* bim = (bigintmat*) v->Data(); |
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172 | gfan::ZMatrix* zm = bigintmatToZMatrix(bim->transpose()); |
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173 | gfan::ZCone support = gfan::ZCone::givenByRays(*zm, gfan::ZMatrix(0, zm->getWidth())); |
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174 | delete zm; |
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175 | |
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176 | /*** |
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177 | * Randomly compute a first full-dimensional cone and insert it into the fan. |
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178 | * Compute a list of facets and relative interior points. |
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179 | * The relative interior points are unique, assuming the cone is stored in canonical form, |
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180 | * which is the case in our algorithm, as we supply no redundant inequalities. |
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181 | * Hence we can decide whether a facet need to be traversed by crosschecking |
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182 | * its relative interior point with this list. |
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183 | **/ |
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184 | gfan::ZCone lambda; gfan::ZVector point; |
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185 | do |
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186 | { |
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187 | point = randomPoint(&support); |
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188 | lambda = subcone(cones, point); |
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189 | } |
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190 | while (lambda.dimension() < lambda.ambientDimension()); |
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191 | int iterationNumber = 1; |
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192 | std::cout << "cones found: " << iterationNumber++ << std::endl; |
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193 | |
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194 | lambda.canonicalize(); |
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195 | gfan::ZFan* Sigma = new gfan::ZFan(lambda.ambientDimension()); |
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196 | Sigma->insert(lambda); |
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197 | gitfan::facets F = interiorFacets(lambda, support); |
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198 | if (F.empty()) |
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199 | { |
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200 | res->rtyp = fanID; |
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201 | res->data = (void*) Sigma; |
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202 | return FALSE; |
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203 | } |
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204 | int mu = 1024; |
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205 | |
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206 | gitfan::facet f; |
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207 | gfan::ZCone eta; |
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208 | gfan::ZVector interiorPoint; |
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209 | gfan::ZVector facetNormal; |
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210 | gitfan::facets newFacets; |
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211 | while (!F.empty()) |
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212 | { |
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213 | /*** |
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214 | * Extract a facet to traverse and its relative interior point. |
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215 | **/ |
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216 | f = *(F.begin()); |
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217 | eta = f.getEta(); |
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218 | interiorPoint = f.getInteriorPoint(); |
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219 | facetNormal = f.getFacetNormal(); |
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220 | |
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221 | /*** |
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222 | * construct a point, which lies on the other side of the facet. |
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223 | * make sure it lies in the known support of our fan |
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224 | * and that the cone around the point is maximal, containing eta. |
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225 | **/ |
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226 | point = mu * interiorPoint - facetNormal; |
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227 | while (!support.containsRelatively(point)) |
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228 | { |
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229 | mu = mu * 16; |
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230 | point = mu * interiorPoint - facetNormal; |
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231 | } |
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232 | |
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233 | lambda = subcone(cones,point); |
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234 | while ((lambda.dimension() < lambda.ambientDimension()) && !(lambda.contains(interiorPoint))) |
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235 | { |
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236 | mu = mu * 16; |
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237 | point = mu * interiorPoint - facetNormal; |
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238 | lambda = subcone(cones,point); |
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239 | } |
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240 | std::cout << "cones found: " << iterationNumber++ << std::endl; |
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241 | |
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242 | /*** |
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243 | * insert lambda into Sigma, and create a list of facets of lambda. |
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244 | * merge the two lists of facets |
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245 | **/ |
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246 | lambda.canonicalize(); |
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247 | Sigma->insert(lambda); |
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248 | newFacets = interiorFacets(lambda, support); |
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249 | mergeFacets(F,newFacets); |
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250 | newFacets.clear(); |
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251 | } |
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252 | res->rtyp = fanID; |
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253 | res->data = (void*) Sigma; |
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254 | return FALSE; |
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255 | } |
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256 | } |
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257 | WerrorS("refineCones: unexpected parameters"); |
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258 | return TRUE; |
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259 | } |
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260 | |
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261 | |
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262 | static int binomial(int n, int k) |
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263 | { |
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264 | if (n<k) |
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265 | return(0); |
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266 | gfan::Integer num = 1; |
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267 | gfan::Integer den = 1; |
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268 | for (int i=1; i<=k; i++) |
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269 | den = den*i; |
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270 | for (int j=n-k+1; j<=n; j++) |
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271 | num = num*j; |
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272 | gfan::Integer bin = num/den; |
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273 | return(bin.toInt()); |
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274 | } |
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275 | |
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276 | |
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277 | intvec* intToAface(unsigned int v0, int n, int k) |
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278 | { |
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279 | intvec* v = new intvec(k); |
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280 | int j = 0; |
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281 | for (int i=0; i<n; i++) |
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282 | { |
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283 | if (v0 & (1<<i)) |
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284 | (*v)[j++] = i+1; |
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285 | } |
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286 | return v; |
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287 | } |
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288 | |
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289 | |
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290 | BOOLEAN listOfAfacesToCheck(leftv res, leftv args) |
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291 | { |
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292 | leftv u = args; |
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293 | if ((u != NULL) && (u->Typ() == INT_CMD)) |
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294 | { |
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295 | leftv v = u->next; |
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296 | if ((v != NULL) && (v->Typ() == INT_CMD)) |
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297 | { |
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298 | int n = (int)(long) u->Data(); |
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299 | int k = (int)(long) v->Data(); |
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300 | unsigned int v = 0; |
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301 | for (int i=0; i<k; i++) |
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302 | v |= 1<<i; // sets the first k bits of v as 1 |
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303 | |
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304 | lists L = (lists)omAllocBin(slists_bin); |
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305 | int count = (int) binomial(n,k); L->Init(count); |
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306 | unsigned int t; |
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307 | while (!(v & (1<<n))) |
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308 | { |
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309 | L->m[--count].rtyp = INTVEC_CMD; |
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310 | L->m[count].data = (void*) intToAface(v,n,k); |
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311 | |
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312 | // t gets v's least significant 0 bits set to 1 |
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313 | t = v | (v - 1); |
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314 | // Next set to 1 the most significant bit to change, |
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315 | // set to 0 the least significant ones, and add the necessary 1 bits. |
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316 | v = (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(v) + 1)); |
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317 | } |
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318 | res->rtyp = LIST_CMD; |
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319 | res->data = (void*) L; |
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320 | return FALSE; |
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321 | } |
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322 | } |
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323 | WerrorS("listOfAfacesToCheck: unexpected parameter"); |
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324 | return TRUE; |
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325 | } |
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326 | |
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327 | |
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328 | BOOLEAN nextAfaceToCheck(leftv res, leftv args) |
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329 | { |
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330 | leftv u = args; |
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331 | if ((u != NULL) && (u->Typ() == INTVEC_CMD)) |
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332 | { |
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333 | leftv v = u->next; |
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334 | if ((v != NULL) && (v->Typ() == INT_CMD)) |
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335 | { |
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336 | leftv w = v->next; |
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337 | if ((w != NULL) && (w->Typ() == INT_CMD)) |
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338 | { |
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339 | intvec* aface = (intvec*) u->Data(); |
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340 | int ambientDimension = (int)(long) v->Data(); |
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341 | int dimension = (int)(long) w->Data(); |
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342 | |
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343 | unsigned int af = 0; |
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344 | for (int i=0; i<aface->length(); i++) |
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345 | af |= 1<<((*aface)[i]-1); |
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346 | |
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347 | unsigned int t = af | (af - 1); |
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348 | af = (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(af) + 1)); |
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349 | |
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350 | if (af & (1<<ambientDimension)) |
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351 | { |
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352 | res->rtyp = INTVEC_CMD; |
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353 | res->data = (void*) new intvec(1); |
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354 | return FALSE; |
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355 | } |
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356 | |
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357 | res->rtyp = INTVEC_CMD; |
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358 | res->data = (void*) intToAface(af,ambientDimension,dimension); |
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359 | return FALSE; |
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360 | } |
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361 | } |
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362 | } |
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363 | WerrorS("nextAfaceToCheck: unexpected parameter"); |
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364 | return TRUE; |
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365 | } |
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366 | |
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367 | |
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368 | BOOLEAN checkSigns(leftv res, leftv args) |
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369 | { |
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370 | leftv u = args; |
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371 | if ((u != NULL) && (u->Typ()==BIGINTMAT_CMD || u->Typ()==INTMAT_CMD)) |
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372 | { |
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373 | leftv v = u->next; |
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374 | if ((v != NULL) && (v->Typ() == INTVEC_CMD) && (v->next == NULL)) |
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375 | { |
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376 | bigintmat* interiorPoint = NULL; |
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377 | if (u->Typ() == INTMAT_CMD) |
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378 | { |
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379 | intvec* p0 = (intvec*) u->Data(); |
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380 | interiorPoint = iv2bim(p0,coeffs_BIGINT); |
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381 | } |
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382 | else |
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383 | interiorPoint = (bigintmat*) u->Data(); |
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384 | intvec* hash = (intvec*) v->Data(); |
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385 | res->rtyp = INT_CMD; |
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386 | for (int i=0; i<hash->length(); i++) |
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387 | { |
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388 | if ( (*hash)[i]<0 && n_GreaterZero((*interiorPoint)[i],interiorPoint->basecoeffs()) ) |
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389 | { |
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390 | res->data = (void*) (long) 0; |
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391 | return FALSE; |
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392 | } |
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393 | if ( (*hash)[i]>0 && !n_IsZero((*interiorPoint)[i],interiorPoint->basecoeffs()) ) |
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394 | { |
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395 | number neg = n_Copy((*interiorPoint)[i],interiorPoint->basecoeffs()); |
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396 | neg = n_InpNeg(neg,interiorPoint->basecoeffs()); |
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397 | if (n_GreaterZero(neg,interiorPoint->basecoeffs())) |
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398 | { |
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399 | n_Delete(&neg,interiorPoint->basecoeffs()); |
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400 | res->data = (void*) (long) 0; |
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401 | return FALSE; |
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402 | } |
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403 | n_Delete(&neg,interiorPoint->basecoeffs()); |
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404 | } |
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405 | } |
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406 | res->data = (void*) (long) 1; |
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407 | if (v->Typ() == INTMAT_CMD) |
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408 | delete interiorPoint; |
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409 | return FALSE; |
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410 | } |
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411 | } |
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412 | WerrorS("checkSigns: unexpected parameter"); |
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413 | return TRUE; |
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414 | } |
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415 | |
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416 | |
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417 | BOOLEAN binaryToBigint(leftv res, leftv args) |
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418 | { |
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419 | leftv u = args; |
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420 | if ((u != NULL) && (u->Typ() == INTVEC_CMD) && (u->next == NULL)) |
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421 | { |
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422 | intvec* iv = (intvec*) u->Data(); |
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423 | const int l = (iv->rows())*(iv->cols()); |
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424 | number base = n_Init(2,coeffs_BIGINT); |
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425 | number endResult; |
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426 | n_Power(base,(*iv)[0]-1,&endResult,coeffs_BIGINT); |
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427 | for (int i=1; i<l; i++) |
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428 | { |
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429 | number endResultCache; |
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430 | number currentBit; |
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431 | n_Power(base,(*iv)[i]-1,¤tBit,coeffs_BIGINT); |
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432 | endResultCache = n_Add(endResult,currentBit,coeffs_BIGINT); |
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433 | n_Delete(&endResult,coeffs_BIGINT); |
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434 | n_Delete(¤tBit,coeffs_BIGINT); |
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435 | endResult = endResultCache; |
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436 | endResultCache = NULL; |
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437 | } |
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438 | n_Delete(&base,coeffs_BIGINT); |
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439 | res->rtyp = BIGINT_CMD; |
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440 | res->data = (void*) endResult; |
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441 | return FALSE; |
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442 | } |
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443 | WerrorS("binaryToBigint: unexpected parameter"); |
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444 | return TRUE; |
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445 | } |
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446 | |
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447 | |
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448 | BOOLEAN composeIntvecs(leftv res, leftv args) |
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449 | { |
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450 | leftv u = args; |
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451 | if ((u!=NULL) && (u->Typ()==INTVEC_CMD)) |
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452 | { |
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453 | leftv v = u->next; |
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454 | if ((v!=NULL) && (v->Typ()==INTVEC_CMD) && (v->next==NULL)) |
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455 | { |
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456 | intvec* iv1 = (intvec*) u->Data(); |
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457 | intvec* iv2 = (intvec*) v->Data(); |
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458 | int k = iv2->length(); |
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459 | intvec* composedIntvec = new intvec(k); |
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460 | for (int i=0; i<k; i++) |
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461 | (*composedIntvec)[i] = (*iv1)[(*iv2)[i]-1]; |
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462 | res->rtyp = INTVEC_CMD; |
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463 | res->data = (void*) composedIntvec; |
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464 | return FALSE; |
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465 | } |
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466 | } |
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467 | WerrorS("composeIntvecs: unexpected parameter"); |
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468 | return TRUE; |
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469 | } |
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470 | |
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471 | |
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472 | BOOLEAN findPlaceToInsert(leftv res, leftv args) |
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473 | { |
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474 | leftv u = args; |
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475 | if ((u!=NULL) && (u->Typ()==LIST_CMD)) |
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476 | { |
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477 | leftv v = u->next; |
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478 | if ((v!=NULL) && (v->Typ()==BIGINT_CMD) && (v->next==NULL)) |
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479 | { |
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480 | lists listOfNumbers = (lists) u->Data(); |
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481 | number numberToInsert = (number) v->Data(); |
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482 | int lowerBound = 0; |
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483 | int upperBound = lSize(listOfNumbers); |
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484 | if (upperBound<0) |
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485 | { |
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486 | res->rtyp = INT_CMD; |
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487 | res->data = (void*) (long) (lowerBound+1); |
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488 | return FALSE; |
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489 | } |
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490 | |
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491 | number lowerNumber = (number) listOfNumbers->m[lowerBound].Data(); |
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492 | if (n_Equal(lowerNumber,numberToInsert,coeffs_BIGINT)) |
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493 | { |
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494 | res->rtyp = INT_CMD; |
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495 | res->data = (void*) (long) (-1); |
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496 | return FALSE; |
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497 | } |
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498 | if (n_Greater(lowerNumber,numberToInsert,coeffs_BIGINT)) |
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499 | { |
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500 | res->rtyp = INT_CMD; |
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501 | res->data = (void*) (long) (lowerBound+1); |
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502 | return FALSE; |
---|
503 | } |
---|
504 | |
---|
505 | number upperNumber = (number) listOfNumbers->m[upperBound].Data(); |
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506 | if (n_Equal(numberToInsert,upperNumber,coeffs_BIGINT)) |
---|
507 | { |
---|
508 | res->rtyp = INT_CMD; |
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509 | res->data = (void*) (long) (-1); |
---|
510 | return FALSE; |
---|
511 | } |
---|
512 | if (n_Greater(numberToInsert,upperNumber,coeffs_BIGINT)) |
---|
513 | { |
---|
514 | res->rtyp = INT_CMD; |
---|
515 | res->data = (void*) (long) (upperBound+2); |
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516 | return FALSE; |
---|
517 | } |
---|
518 | |
---|
519 | while (lowerBound+1<upperBound) |
---|
520 | { |
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521 | int middle = lowerBound + (upperBound-lowerBound) / 2; |
---|
522 | number lowerNumber = (number) listOfNumbers->m[lowerBound].Data(); |
---|
523 | number upperNumber = (number) listOfNumbers->m[upperBound].Data(); |
---|
524 | number middleNumber = (number) listOfNumbers->m[middle].Data(); |
---|
525 | if ((n_Equal(lowerNumber,numberToInsert,coeffs_BIGINT)) || |
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526 | (n_Equal(middleNumber,numberToInsert,coeffs_BIGINT)) || |
---|
527 | (n_Equal(upperNumber,numberToInsert,coeffs_BIGINT))) |
---|
528 | { |
---|
529 | res->rtyp = INT_CMD; |
---|
530 | res->data = (void*) (long) -1; |
---|
531 | return FALSE; |
---|
532 | } |
---|
533 | if (n_Greater(numberToInsert,middleNumber,coeffs_BIGINT)) |
---|
534 | lowerBound = middle; |
---|
535 | if (n_Greater(middleNumber,numberToInsert,coeffs_BIGINT)) |
---|
536 | upperBound = middle; |
---|
537 | } |
---|
538 | |
---|
539 | res->rtyp = INT_CMD; |
---|
540 | res->data = (void*) (long) (upperBound+1); |
---|
541 | return FALSE; |
---|
542 | } |
---|
543 | } |
---|
544 | WerrorS("findPlaceToInsert: unexpected parameter"); |
---|
545 | return TRUE; |
---|
546 | } |
---|
547 | |
---|
548 | |
---|
549 | void subset(std::vector<int> &arr, int size, int left, int index, std::vector<int> &l, std::vector<std::vector<int> > &L) |
---|
550 | { |
---|
551 | if(left==0) |
---|
552 | { |
---|
553 | L.push_back(l); |
---|
554 | return; |
---|
555 | } |
---|
556 | |
---|
557 | for(int i=index; i<size;i++) |
---|
558 | { |
---|
559 | l.push_back(arr[i]); |
---|
560 | subset(arr,size,left-1,i+1,l,L); |
---|
561 | l.pop_back(); |
---|
562 | } |
---|
563 | } |
---|
564 | |
---|
565 | extern "C" int SI_MOD_INIT(gitfan) (SModulFunctions* p) |
---|
566 | { |
---|
567 | gfan::initializeCddlibIfRequired(); |
---|
568 | p->iiAddCproc("gitfan.lib","refineCones",FALSE,refineCones); |
---|
569 | p->iiAddCproc("gitfan.lib","listOfAfacesToCheck",FALSE,listOfAfacesToCheck); |
---|
570 | p->iiAddCproc("gitfan.lib","nextAfaceToCheck",FALSE,nextAfaceToCheck); |
---|
571 | p->iiAddCproc("gitfan.lib","checkSigns",FALSE,checkSigns); |
---|
572 | p->iiAddCproc("gitfan.lib","binaryToBigint",FALSE,binaryToBigint); |
---|
573 | p->iiAddCproc("gitfan.lib","composeIntvecs",FALSE,composeIntvecs); |
---|
574 | p->iiAddCproc("gitfan.lib","findPlaceToInsert",FALSE,findPlaceToInsert); |
---|
575 | return (MAX_TOK); |
---|
576 | } |
---|
577 | |
---|
578 | #endif |
---|