1 | /* |
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2 | * lib_cone.cpp |
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3 | * |
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4 | * Created on: Sep 29, 2010 |
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5 | * Author: anders |
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6 | */ |
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7 | #include <stddef.h> |
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8 | #include "gfanlib_zcone.h" |
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9 | |
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10 | #include <vector> |
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11 | #include <set> |
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12 | #include <sstream> |
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13 | |
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14 | #include <config.h> |
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15 | extern "C" |
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16 | { |
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17 | #ifdef HAVE_CDD_SETOPER_H |
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18 | #include <cdd/setoper.h> |
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19 | #include <cdd/cdd.h> |
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20 | #else |
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21 | #ifdef HAVE_CDDLIB_SETOPER_H |
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22 | #include <cddlib/setoper.h> |
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23 | #include <cddlib/cdd.h> |
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24 | #else |
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25 | #include <setoper.h> |
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26 | #include <cdd.h> |
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27 | #endif //HAVE_CDDLIB_SETOPER_H |
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28 | #endif //HAVE_CDD_SETOPER_H |
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29 | } |
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30 | extern "C" time_t dd_statStartTime; /*cddlib*/ |
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31 | |
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32 | namespace gfan{ |
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33 | bool isCddlibRequired() |
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34 | { |
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35 | return true; |
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36 | } |
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37 | void initializeCddlibIfRequired() // calling this frequently will cause memory leaks because deinitialisation is not possible with old versions of cddlib. |
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38 | { |
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39 | if (dd_statStartTime==0) |
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40 | { |
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41 | dd_set_global_constants(); |
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42 | } |
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43 | } |
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44 | void deinitializeCddlibIfRequired() |
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45 | { |
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46 | #ifdef HAVE_DD_FREE_GLOBAL_CONSTANTS |
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47 | // dd_free_global_constants(); |
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48 | #endif |
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49 | } |
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50 | static void ensureCddInitialisation() |
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51 | { |
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52 | // A more complicated initialisation than the following (meaning attempts to count the number of times |
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53 | // cddlib was requested to be initialised) would require cddlib to be thread aware. |
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54 | // The error below is implemented with an assert(0) because throwing an exception may leave the impression that |
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55 | // it is possible to recover from this error. While that may be true, it would not work in full generality, |
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56 | // as the following if statement cannot test whether dd_free_global_constants() has also been called. |
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57 | // Moverover, in multithreaded environments it would be quite difficult to decide if cddlib was initialised. |
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58 | if(!dd_one[0]._mp_num._mp_d) |
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59 | { |
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60 | std::cerr<<"CDDLIB HAS NOT BEEN INITIALISED!\n" |
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61 | "\n" |
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62 | "Fix this problem by calling the following function in your initialisation code:\n" |
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63 | "dd_set_global_constants();\n" |
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64 | "(after possibly setting the gmp allocators) and\n" |
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65 | "dd_free_global_constants()\n" |
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66 | "in your deinitialisation code (only available for cddlib version>=094d).\n" |
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67 | "This requires the header includes:\n" |
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68 | "#include \"cdd/setoper.h\"\n" |
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69 | "#include \"cdd/cdd.h\"\n" |
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70 | "\n" |
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71 | "Alternatively, you may call gfan:initializeCddlibIfRequired() and deinitializeCddlibIfRequired()\n" |
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72 | "if gfanlib is the only code using cddlib. If at some point cddlib is no longer required by gfanlib\n" |
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73 | "these functions may do nothing.\n" |
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74 | "Because deinitialisation is not possible in cddlib <094d, the functions may leak memory and should not be called often.\n" |
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75 | "\n" |
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76 | "This error message will never appear if the initialisation was done properly, and therefore never appear in a shipping version of your software.\n"; |
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77 | assert(0); |
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78 | } |
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79 | /* |
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80 | static bool initialized; |
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81 | if(!initialized) |
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82 | { |
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83 | dd_set_global_constants(); |
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84 | initialized=true; |
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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 | class LpSolver |
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90 | { |
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91 | static dd_MatrixPtr ZMatrix2MatrixGmp(ZMatrix const &g, dd_ErrorType *Error) |
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92 | { |
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93 | int n=g.getWidth(); |
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94 | dd_MatrixPtr M=NULL; |
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95 | dd_rowrange m_input,i; |
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96 | dd_colrange d_input,j; |
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97 | dd_RepresentationType rep=dd_Inequality; |
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98 | // dd_boolean found=dd_FALSE, newformat=dd_FALSE, successful=dd_FALSE; |
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99 | char command[dd_linelenmax], comsave[dd_linelenmax]; |
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100 | dd_NumberType NT; |
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101 | |
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102 | (*Error)=dd_NoError; |
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103 | |
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104 | rep=dd_Inequality; // newformat=dd_TRUE; |
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105 | |
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106 | m_input=g.getHeight(); |
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107 | d_input=n+1; |
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108 | |
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109 | NT=dd_Rational; |
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110 | |
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111 | M=dd_CreateMatrix(m_input, d_input); |
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112 | M->representation=rep; |
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113 | M->numbtype=NT; |
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114 | |
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115 | for (i = 0; i < m_input; i++) { |
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116 | dd_set_si(M->matrix[i][0],0); |
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117 | for (j = 1; j < d_input; j++) { |
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118 | g[i][j-1].setGmp(mpq_numref(M->matrix[i][j])); |
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119 | mpz_set_ui(mpq_denref(M->matrix[i][j]), 1); |
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120 | mpq_canonicalize(M->matrix[i][j]); |
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121 | } |
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122 | } |
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123 | |
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124 | // successful=dd_TRUE; |
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125 | |
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126 | return M; |
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127 | } |
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128 | static dd_MatrixPtr ZMatrix2MatrixGmp(ZMatrix const &inequalities, ZMatrix const &equations, dd_ErrorType *err) |
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129 | { |
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130 | ZMatrix g=inequalities; |
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131 | g.append(equations); |
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132 | int numberOfInequalities=inequalities.getHeight(); |
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133 | int numberOfRows=g.getHeight(); |
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134 | dd_MatrixPtr A=NULL; |
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135 | ensureCddInitialisation(); |
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136 | A=ZMatrix2MatrixGmp(g, err); |
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137 | for(int i=numberOfInequalities;i<numberOfRows;i++) |
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138 | set_addelem(A->linset,i+1); |
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139 | return A; |
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140 | } |
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141 | static ZMatrix getConstraints(dd_MatrixPtr A, bool returnEquations) |
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142 | { |
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143 | int rowsize=A->rowsize; |
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144 | int n=A->colsize-1; |
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145 | |
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146 | ZMatrix ret(0,n); |
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147 | for(int i=0;i<rowsize;i++) |
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148 | { |
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149 | bool isEquation=set_member(i+1,A->linset); |
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150 | if(isEquation==returnEquations) |
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151 | { |
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152 | QVector v(n); |
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153 | for(int j=0;j<n;j++)v[j]=Rational(A->matrix[i][j+1]); |
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154 | ret.appendRow(QToZVectorPrimitive(v)); |
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155 | } |
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156 | } |
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157 | return ret; |
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158 | } |
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159 | static bool isFacet(ZMatrix const &g, int index) |
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160 | { |
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161 | bool ret; |
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162 | // dd_MatrixPtr M=NULL,M2=NULL,M3=NULL; |
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163 | dd_MatrixPtr M=NULL; |
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164 | // dd_colrange d; |
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165 | dd_ErrorType err=dd_NoError; |
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166 | // dd_rowset redrows,linrows,ignoredrows, basisrows; |
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167 | // dd_colset ignoredcols, basiscols; |
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168 | // dd_DataFileType inputfile; |
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169 | FILE *reading=NULL; |
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170 | |
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171 | ensureCddInitialisation(); |
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172 | |
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173 | M=ZMatrix2MatrixGmp(g, &err); |
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174 | if (err!=dd_NoError) goto _L99; |
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175 | |
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176 | // d=M->colsize; |
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177 | |
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178 | //static dd_Arow temp; |
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179 | dd_Arow temp; |
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180 | dd_InitializeArow(g.getWidth()+1,&temp); |
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181 | |
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182 | ret= !dd_Redundant(M,index+1,temp,&err); |
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183 | |
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184 | dd_FreeMatrix(M); |
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185 | dd_FreeArow(g.getWidth()+1,temp); |
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186 | |
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187 | if (err!=dd_NoError) goto _L99; |
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188 | return ret; |
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189 | _L99: |
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190 | assert(0); |
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191 | return false; |
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192 | } |
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193 | |
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194 | /* |
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195 | Heuristic for checking if inequality of full dimensional cone is a |
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196 | facet. If the routine returns true then the inequality is a |
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197 | facet. If it returns false it is unknown. |
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198 | */ |
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199 | static bool fastIsFacetCriterion(ZMatrix const &normals, int i) |
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200 | { |
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201 | int n=normals.getWidth(); |
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202 | for(int j=0;j<n;j++) |
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203 | if(normals[i][j].sign()!=0) |
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204 | { |
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205 | int sign=normals[i][j].sign(); |
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206 | bool isTheOnly=true; |
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207 | for(int k=0;k<normals.getHeight();k++) |
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208 | if(k!=i) |
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209 | { |
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210 | if(normals[i][j].sign()==sign) |
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211 | { |
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212 | isTheOnly=false; |
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213 | break; |
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214 | } |
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215 | } |
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216 | if(isTheOnly)return true; |
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217 | } |
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218 | return false; |
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219 | } |
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220 | |
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221 | static bool fastIsFacet(ZMatrix const &normals, int i) |
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222 | { |
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223 | if(fastIsFacetCriterion(normals,i))return true; |
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224 | return isFacet(normals,i); |
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225 | } |
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226 | |
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227 | class MyHashMap |
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228 | { |
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229 | typedef std::vector<std::set<ZVector> > Container; |
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230 | Container container; |
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231 | int tableSize; |
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232 | public: |
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233 | class iterator |
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234 | { |
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235 | class MyHashMap &hashMap; |
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236 | int index; // having index==-1 means that we are before/after the elements. |
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237 | std::set<ZVector>::iterator i; |
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238 | public: |
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239 | bool operator++() |
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240 | { |
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241 | if(index==-1)goto search; |
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242 | i++; |
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243 | while(i==hashMap.container[index].end()) |
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244 | { |
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245 | search: |
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246 | index++; |
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247 | if(index>=hashMap.tableSize){ |
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248 | index=-1; |
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249 | return false; |
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250 | } |
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251 | i=hashMap.container[index].begin(); |
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252 | } |
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253 | return true; |
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254 | } |
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255 | ZVector const & operator*()const |
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256 | { |
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257 | return *i; |
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258 | } |
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259 | ZVector operator*() |
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260 | { |
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261 | return *i; |
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262 | } |
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263 | iterator(MyHashMap &hashMap_): |
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264 | hashMap(hashMap_) |
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265 | { |
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266 | index=-1; |
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267 | } |
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268 | }; |
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269 | unsigned int function(const ZVector &v) |
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270 | { |
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271 | unsigned int ret=0; |
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272 | int n=v.size(); |
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273 | for(int i=0;i<n;i++) |
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274 | ret=(ret<<3)+(ret>>29)+v.UNCHECKEDACCESS(i).hashValue(); |
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275 | return ret%tableSize; |
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276 | } |
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277 | MyHashMap(int tableSize_): |
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278 | container(tableSize_), |
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279 | tableSize(tableSize_) |
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280 | { |
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281 | assert(tableSize_>0); |
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282 | } |
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283 | void insert(const ZVector &v) |
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284 | { |
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285 | container[function(v)].insert(v); |
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286 | } |
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287 | void erase(ZVector const &v) |
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288 | { |
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289 | container[function(v)].erase(v); |
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290 | } |
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291 | iterator begin() |
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292 | { |
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293 | iterator ret(*this); |
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294 | ++ ret; |
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295 | return ret; |
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296 | } |
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297 | int size() |
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298 | { |
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299 | iterator i=begin(); |
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300 | int ret=0; |
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301 | do{ret++;}while(++i); |
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302 | return ret; |
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303 | } |
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304 | }; |
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305 | |
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306 | |
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307 | static ZMatrix normalizedWithSumsAndDuplicatesRemoved(ZMatrix const &a) |
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308 | { |
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309 | // TODO: write a version of this function which will work faster if the entries fit in 32bit |
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310 | if(a.getHeight()==0)return a; |
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311 | int n=a.getWidth(); |
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312 | ZVector temp1(n); |
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313 | // ZVector temp2(n); |
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314 | ZMatrix ret(0,n); |
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315 | MyHashMap b(a.getHeight()); |
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316 | |
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317 | for(int i=0;i<a.getHeight();i++) |
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318 | { |
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319 | assert(!(a[i].toVector().isZero())); |
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320 | b.insert(a[i].toVector().normalized()); |
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321 | } |
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322 | |
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323 | { |
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324 | MyHashMap::iterator i=b.begin(); |
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325 | |
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326 | do |
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327 | { |
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328 | MyHashMap::iterator j=i; |
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329 | while(++j) |
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330 | { |
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331 | ZVector const &I=*i; |
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332 | ZVector const &J=*j; |
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333 | for(int k=0;k<n;k++)temp1[k]=I.UNCHECKEDACCESS(k)+J.UNCHECKEDACCESS(k); |
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334 | // normalizedLowLevel(temp1,temp2); |
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335 | // b.erase(temp2);//this can never remove *i or *j |
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336 | b.erase(temp1.normalized());//this can never remove *i or *j |
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337 | } |
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338 | } |
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339 | while(++i); |
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340 | } |
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341 | ZMatrix original(0,n); |
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342 | { |
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343 | MyHashMap::iterator i=b.begin(); |
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344 | do |
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345 | { |
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346 | original.appendRow(*i); |
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347 | } |
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348 | while(++i); |
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349 | } |
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350 | |
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351 | for(int i=0;i!=original.getHeight();i++) |
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352 | for(int j=0;j!=a.getHeight();j++) |
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353 | if(!dependent(original[i].toVector(),a[j].toVector())) |
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354 | { |
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355 | ZVector const &I=original[i]; |
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356 | ZVector const &J=a[j]; |
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357 | for(int k=0;k<n;k++)temp1[k]=I.UNCHECKEDACCESS(k)+J.UNCHECKEDACCESS(k); |
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358 | // normalizedLowLevel(temp1,temp2); |
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359 | // b.erase(temp2);//this can never remove *i or *j |
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360 | b.erase(temp1.normalized());//this can never remove *i or *j |
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361 | } |
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362 | { |
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363 | MyHashMap::iterator i=b.begin(); |
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364 | do |
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365 | { |
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366 | ZVector temp=*i; |
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367 | ret.appendRow(temp); |
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368 | } |
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369 | while(++i); |
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370 | } |
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371 | return ret; |
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372 | } |
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373 | public: |
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374 | static ZMatrix fastNormals(ZMatrix const &inequalities) |
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375 | { |
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376 | ZMatrix normals=normalizedWithSumsAndDuplicatesRemoved(inequalities); |
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377 | for(int i=0;i!=normals.getHeight();i++) |
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378 | if(!fastIsFacet(normals,i)) |
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379 | { |
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380 | normals[i]=normals[normals.getHeight()-1]; |
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381 | normals.eraseLastRow(); |
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382 | i--; |
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383 | } |
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384 | return normals; |
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385 | } |
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386 | void removeRedundantRows(ZMatrix &inequalities, ZMatrix &equations, bool removeInequalityRedundancies) |
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387 | { |
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388 | ensureCddInitialisation(); |
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389 | |
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390 | int numberOfEqualities=equations.getHeight(); |
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391 | int numberOfInequalities=inequalities.getHeight(); |
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392 | int numberOfRows=numberOfEqualities+numberOfInequalities; |
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393 | |
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394 | if(numberOfRows==0)return;//the full space, so description is already irredundant |
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395 | |
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396 | // dd_rowset r=NULL; |
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397 | ZMatrix g=inequalities; |
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398 | g.append(equations); |
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399 | |
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400 | // dd_LPSolverType solver=dd_DualSimplex; |
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401 | dd_MatrixPtr A=NULL; |
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402 | dd_ErrorType err=dd_NoError; |
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403 | |
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404 | A=ZMatrix2MatrixGmp(g,&err); |
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405 | if (err!=dd_NoError) goto _L99; |
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406 | |
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407 | for(int i=numberOfInequalities;i<numberOfRows;i++) |
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408 | set_addelem(A->linset,i+1); |
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409 | |
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410 | A->objective=dd_LPmax; |
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411 | |
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412 | dd_rowset impl_linset; |
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413 | dd_rowset redset; |
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414 | dd_rowindex newpos; |
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415 | |
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416 | if(removeInequalityRedundancies) |
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417 | dd_MatrixCanonicalize(&A, &impl_linset, &redset, &newpos, &err); |
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418 | else |
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419 | dd_MatrixCanonicalizeLinearity(&A, &impl_linset, &newpos, &err); |
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420 | |
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421 | if (err!=dd_NoError) goto _L99; |
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422 | |
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423 | { |
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424 | int n=A->colsize-1; |
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425 | equations=ZMatrix(0,n); //TODO: the number of rows needed is actually known |
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426 | inequalities=ZMatrix(0,n); //is known by set_card(). That might save some copying. |
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427 | |
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428 | { |
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429 | int rowsize=A->rowsize; |
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430 | QVector point(n); |
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431 | for(int i=0;i<rowsize;i++) |
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432 | { |
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433 | for(int j=0;j<n;j++)point[j]=Rational(A->matrix[i][j+1]); |
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434 | ((set_member(i+1,A->linset))?equations:inequalities).appendRow(QToZVectorPrimitive(point)); |
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435 | } |
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436 | } |
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437 | assert(set_card(A->linset)==equations.getHeight()); |
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438 | assert(A->rowsize==equations.getHeight()+inequalities.getHeight()); |
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439 | |
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440 | set_free(impl_linset); |
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441 | if(removeInequalityRedundancies) |
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442 | set_free(redset); |
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443 | free(newpos); |
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444 | |
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445 | dd_FreeMatrix(A); |
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446 | return; |
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447 | } |
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448 | _L99: |
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449 | assert(!"Cddlib reported error when called by Gfanlib."); |
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450 | } |
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451 | ZVector relativeInteriorPoint(const ZMatrix &inequalities, const ZMatrix &equations) |
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452 | { |
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453 | QVector retUnscaled(inequalities.getWidth()); |
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454 | ensureCddInitialisation(); |
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455 | int numberOfEqualities=equations.getHeight(); |
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456 | int numberOfInequalities=inequalities.getHeight(); |
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457 | int numberOfRows=numberOfEqualities+numberOfInequalities; |
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458 | |
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459 | // dd_rowset r=NULL; |
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460 | ZMatrix g=inequalities; |
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461 | g.append(equations); |
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462 | |
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463 | dd_LPSolverType solver=dd_DualSimplex; |
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464 | dd_MatrixPtr A=NULL; |
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465 | dd_ErrorType err=dd_NoError; |
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466 | |
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467 | A=ZMatrix2MatrixGmp(g,&err); |
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468 | if (err!=dd_NoError) goto _L99; |
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469 | { |
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470 | dd_LPSolutionPtr lps1; |
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471 | dd_LPPtr lp,lp1; |
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472 | |
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473 | for(int i=0;i<numberOfInequalities;i++) |
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474 | dd_set_si(A->matrix[i][0],-1); |
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475 | for(int i=numberOfInequalities;i<numberOfRows;i++) |
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476 | set_addelem(A->linset,i+1); |
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477 | |
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478 | A->objective=dd_LPmax; |
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479 | lp=dd_Matrix2LP(A, &err); |
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480 | if (err!=dd_NoError) goto _L99; |
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481 | |
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482 | lp1=dd_MakeLPforInteriorFinding(lp); |
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483 | dd_LPSolve(lp1,solver,&err); |
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484 | if (err!=dd_NoError) goto _L99; |
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485 | |
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486 | lps1=dd_CopyLPSolution(lp1); |
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487 | |
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488 | assert(!dd_Negative(lps1->optvalue)); |
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489 | |
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490 | for (int j=1; j <(lps1->d)-1; j++) |
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491 | retUnscaled[j-1]=Rational(lps1->sol[j]); |
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492 | |
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493 | dd_FreeLPData(lp); |
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494 | dd_FreeLPSolution(lps1); |
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495 | dd_FreeLPData(lp1); |
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496 | dd_FreeMatrix(A); |
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497 | return QToZVectorPrimitive(retUnscaled); |
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498 | } |
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499 | _L99: |
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500 | assert(0); |
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501 | return QToZVectorPrimitive(retUnscaled); |
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502 | } |
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503 | void dual(ZMatrix const &inequalities, ZMatrix const &equations, ZMatrix &dualInequalities, ZMatrix &dualEquations) |
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504 | { |
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505 | int result; |
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506 | |
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507 | dd_MatrixPtr A=NULL; |
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508 | dd_ErrorType err=dd_NoError; |
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509 | |
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510 | ensureCddInitialisation(); |
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511 | |
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512 | A=ZMatrix2MatrixGmp(inequalities, equations, &err); |
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513 | |
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514 | dd_PolyhedraPtr poly; |
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515 | poly=dd_DDMatrix2Poly2(A, dd_LexMin, &err); |
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516 | |
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517 | if (poly->child==NULL || poly->child->CompStatus!=dd_AllFound) assert(0); |
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518 | |
---|
519 | dd_MatrixPtr A2=dd_CopyGenerators(poly); |
---|
520 | |
---|
521 | dualInequalities=getConstraints(A2,false); |
---|
522 | dualEquations=getConstraints(A2,true); |
---|
523 | |
---|
524 | dd_FreeMatrix(A2); |
---|
525 | dd_FreeMatrix(A); |
---|
526 | dd_FreePolyhedra(poly); |
---|
527 | |
---|
528 | return; |
---|
529 | _L99: |
---|
530 | assert(0); |
---|
531 | } |
---|
532 | // this procedure is take from cddio.c. |
---|
533 | static void dd_ComputeAinc(dd_PolyhedraPtr poly) |
---|
534 | { |
---|
535 | /* This generates the input incidence array poly->Ainc, and |
---|
536 | two sets: poly->Ared, poly->Adom. |
---|
537 | */ |
---|
538 | dd_bigrange k; |
---|
539 | dd_rowrange i,m1; |
---|
540 | dd_colrange j; |
---|
541 | dd_boolean redundant; |
---|
542 | dd_MatrixPtr M=NULL; |
---|
543 | mytype sum,temp; |
---|
544 | |
---|
545 | dd_init(sum); dd_init(temp); |
---|
546 | if (poly->AincGenerated==dd_TRUE) goto _L99; |
---|
547 | |
---|
548 | M=dd_CopyOutput(poly); |
---|
549 | poly->n=M->rowsize; |
---|
550 | m1=poly->m1; |
---|
551 | |
---|
552 | /* this number is same as poly->m, except when |
---|
553 | poly is given by nonhomogeneous inequalty: |
---|
554 | !(poly->homogeneous) && poly->representation==Inequality, |
---|
555 | it is poly->m+1. See dd_ConeDataLoad. |
---|
556 | */ |
---|
557 | poly->Ainc=(set_type*)calloc(m1, sizeof(set_type)); |
---|
558 | for(i=1; i<=m1; i++) set_initialize(&(poly->Ainc[i-1]),poly->n); |
---|
559 | set_initialize(&(poly->Ared), m1); |
---|
560 | set_initialize(&(poly->Adom), m1); |
---|
561 | |
---|
562 | for (k=1; k<=poly->n; k++){ |
---|
563 | for (i=1; i<=poly->m; i++){ |
---|
564 | dd_set(sum,dd_purezero); |
---|
565 | for (j=1; j<=poly->d; j++){ |
---|
566 | dd_mul(temp,poly->A[i-1][j-1],M->matrix[k-1][j-1]); |
---|
567 | dd_add(sum,sum,temp); |
---|
568 | } |
---|
569 | if (dd_EqualToZero(sum)) { |
---|
570 | set_addelem(poly->Ainc[i-1], k); |
---|
571 | } |
---|
572 | } |
---|
573 | if (!(poly->homogeneous) && poly->representation==dd_Inequality){ |
---|
574 | if (dd_EqualToZero(M->matrix[k-1][0])) { |
---|
575 | set_addelem(poly->Ainc[m1-1], k); /* added infinity inequality (1,0,0,...,0) */ |
---|
576 | } |
---|
577 | } |
---|
578 | } |
---|
579 | |
---|
580 | for (i=1; i<=m1; i++){ |
---|
581 | if (set_card(poly->Ainc[i-1])==M->rowsize){ |
---|
582 | set_addelem(poly->Adom, i); |
---|
583 | } |
---|
584 | } |
---|
585 | for (i=m1; i>=1; i--){ |
---|
586 | if (set_card(poly->Ainc[i-1])==0){ |
---|
587 | redundant=dd_TRUE; |
---|
588 | set_addelem(poly->Ared, i); |
---|
589 | }else { |
---|
590 | redundant=dd_FALSE; |
---|
591 | for (k=1; k<=m1; k++) { |
---|
592 | if (k!=i && !set_member(k, poly->Ared) && !set_member(k, poly->Adom) && |
---|
593 | set_subset(poly->Ainc[i-1], poly->Ainc[k-1])){ |
---|
594 | if (!redundant){ |
---|
595 | redundant=dd_TRUE; |
---|
596 | } |
---|
597 | set_addelem(poly->Ared, i); |
---|
598 | } |
---|
599 | } |
---|
600 | } |
---|
601 | } |
---|
602 | dd_FreeMatrix(M); |
---|
603 | poly->AincGenerated=dd_TRUE; |
---|
604 | _L99:; |
---|
605 | dd_clear(sum); dd_clear(temp); |
---|
606 | } |
---|
607 | |
---|
608 | |
---|
609 | std::vector<std::vector<int> > extremeRaysInequalityIndices(const ZMatrix &inequalities) |
---|
610 | { |
---|
611 | int dim2=inequalities.getHeight(); |
---|
612 | if(dim2==0)return std::vector<std::vector<int> >(); |
---|
613 | // int dimension=inequalities.getWidth(); |
---|
614 | |
---|
615 | dd_MatrixPtr A=NULL; |
---|
616 | dd_ErrorType err=dd_NoError; |
---|
617 | |
---|
618 | ensureCddInitialisation(); |
---|
619 | A=ZMatrix2MatrixGmp(inequalities, &err); |
---|
620 | |
---|
621 | dd_PolyhedraPtr poly; |
---|
622 | poly=dd_DDMatrix2Poly2(A, dd_LexMin, &err); |
---|
623 | |
---|
624 | if (poly->child==NULL || poly->child->CompStatus!=dd_AllFound) assert(0); |
---|
625 | if (poly->AincGenerated==dd_FALSE) dd_ComputeAinc(poly); |
---|
626 | |
---|
627 | std::vector<std::vector<int> > ret; |
---|
628 | |
---|
629 | /* |
---|
630 | How do we interpret the cddlib output? For a long ting gfan has |
---|
631 | been using poly->n as the number of rays of the cone and thus |
---|
632 | returned sets of indices that actually gave the lineality |
---|
633 | space. The mistake was then caught later in PolyhedralCone. On Feb |
---|
634 | 17 2009 gfan was changed to check the length of each set to make |
---|
635 | sure that it does not specify the lineality space and only return |
---|
636 | those sets giving rise to rays. This does not seem to be the best |
---|
637 | strategy and might even be wrong. |
---|
638 | */ |
---|
639 | |
---|
640 | |
---|
641 | for (int k=1; k<=poly->n; k++) |
---|
642 | { |
---|
643 | int length=0; |
---|
644 | for (int i=1; i<=poly->m1; i++) |
---|
645 | if(set_member(k,poly->Ainc[i-1]))length++; |
---|
646 | if(length!=dim2) |
---|
647 | { |
---|
648 | std::vector<int> v(length); |
---|
649 | int j=0; |
---|
650 | for (int i=1; i<=poly->m1; i++) |
---|
651 | if(set_member(k,poly->Ainc[i-1]))v[j++]=i-1; |
---|
652 | ret.push_back(v); |
---|
653 | } |
---|
654 | } |
---|
655 | |
---|
656 | dd_FreeMatrix(A); |
---|
657 | dd_FreePolyhedra(poly); |
---|
658 | |
---|
659 | return ret; |
---|
660 | _L99: |
---|
661 | assert(0); |
---|
662 | return std::vector<std::vector<int> >(); |
---|
663 | } |
---|
664 | |
---|
665 | }; |
---|
666 | |
---|
667 | LpSolver lpSolver; |
---|
668 | |
---|
669 | bool ZCone::isInStateMinimum(int s)const |
---|
670 | { |
---|
671 | return state>=s; |
---|
672 | } |
---|
673 | |
---|
674 | |
---|
675 | bool operator<(ZCone const &a, ZCone const &b) |
---|
676 | { |
---|
677 | assert(a.state>=3); |
---|
678 | assert(b.state>=3); |
---|
679 | |
---|
680 | if(a.n<b.n)return true; |
---|
681 | if(a.n>b.n)return false; |
---|
682 | |
---|
683 | if(a.equations<b.equations)return true; |
---|
684 | if(b.equations<a.equations)return false; |
---|
685 | |
---|
686 | if(a.inequalities<b.inequalities)return true; |
---|
687 | if(b.inequalities<a.inequalities)return false; |
---|
688 | |
---|
689 | return false; |
---|
690 | } |
---|
691 | |
---|
692 | |
---|
693 | bool operator!=(ZCone const &a, ZCone const &b) |
---|
694 | { |
---|
695 | return (a<b)||(b<a); |
---|
696 | } |
---|
697 | |
---|
698 | |
---|
699 | void ZCone::ensureStateAsMinimum(int s)const |
---|
700 | { |
---|
701 | if((state<1) && (s==1)) |
---|
702 | { |
---|
703 | { |
---|
704 | QMatrix m=ZToQMatrix(equations); |
---|
705 | m.reduce(); |
---|
706 | m.removeZeroRows(); |
---|
707 | |
---|
708 | ZMatrix newInequalities(0,inequalities.getWidth()); |
---|
709 | for(int i=0;i<inequalities.getHeight();i++) |
---|
710 | { |
---|
711 | QVector w=ZToQVector(inequalities[i]); |
---|
712 | w=m.canonicalize(w); |
---|
713 | if(!w.isZero()) |
---|
714 | newInequalities.appendRow(QToZVectorPrimitive(w)); |
---|
715 | } |
---|
716 | |
---|
717 | inequalities=newInequalities; |
---|
718 | inequalities.sortAndRemoveDuplicateRows(); |
---|
719 | equations=QToZMatrixPrimitive(m); |
---|
720 | } |
---|
721 | |
---|
722 | if(!(preassumptions&PCP_impliedEquationsKnown)) |
---|
723 | if(inequalities.getHeight()>1)//there can be no implied equation unless we have at least two inequalities |
---|
724 | lpSolver.removeRedundantRows(inequalities,equations,false); |
---|
725 | |
---|
726 | assert(inequalities.getWidth()==equations.getWidth()); |
---|
727 | } |
---|
728 | if((state<2) && (s>=2) && !(preassumptions&PCP_facetsKnown)) |
---|
729 | { |
---|
730 | /* if(inequalities.size()>25) |
---|
731 | { |
---|
732 | IntegerVectorList h1; |
---|
733 | IntegerVectorList h2; |
---|
734 | bool a=false; |
---|
735 | for(IntegerVectorList::const_iterator i=inequalities.begin();i!=inequalities.end();i++) |
---|
736 | { |
---|
737 | if(a) |
---|
738 | h1.push_back(*i); |
---|
739 | else |
---|
740 | h2.push_back(*i); |
---|
741 | a=!a; |
---|
742 | } |
---|
743 | PolyhedralCone c1(h1,equations); |
---|
744 | PolyhedralCone c2(h2,equations); |
---|
745 | c1.ensureStateAsMinimum(2); |
---|
746 | c2.ensureStateAsMinimum(2); |
---|
747 | inequalities=c1.inequalities; |
---|
748 | for(IntegerVectorList::const_iterator i=c2.inequalities.begin();i!=c2.inequalities.end();i++) |
---|
749 | inequalities.push_back(*i); |
---|
750 | } |
---|
751 | */ |
---|
752 | if(equations.getHeight()) |
---|
753 | { |
---|
754 | QMatrix m=ZToQMatrix(equations); |
---|
755 | m.reduce(); |
---|
756 | m.REformToRREform(); |
---|
757 | ZMatrix inequalities2(0,equations.getWidth()); |
---|
758 | for(int i=0;i<inequalities.getHeight();i++) |
---|
759 | { |
---|
760 | inequalities2.appendRow(QToZVectorPrimitive(m.canonicalize(ZToQVector(inequalities[i])))); |
---|
761 | } |
---|
762 | inequalities=LpSolver::fastNormals(inequalities2); |
---|
763 | goto noFallBack; |
---|
764 | fallBack://alternativ (disabled) |
---|
765 | lpSolver.removeRedundantRows(inequalities,equations,true); |
---|
766 | noFallBack:; |
---|
767 | } |
---|
768 | else |
---|
769 | inequalities=LpSolver::fastNormals(inequalities); |
---|
770 | } |
---|
771 | if((state<3) && (s>=3)) |
---|
772 | { |
---|
773 | QMatrix equations2=ZToQMatrix(equations); |
---|
774 | equations2.reduce(false,false,true); |
---|
775 | equations2.REformToRREform(true); |
---|
776 | for(int i=0;i<inequalities.getHeight();i++) |
---|
777 | { |
---|
778 | inequalities[i]=QToZVectorPrimitive(equations2.canonicalize(ZToQVector(inequalities[i]))); |
---|
779 | } |
---|
780 | inequalities.sortRows(); |
---|
781 | equations=QToZMatrixPrimitive(equations2); |
---|
782 | } |
---|
783 | if(state<s) |
---|
784 | state=s; |
---|
785 | } |
---|
786 | |
---|
787 | std::ostream &operator<<(std::ostream &f, ZCone const &c) |
---|
788 | { |
---|
789 | f<<"Ambient dimension:"<<c.n<<std::endl; |
---|
790 | f<<"Inequalities:"<<std::endl; |
---|
791 | f<<c.inequalities<<std::endl; |
---|
792 | f<<"Equations:"<<std::endl; |
---|
793 | f<<c.equations<<std::endl; |
---|
794 | return f; |
---|
795 | } |
---|
796 | |
---|
797 | std::string ZCone::toString()const |
---|
798 | { |
---|
799 | std::stringstream f; |
---|
800 | f<<*this; |
---|
801 | return f.str(); |
---|
802 | } |
---|
803 | |
---|
804 | ZCone::ZCone(int ambientDimension): |
---|
805 | preassumptions(PCP_impliedEquationsKnown|PCP_facetsKnown), |
---|
806 | state(1), |
---|
807 | n(ambientDimension), |
---|
808 | multiplicity(1), |
---|
809 | linearForms(ZMatrix(0,ambientDimension)), |
---|
810 | inequalities(ZMatrix(0,ambientDimension)), |
---|
811 | equations(ZMatrix(0,ambientDimension)), |
---|
812 | haveExtremeRaysBeenCached(false) |
---|
813 | { |
---|
814 | } |
---|
815 | |
---|
816 | |
---|
817 | ZCone::ZCone(ZMatrix const &inequalities_, ZMatrix const &equations_, int preassumptions_): |
---|
818 | preassumptions(preassumptions_), |
---|
819 | state(0), |
---|
820 | n(inequalities_.getWidth()), |
---|
821 | multiplicity(1), |
---|
822 | linearForms(ZMatrix(0,inequalities_.getWidth())), |
---|
823 | inequalities(inequalities_), |
---|
824 | equations(equations_), |
---|
825 | haveExtremeRaysBeenCached(false) |
---|
826 | { |
---|
827 | assert(preassumptions_<4);//OTHERWISE WE ARE DOING SOMETHING STUPID LIKE SPECIFYING AMBIENT DIMENSION |
---|
828 | assert(equations_.getWidth()==n); |
---|
829 | ensureStateAsMinimum(1); |
---|
830 | } |
---|
831 | |
---|
832 | void ZCone::canonicalize() |
---|
833 | { |
---|
834 | ensureStateAsMinimum(3); |
---|
835 | } |
---|
836 | |
---|
837 | void ZCone::findFacets() |
---|
838 | { |
---|
839 | ensureStateAsMinimum(2); |
---|
840 | } |
---|
841 | |
---|
842 | ZMatrix ZCone::getFacets()const |
---|
843 | { |
---|
844 | ensureStateAsMinimum(2); |
---|
845 | return inequalities; |
---|
846 | } |
---|
847 | |
---|
848 | void ZCone::findImpliedEquations() |
---|
849 | { |
---|
850 | ensureStateAsMinimum(1); |
---|
851 | } |
---|
852 | |
---|
853 | ZMatrix ZCone::getImpliedEquations()const |
---|
854 | { |
---|
855 | ensureStateAsMinimum(1); |
---|
856 | return equations; |
---|
857 | } |
---|
858 | |
---|
859 | ZVector ZCone::getRelativeInteriorPoint()const |
---|
860 | { |
---|
861 | ensureStateAsMinimum(1); |
---|
862 | // assert(state>=1); |
---|
863 | |
---|
864 | return lpSolver.relativeInteriorPoint(inequalities,equations); |
---|
865 | } |
---|
866 | |
---|
867 | ZVector ZCone::getUniquePoint()const |
---|
868 | { |
---|
869 | ZMatrix rays=extremeRays(); |
---|
870 | ZVector ret(n); |
---|
871 | for(int i=0;i<rays.getHeight();i++) |
---|
872 | ret+=rays[i]; |
---|
873 | |
---|
874 | return ret; |
---|
875 | } |
---|
876 | |
---|
877 | ZVector ZCone::getUniquePointFromExtremeRays(ZMatrix const &extremeRays)const |
---|
878 | { |
---|
879 | ZVector ret(n); |
---|
880 | for(int i=0;i<extremeRays.getHeight();i++) |
---|
881 | if(contains(extremeRays[i]))ret+=extremeRays[i]; |
---|
882 | return ret; |
---|
883 | } |
---|
884 | |
---|
885 | |
---|
886 | int ZCone::ambientDimension()const |
---|
887 | { |
---|
888 | return n; |
---|
889 | } |
---|
890 | |
---|
891 | |
---|
892 | int ZCone::codimension()const |
---|
893 | { |
---|
894 | return ambientDimension()-dimension(); |
---|
895 | } |
---|
896 | |
---|
897 | |
---|
898 | int ZCone::dimension()const |
---|
899 | { |
---|
900 | // assert(state>=1); |
---|
901 | ensureStateAsMinimum(1); |
---|
902 | return ambientDimension()-equations.getHeight(); |
---|
903 | } |
---|
904 | |
---|
905 | |
---|
906 | int ZCone::dimensionOfLinealitySpace()const |
---|
907 | { |
---|
908 | ZMatrix temp=inequalities; |
---|
909 | temp.append(equations); |
---|
910 | ZCone temp2(ZMatrix(0,n),temp); |
---|
911 | return temp2.dimension(); |
---|
912 | } |
---|
913 | |
---|
914 | |
---|
915 | bool ZCone::isOrigin()const |
---|
916 | { |
---|
917 | return dimension()==0; |
---|
918 | } |
---|
919 | |
---|
920 | |
---|
921 | bool ZCone::isFullSpace()const |
---|
922 | { |
---|
923 | for(int i=0;i<inequalities.getHeight();i++) |
---|
924 | if(!inequalities[i].isZero())return false; |
---|
925 | for(int i=0;i<equations.getHeight();i++) |
---|
926 | if(!equations[i].isZero())return false; |
---|
927 | return true; |
---|
928 | } |
---|
929 | |
---|
930 | |
---|
931 | ZCone intersection(const ZCone &a, const ZCone &b) |
---|
932 | { |
---|
933 | assert(a.ambientDimension()==b.ambientDimension()); |
---|
934 | ZMatrix inequalities=a.inequalities; |
---|
935 | inequalities.append(b.inequalities); |
---|
936 | ZMatrix equations=a.equations; |
---|
937 | equations.append(b.equations); |
---|
938 | |
---|
939 | equations.sortAndRemoveDuplicateRows(); |
---|
940 | inequalities.sortAndRemoveDuplicateRows(); |
---|
941 | |
---|
942 | { |
---|
943 | ZMatrix Aequations=a.equations; |
---|
944 | ZMatrix Ainequalities=a.inequalities; |
---|
945 | Aequations.sortAndRemoveDuplicateRows(); |
---|
946 | Ainequalities.sortAndRemoveDuplicateRows(); |
---|
947 | if((Ainequalities.getHeight()==inequalities.getHeight()) && (Aequations.getHeight()==equations.getHeight()))return a; |
---|
948 | ZMatrix Bequations=b.equations; |
---|
949 | ZMatrix Binequalities=b.inequalities; |
---|
950 | Bequations.sortAndRemoveDuplicateRows(); |
---|
951 | Binequalities.sortAndRemoveDuplicateRows(); |
---|
952 | if((Binequalities.getHeight()==inequalities.getHeight()) && (Bequations.getHeight()==equations.getHeight()))return b; |
---|
953 | } |
---|
954 | |
---|
955 | return ZCone(inequalities,equations); |
---|
956 | } |
---|
957 | |
---|
958 | /* |
---|
959 | PolyhedralCone product(const PolyhedralCone &a, const PolyhedralCone &b) |
---|
960 | { |
---|
961 | IntegerVectorList equations2; |
---|
962 | IntegerVectorList inequalities2; |
---|
963 | |
---|
964 | int n1=a.n; |
---|
965 | int n2=b.n; |
---|
966 | |
---|
967 | for(IntegerVectorList::const_iterator i=a.equations.begin();i!=a.equations.end();i++) |
---|
968 | equations2.push_back(concatenation(*i,IntegerVector(n2))); |
---|
969 | for(IntegerVectorList::const_iterator i=b.equations.begin();i!=b.equations.end();i++) |
---|
970 | equations2.push_back(concatenation(IntegerVector(n1),*i)); |
---|
971 | for(IntegerVectorList::const_iterator i=a.inequalities.begin();i!=a.inequalities.end();i++) |
---|
972 | inequalities2.push_back(concatenation(*i,IntegerVector(n2))); |
---|
973 | for(IntegerVectorList::const_iterator i=b.inequalities.begin();i!=b.inequalities.end();i++) |
---|
974 | inequalities2.push_back(concatenation(IntegerVector(n1),*i)); |
---|
975 | |
---|
976 | PolyhedralCone ret(inequalities2,equations2,n1+n2); |
---|
977 | ret.setMultiplicity(a.getMultiplicity()*b.getMultiplicity()); |
---|
978 | ret.setLinearForm(concatenation(a.getLinearForm(),b.getLinearForm())); |
---|
979 | |
---|
980 | ret.ensureStateAsMinimum(a.state); |
---|
981 | ret.ensureStateAsMinimum(b.state); |
---|
982 | |
---|
983 | return ret; |
---|
984 | }*/ |
---|
985 | |
---|
986 | |
---|
987 | ZCone ZCone::positiveOrthant(int dimension) |
---|
988 | { |
---|
989 | return ZCone(ZMatrix::identity(dimension),ZMatrix(0,dimension)); |
---|
990 | } |
---|
991 | |
---|
992 | |
---|
993 | ZCone ZCone::givenByRays(ZMatrix const &generators, ZMatrix const &linealitySpace) |
---|
994 | { |
---|
995 | //rewrite modulo lineality space |
---|
996 | /* ZMatrix newGenerators(generators.getHeight(),generators.getWidth()); |
---|
997 | { |
---|
998 | QMatrix l=ZToQMatrix(linealitySpace); |
---|
999 | l.reduce(); |
---|
1000 | for(int i=0;i<generators.getHeight();i++) |
---|
1001 | newGenerators[i]=QToZVectorPrimitive(l.canonicalize(ZToQVector(generators[i]))); |
---|
1002 | } |
---|
1003 | */ |
---|
1004 | // ZCone dual(newGenerators,linealitySpace); |
---|
1005 | ZCone dual(generators,linealitySpace); |
---|
1006 | // dual.findFacets(); |
---|
1007 | // dual.canonicalize(); |
---|
1008 | ZMatrix inequalities=dual.extremeRays(); |
---|
1009 | |
---|
1010 | /* ZMatrix span=generators; |
---|
1011 | span.append(linealitySpace); |
---|
1012 | QMatrix m2Q=ZToQMatrix(span); |
---|
1013 | ZMatrix equations=QToZMatrixPrimitive(m2Q.reduceAndComputeKernel()); |
---|
1014 | */ |
---|
1015 | ZMatrix equations=dual.generatorsOfLinealitySpace(); |
---|
1016 | // equations.reduce();equations.removeZeroRows(); |
---|
1017 | |
---|
1018 | |
---|
1019 | return ZCone(inequalities,equations,PCP_impliedEquationsKnown|PCP_facetsKnown); |
---|
1020 | } |
---|
1021 | |
---|
1022 | |
---|
1023 | bool ZCone::containsPositiveVector()const |
---|
1024 | { |
---|
1025 | ZCone temp=intersection(*this,ZCone::positiveOrthant(n)); |
---|
1026 | return temp.getRelativeInteriorPoint().isPositive(); |
---|
1027 | } |
---|
1028 | |
---|
1029 | |
---|
1030 | bool ZCone::contains(ZVector const &v)const |
---|
1031 | { |
---|
1032 | for(int i=0;i<equations.getHeight();i++) |
---|
1033 | { |
---|
1034 | if(!dot(equations[i],v).isZero())return false; |
---|
1035 | } |
---|
1036 | for(int i=0;i<inequalities.getHeight();i++) |
---|
1037 | { |
---|
1038 | if(dot(inequalities[i],v).sign()<0)return false; |
---|
1039 | } |
---|
1040 | return true; |
---|
1041 | } |
---|
1042 | |
---|
1043 | |
---|
1044 | bool ZCone::containsRowsOf(ZMatrix const &m)const |
---|
1045 | { |
---|
1046 | for(int i=0;i<m.getHeight();i++) |
---|
1047 | if(!contains(m[i]))return false; |
---|
1048 | return true; |
---|
1049 | } |
---|
1050 | |
---|
1051 | |
---|
1052 | bool ZCone::contains(ZCone const &c)const |
---|
1053 | { |
---|
1054 | ZCone c2=intersection(*this,c); |
---|
1055 | ZCone c3=c; |
---|
1056 | c2.canonicalize(); |
---|
1057 | c3.canonicalize(); |
---|
1058 | return !(c2!=c3); |
---|
1059 | } |
---|
1060 | |
---|
1061 | |
---|
1062 | bool ZCone::containsRelatively(ZVector const &v)const |
---|
1063 | { |
---|
1064 | ensureStateAsMinimum(1); |
---|
1065 | // assert(state>=1); |
---|
1066 | for(int i=0;i<equations.getHeight();i++) |
---|
1067 | { |
---|
1068 | if(!dot(equations[i],v).isZero())return false; |
---|
1069 | } |
---|
1070 | for(int i=0;i<inequalities.getHeight();i++) |
---|
1071 | { |
---|
1072 | if(dot(inequalities[i],v).sign()<=0)return false; |
---|
1073 | } |
---|
1074 | return true; |
---|
1075 | } |
---|
1076 | |
---|
1077 | |
---|
1078 | bool ZCone::isSimplicial()const |
---|
1079 | { |
---|
1080 | // assert(state>=2); |
---|
1081 | ensureStateAsMinimum(2); |
---|
1082 | return codimension()+inequalities.getHeight()+dimensionOfLinealitySpace()==n; |
---|
1083 | } |
---|
1084 | |
---|
1085 | |
---|
1086 | ZCone ZCone::linealitySpace()const |
---|
1087 | { |
---|
1088 | ZCone ret(ZMatrix(0,n),combineOnTop(equations,inequalities)); |
---|
1089 | // ret.ensureStateAsMinimum(state); |
---|
1090 | return ret; |
---|
1091 | } |
---|
1092 | |
---|
1093 | |
---|
1094 | ZCone ZCone::dualCone()const |
---|
1095 | { |
---|
1096 | ensureStateAsMinimum(1); |
---|
1097 | // assert(state>=1); |
---|
1098 | |
---|
1099 | ZMatrix dualInequalities,dualEquations; |
---|
1100 | lpSolver.dual(inequalities,equations,dualInequalities,dualEquations); |
---|
1101 | ZCone ret(dualInequalities,dualEquations); |
---|
1102 | ret.ensureStateAsMinimum(state); |
---|
1103 | |
---|
1104 | return ret; |
---|
1105 | } |
---|
1106 | |
---|
1107 | |
---|
1108 | ZCone ZCone::negated()const |
---|
1109 | { |
---|
1110 | ZCone ret(-inequalities,equations,(areFacetsKnown()?PCP_facetsKnown:0)|(areImpliedEquationsKnown()?PCP_impliedEquationsKnown:0)); |
---|
1111 | // ret.ensureStateAsMinimum(state); |
---|
1112 | return ret; |
---|
1113 | } |
---|
1114 | |
---|
1115 | |
---|
1116 | ZMatrix ZCone::extremeRays(ZMatrix const *generatorsOfLinealitySpace)const |
---|
1117 | { |
---|
1118 | // assert((dimension()==ambientDimension()) || (state>=3)); |
---|
1119 | if(dimension()!=ambientDimension()) |
---|
1120 | ensureStateAsMinimum(3); |
---|
1121 | |
---|
1122 | if(haveExtremeRaysBeenCached)return cachedExtremeRays; |
---|
1123 | ZMatrix ret(0,n); |
---|
1124 | std::vector<std::vector<int> > indices=lpSolver.extremeRaysInequalityIndices(inequalities); |
---|
1125 | |
---|
1126 | for(unsigned i=0;i<indices.size();i++) |
---|
1127 | { |
---|
1128 | /* At this point we know lineality space, implied equations and |
---|
1129 | also inequalities for the ray. To construct a vector on the |
---|
1130 | ray which is stable under (or indendent of) angle and |
---|
1131 | linarity preserving transformation we find the dimension 1 |
---|
1132 | subspace orthorgonal to the implied equations and the |
---|
1133 | lineality space and pick a suitable primitive generator */ |
---|
1134 | |
---|
1135 | /* To be more precise, |
---|
1136 | * let E be the set of equations, and v the inequality defining a ray R. |
---|
1137 | * We wish to find a vector satisfying these, but it must also be orthogonal |
---|
1138 | * to the lineality space of the cone, that is, in the span of {E,v}. |
---|
1139 | * One way to get such a vector is to project v to E an get a vector p. |
---|
1140 | * Then v-p is in the span of {E,v} by construction. |
---|
1141 | * The vector v-p is also in the orthogonal complement to E by construction, |
---|
1142 | * that is, the span of R. |
---|
1143 | * We wish to argue that it is not zero. |
---|
1144 | * That would imply that v=p, meaning that v is in the span of the equations. |
---|
1145 | * However, that would contradict that R is a ray. |
---|
1146 | * In case v-p does not satisfy the inequality v (is this possible?), we change the sign. |
---|
1147 | * |
---|
1148 | * As a consequence we need the following procedure |
---|
1149 | * primitiveProjection(): |
---|
1150 | * Input: E,v |
---|
1151 | * Output: A primitive representation of the vector v-p, where p is the projection of v onto E |
---|
1152 | * |
---|
1153 | * Notice that the output is a Q linear combination of the input and that p is |
---|
1154 | * a linear combination of E. The check that p has been computed correctly, |
---|
1155 | * it suffices to check that v-p satisfies the equations E. |
---|
1156 | * The routine will actually first compute a multiple of v-p. |
---|
1157 | * It will do this using floating point arithmetics. It will then transform |
---|
1158 | * the coefficients to get the multiple of v-p into integers. Then it |
---|
1159 | * verifies in exact arithmetics, that with these coefficients we get a point |
---|
1160 | * satisfying E. It then returns the primitive vector on the ray v-p. |
---|
1161 | * In case of a failure it falls back to an implementation using rational arithmetics. |
---|
1162 | */ |
---|
1163 | |
---|
1164 | |
---|
1165 | std::vector<int> asVector(inequalities.getHeight()); |
---|
1166 | for(unsigned j=0;j<indices[i].size();j++){asVector[indices[i][j]]=1;} |
---|
1167 | ZMatrix equations=this->equations; |
---|
1168 | ZVector theInequality; |
---|
1169 | |
---|
1170 | for(unsigned j=0;j<asVector.size();j++) |
---|
1171 | if(asVector[j]) |
---|
1172 | equations.appendRow(inequalities[j]); |
---|
1173 | else |
---|
1174 | theInequality=inequalities[j]; |
---|
1175 | |
---|
1176 | assert(!theInequality.isZero()); |
---|
1177 | |
---|
1178 | ZVector thePrimitiveVector; |
---|
1179 | if(generatorsOfLinealitySpace) |
---|
1180 | { |
---|
1181 | QMatrix temp=ZToQMatrix(combineOnTop(equations,*generatorsOfLinealitySpace)); |
---|
1182 | thePrimitiveVector=QToZVectorPrimitive(temp.reduceAndComputeVectorInKernel()); |
---|
1183 | } |
---|
1184 | else |
---|
1185 | { |
---|
1186 | QMatrix linealitySpaceOrth=ZToQMatrix(combineOnTop(this->equations,inequalities)); |
---|
1187 | |
---|
1188 | |
---|
1189 | QMatrix temp=combineOnTop(linealitySpaceOrth.reduceAndComputeKernel(),ZToQMatrix(equations)); |
---|
1190 | thePrimitiveVector=QToZVectorPrimitive(temp.reduceAndComputeVectorInKernel()); |
---|
1191 | } |
---|
1192 | if(!contains(thePrimitiveVector))thePrimitiveVector=-thePrimitiveVector; |
---|
1193 | ret.appendRow(thePrimitiveVector); |
---|
1194 | } |
---|
1195 | |
---|
1196 | cachedExtremeRays=ret; |
---|
1197 | haveExtremeRaysBeenCached=true; |
---|
1198 | |
---|
1199 | return ret; |
---|
1200 | } |
---|
1201 | |
---|
1202 | |
---|
1203 | Integer ZCone::getMultiplicity()const |
---|
1204 | { |
---|
1205 | return multiplicity; |
---|
1206 | } |
---|
1207 | |
---|
1208 | |
---|
1209 | void ZCone::setMultiplicity(Integer const &m) |
---|
1210 | { |
---|
1211 | multiplicity=m; |
---|
1212 | } |
---|
1213 | |
---|
1214 | |
---|
1215 | ZMatrix ZCone::getLinearForms()const |
---|
1216 | { |
---|
1217 | return linearForms; |
---|
1218 | } |
---|
1219 | |
---|
1220 | |
---|
1221 | void ZCone::setLinearForms(ZMatrix const &linearForms_) |
---|
1222 | { |
---|
1223 | linearForms=linearForms_; |
---|
1224 | } |
---|
1225 | |
---|
1226 | |
---|
1227 | ZMatrix ZCone::quotientLatticeBasis()const |
---|
1228 | { |
---|
1229 | // assert(isInStateMinimum(1));// Implied equations must have been computed in order to know the span of the cone |
---|
1230 | ensureStateAsMinimum(1); |
---|
1231 | |
---|
1232 | |
---|
1233 | int a=equations.getHeight(); |
---|
1234 | int b=inequalities.getHeight(); |
---|
1235 | |
---|
1236 | // Implementation below could be moved to nonLP part of code. |
---|
1237 | |
---|
1238 | // small vector space defined by a+b equations.... big by a equations. |
---|
1239 | |
---|
1240 | ZMatrix M=combineLeftRight(combineLeftRight( |
---|
1241 | equations.transposed(), |
---|
1242 | inequalities.transposed()), |
---|
1243 | ZMatrix::identity(n)); |
---|
1244 | M.reduce(false,true); |
---|
1245 | /* |
---|
1246 | [A|B|I] is reduced to [A'|B'|C'] meaning [A'|B']=C'[A|B] and A'=C'A. |
---|
1247 | |
---|
1248 | [A'|B'] is in row echelon form, implying that the rows of C' corresponding to zero rows |
---|
1249 | of [A'|B'] generate the lattice cokernel of [A|B] - that is the linealityspace intersected with Z^n. |
---|
1250 | |
---|
1251 | [A'] is in row echelon form, implying that the rows of C' corresponding to zero rows of [A'] generate |
---|
1252 | the lattice cokernel of [A] - that is the span of the cone intersected with Z^n. |
---|
1253 | |
---|
1254 | It is clear that the second row set is a superset of the first. Their difference is a basis for the quotient. |
---|
1255 | */ |
---|
1256 | ZMatrix ret(0,n); |
---|
1257 | |
---|
1258 | for(int i=0;i<M.getHeight();i++) |
---|
1259 | if(M[i].toVector().subvector(0,a).isZero()&&!M[i].toVector().subvector(a,a+b).isZero()) |
---|
1260 | { |
---|
1261 | ret.appendRow(M[i].toVector().subvector(a+b,a+b+n)); |
---|
1262 | } |
---|
1263 | |
---|
1264 | return ret; |
---|
1265 | } |
---|
1266 | |
---|
1267 | |
---|
1268 | ZVector ZCone::semiGroupGeneratorOfRay()const |
---|
1269 | { |
---|
1270 | ZMatrix temp=quotientLatticeBasis(); |
---|
1271 | assert(temp.getHeight()==1); |
---|
1272 | for(int i=0;i<inequalities.getHeight();i++) |
---|
1273 | if(dot(temp[0].toVector(),inequalities[i].toVector()).sign()<0) |
---|
1274 | { |
---|
1275 | temp[0]=-temp[0].toVector(); |
---|
1276 | break; |
---|
1277 | } |
---|
1278 | return temp[0]; |
---|
1279 | } |
---|
1280 | |
---|
1281 | |
---|
1282 | ZCone ZCone::link(ZVector const &w)const |
---|
1283 | { |
---|
1284 | /* Observe that the inequalities giving rise to facets |
---|
1285 | * also give facets in the link, if they are kept as |
---|
1286 | * inequalities. This means that the state cannot decrease |
---|
1287 | * when taking links - that is why we specify the PCP flags. |
---|
1288 | */ |
---|
1289 | ZMatrix inequalities2(0,n); |
---|
1290 | for(int j=0;j<inequalities.getHeight();j++) |
---|
1291 | if(dot(w,inequalities[j]).sign()==0)inequalities2.appendRow(inequalities[j]); |
---|
1292 | ZCone C(inequalities2,equations,(areImpliedEquationsKnown()?PCP_impliedEquationsKnown:0)|(areFacetsKnown()?PCP_facetsKnown:0)); |
---|
1293 | C.ensureStateAsMinimum(state); |
---|
1294 | |
---|
1295 | C.setLinearForms(getLinearForms()); |
---|
1296 | C.setMultiplicity(getMultiplicity()); |
---|
1297 | |
---|
1298 | return C; |
---|
1299 | } |
---|
1300 | |
---|
1301 | bool ZCone::hasFace(ZCone const &f)const |
---|
1302 | { |
---|
1303 | if(!contains(f.getRelativeInteriorPoint()))return false; |
---|
1304 | ZCone temp=faceContaining(f.getRelativeInteriorPoint()); |
---|
1305 | temp.canonicalize(); |
---|
1306 | // ZCone temp2=*this; |
---|
1307 | ZCone temp2=f; |
---|
1308 | temp2.canonicalize(); |
---|
1309 | // std::cout << temp << std::endl; |
---|
1310 | // std::cout << temp2 << std::endl; |
---|
1311 | |
---|
1312 | return !(temp2!=temp); |
---|
1313 | } |
---|
1314 | |
---|
1315 | ZCone ZCone::faceContaining(ZVector const &v)const |
---|
1316 | { |
---|
1317 | assert(n==(int)v.size()); |
---|
1318 | assert(contains(v)); |
---|
1319 | ZMatrix newEquations=equations; |
---|
1320 | ZMatrix newInequalities(0,n); |
---|
1321 | for(int i=0;i<inequalities.getHeight();i++) |
---|
1322 | if(dot(inequalities[i],v).sign()!=0) |
---|
1323 | newInequalities.appendRow(inequalities[i]); |
---|
1324 | else |
---|
1325 | newEquations.appendRow(inequalities[i]); |
---|
1326 | |
---|
1327 | ZCone ret(newInequalities,newEquations,(state>=1)?PCP_impliedEquationsKnown:0); |
---|
1328 | ret.ensureStateAsMinimum(state); |
---|
1329 | return ret; |
---|
1330 | } |
---|
1331 | |
---|
1332 | |
---|
1333 | ZMatrix ZCone::getInequalities()const |
---|
1334 | { |
---|
1335 | return inequalities; |
---|
1336 | } |
---|
1337 | |
---|
1338 | |
---|
1339 | ZMatrix ZCone::getEquations()const |
---|
1340 | { |
---|
1341 | return equations; |
---|
1342 | } |
---|
1343 | |
---|
1344 | |
---|
1345 | ZMatrix ZCone::generatorsOfSpan()const |
---|
1346 | { |
---|
1347 | ensureStateAsMinimum(1); |
---|
1348 | QMatrix l=ZToQMatrix(equations); |
---|
1349 | return QToZMatrixPrimitive(l.reduceAndComputeKernel()); |
---|
1350 | } |
---|
1351 | |
---|
1352 | |
---|
1353 | ZMatrix ZCone::generatorsOfLinealitySpace()const |
---|
1354 | { |
---|
1355 | QMatrix l=ZToQMatrix(combineOnTop(inequalities,equations)); |
---|
1356 | return QToZMatrixPrimitive(l.reduceAndComputeKernel()); |
---|
1357 | } |
---|
1358 | |
---|
1359 | } |
---|