1 | // matrix.h |
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2 | |
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3 | |
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4 | // This class is designed to handle the input of the integer programming |
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5 | // problem. It offers facilities to convert a two-dimensional integer array |
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6 | // into a matrix and to read a matrix from an input file. |
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7 | // Furthermore, some special routines needed by the IP-algorithms are |
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8 | // implemented: |
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9 | // - the computation of a lattice basis for the integer kernel via the LLL |
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10 | // algorithm; |
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11 | // - the computation of a kernel vector which has no zero components (if |
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12 | // such a vector exists) and is a basis vector for the kernel lattice; |
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13 | // - the procedure of Hosten and Shapiro computing a small set of saturation |
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14 | // variables for the toric ideal given by the matrix kernel. |
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15 | |
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16 | |
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17 | |
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18 | #ifndef MATRIX_H |
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19 | #define MATRIX_H |
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20 | |
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21 | |
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22 | |
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23 | #include "LLL.h" |
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24 | |
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25 | |
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26 | |
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27 | class matrix |
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28 | { |
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29 | |
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30 | |
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31 | |
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32 | private: |
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33 | |
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34 | int rows; |
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35 | |
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36 | int columns; |
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37 | // Also used as error flag (values <0): |
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38 | // -1 indicates a "semantic" error (which occurs e.g. if some constructor |
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39 | // argument is out of range) |
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40 | // -2 indicates an error occurred when reading from a file |
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41 | |
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42 | Integer **coefficients; |
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43 | // the matrix entries |
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44 | |
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45 | BigInt **H; |
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46 | // This array is used to store the LLL-reduced lattice basis of the kernel. |
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47 | // Memory allocation is done in the LLL-routines, so the array is only |
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48 | // allocated if such a basis is really computed. |
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49 | |
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50 | int _kernel_dimension; |
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51 | // the number of vectors stored in H (the size of these vectors is columns) |
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52 | // If _kernel_dimension==-2, no kernel basis has been computed yet. |
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53 | // If _kernel_dimension==-1, an error has occurred during the kernel basis |
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54 | // computation. |
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55 | |
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56 | |
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57 | |
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58 | public: |
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59 | |
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60 | |
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61 | |
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62 | // constructors and destructor |
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63 | |
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64 | matrix(const int& row_number, const int& column_number); |
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65 | // Creates a zero matrix of the specified size. |
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66 | |
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67 | matrix(const int& row_number, const int& column_number, |
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68 | Integer** entries); |
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69 | // Builds a matrix from its coefficient array. |
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70 | |
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71 | matrix(ifstream& input); |
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72 | // Reads a matrix from the given ifstream. |
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73 | // The input stream must have the following format: |
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74 | // |
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75 | // m=number of rows |
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76 | // n=number of columns |
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77 | // coefficients 0..n-1 of row 1 |
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78 | // coefficients 0..n-1 of row 2 |
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79 | // ... |
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80 | // coefficients 0..n-1 of row m |
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81 | |
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82 | matrix(const int& m, const int& n, ifstream& input); |
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83 | // Reads a (m x n)-matrix from the given ifstream. |
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84 | // The input stream must have the following format: |
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85 | // |
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86 | // coefficients 0..n-1 of row 1; |
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87 | // coefficients 0..n-1 of row 2; |
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88 | // ... |
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89 | // coefficients 0..n-1 of row m. |
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90 | |
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91 | matrix(const matrix&); |
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92 | // copy-constructor (also copies H) |
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93 | |
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94 | ~matrix(); |
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95 | // destructor |
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96 | |
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97 | |
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98 | |
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99 | // object properties |
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100 | |
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101 | BOOLEAN is_nonnegative() const; |
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102 | // Returns TRUE, if all entries of the matrix are >=0, else FALSE. |
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103 | |
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104 | int error_status() const; |
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105 | // Returns columns iff columns<0 (this is the "error flag"), else 0. |
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106 | |
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107 | int row_number() const; |
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108 | // Returns the row number. |
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109 | |
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110 | int column_number() const; |
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111 | // Returns the column number. |
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112 | |
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113 | int kernel_dimension() const; |
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114 | // Returns the kernel dimension. |
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115 | |
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116 | |
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117 | |
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118 | // special routines for the IP-algorithms |
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119 | |
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120 | int LLL_kernel_basis(); |
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121 | // Computes a LLL-reduced integer basis of the matrix kernel and returns |
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122 | // the kernel dimension (-1 if an error has occurred). |
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123 | // This dimension is also stored in the member kernel_dimension. |
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124 | |
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125 | int compute_nonzero_kernel_vector(); |
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126 | // Transforms the kernel lattice basis stored in H so that it contains |
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127 | // a vector whose components are all !=0; |
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128 | // returns 0 if no such vector exists, else 1. |
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129 | // If no such basis has been computed before, this is done now. |
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130 | |
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131 | int compute_flip_variables(int*&); |
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132 | // Computes a set of flip variables for the algorithm of DiBiase and |
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133 | // Urbanke from a kernel vector with no zero components. |
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134 | // Returns the size of that set if such a kernel vector exists, else -1. |
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135 | // If necessary, such a vector is computed. |
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136 | // The computed set is copied to the argument pointer (memory allocation |
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137 | // is done in the routine) to be accessible for the calling function. |
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138 | |
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139 | int hosten_shapiro(int*& sat_var); |
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140 | // Computes a set of saturation variables for the ideal defined by the |
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141 | // kernel lattice and returns the size of that set. |
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142 | // If no lattice basis has been computed before, this is done now. |
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143 | // The computed set is stored in the argument pointer (memory allocation |
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144 | // is done in the routine) to be accessible for the calling function. |
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145 | // This routine implements the most simple strategy for computing this set: |
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146 | // The kernel vectors are examined in their actual. A "greedy" strategy |
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147 | // choosing "clever" kernel vectors to begin with could give better results |
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148 | // in many cases, but this is not guaranteed... |
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149 | // (And what is a clever choice?) |
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150 | |
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151 | // output |
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152 | |
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153 | void print() const; |
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154 | // Writes the matrix to the standard output medium. |
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155 | |
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156 | void print(FILE*) const; |
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157 | // Writes the matrix to the referenced file which has to be opened |
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158 | // for writing before. |
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159 | |
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160 | void print(ofstream&) const; |
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161 | // Writes the matrix to the given ofstream. |
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162 | |
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163 | friend class ideal; |
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164 | // Our toric ideals are all constructed from matrices, and the matrix class |
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165 | // is designed only for the needs of these constructors. So it would be |
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166 | // unnecessary overhead to hide the matrix members from these constructors. |
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167 | |
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168 | }; |
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169 | #endif |
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