1 | #ifndef MINOR_PROCESSOR_H |
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2 | #define MINOR_PROCESSOR_H |
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3 | |
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4 | #include "polys/monomials/ring.h" |
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5 | #include "kernel/polys.h" |
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6 | #include "kernel/linear_algebra/Cache.h" |
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7 | #include "kernel/linear_algebra/Minor.h" |
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8 | |
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9 | // #include <assert.h> |
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10 | #include <string> |
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11 | |
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12 | /* write "##define COUNT_AND_PRINT_OPERATIONS x" if you want |
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13 | to count all basic operations and have them printed when |
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14 | one of the methods documented herein will be invoked; |
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15 | otherwise, comment this line; |
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16 | x = 1: only final counters (after computing ALL |
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17 | specified minors) will be printed, i.e., no |
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18 | intermediate results; |
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19 | x = 2: print counters after the computation of each |
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20 | minor; this will be much more information |
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21 | x = 3: print also all intermediate matrices with the |
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22 | numbers of monomials in each entry; |
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23 | this will be much much more information */ |
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24 | //#define COUNT_AND_PRINT_OPERATIONS 2 |
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25 | |
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26 | void printCounters (char* prefix, bool resetToZero); |
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27 | |
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28 | /*! \class MinorProcessor |
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29 | \brief Class MinorProcessor implements the key methods for computing one |
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30 | or all sub-determinantes of a given size in a pre-defined matrix; either |
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31 | without caching or by using a cache. |
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32 | |
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33 | After defining the entire matrix (e.g. 10 x 14) using<br> |
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34 | MinorProcessor::defineMatrix (const int, const int, const int*),<br> |
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35 | the user may do two different things:<br> |
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36 | 1. He/she can simply compute a minor in this matrix using<br> |
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37 | MinorProcessor::getMinor (const int, const int*, const int*, |
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38 | Cache<MinorKey, MinorValue>&), or<br> |
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39 | MinorProcessor::getMinor (const int, const int*, const int*);<br> |
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40 | depending on whether a cache shall or shall not be used, respectively.<br> |
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41 | In the first case, the user simply provides all row and column indices of |
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42 | the desired minor. |
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43 | 2. He/she may define a smaller sub-matrix (e.g. 8 x 7) using |
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44 | MinorValue::defineSubMatrix (const int, const int*, const int, const int*). |
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45 | Afterwards, he/she may compute all minors of an even smaller size (e.g. |
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46 | 5 x 5) that consist exclusively of rows and columns of this (8 x 7) |
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47 | sub-matrix (inside the entire 10 x 14 matrix).<br> |
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48 | The implementation at hand eases the iteration over all such minors. Also |
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49 | in the second case there are both implementations, i.e., with and without |
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50 | using a cache.<br><br> |
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51 | MinorProcessor makes use of MinorKey, MinorValue, and Cache. The |
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52 | implementation of all mentioned classes (MinorKey, MinorValue, and |
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53 | MinorProcessor) is generic to allow for the use of different types of |
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54 | keys and values. |
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55 | \author Frank Seelisch, http://www.mathematik.uni-kl.de/~seelisch |
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56 | */ |
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57 | class MinorProcessor |
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58 | { |
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59 | protected: |
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60 | /** |
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61 | * A static method for computing the maximum number of retrievals of a |
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62 | * minor.<br> |
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63 | * More concretely, we are given a matrix of size \c rows x \c columns. We |
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64 | * furthermore assume that we have - as part of this matrix - a minor of |
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65 | * size \c containerMinorSize x \c containerMinorSize. Now we are |
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66 | * interested in the number of times a minor of yet smaller size |
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67 | * \c minorSize x \c minorSize will be needed when we compute the |
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68 | * containerMinor by Laplace's Theorem.<br> |
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69 | * The method returns the combinatorial results for both cases: |
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70 | * containerMinor is fixed within the matrix |
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71 | * (<c>multipleMinors == false</c>), or it can vary inside the matrix |
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72 | * (<c>multipleMinors == true</c>).<br> |
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73 | * The notion is here that we want to cache the small minor of size |
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74 | * \c minorSize x \c minorSize, i.e. compute it just once. |
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75 | * @param rows the number of rows of the underlying matrix |
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76 | * @param columns the number of columns of the underlying matrix |
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77 | * @param containerMinorSize the size of the container minor |
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78 | * @param minorSize the size of the small minor (which may be retrieved |
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79 | * multiple times) |
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80 | * @param multipleMinors decides whether containerMinor is fixed within |
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81 | * the underlying matrix or not |
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82 | * @return the number of times, the small minor will be needed when |
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83 | * computing one or all containerMinors |
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84 | */ |
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85 | static int NumberOfRetrievals (const int rows, const int columns, |
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86 | const int containerMinorSize, |
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87 | const int minorSize, |
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88 | const bool multipleMinors); |
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89 | /** |
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90 | * A static method for computing the binomial coefficient i over j. |
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91 | * \par Assert |
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92 | * The method checks whether <em>i >= j >= 0</em>. |
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93 | * @param i a positive integer greater than or equal to \a j |
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94 | * @param j a positive integer less than or equal to \a i, and greater |
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95 | * than or equal to \e 0. |
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96 | * @return the binomial coefficient i over j |
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97 | */ |
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98 | static int IOverJ (const int i, const int j); |
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99 | |
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100 | /** |
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101 | * A static method for computing the factorial of i. |
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102 | * \par Assert |
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103 | * The method checks whether <em>i >= 0</em>. |
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104 | * @param i an integer greater than or equal to \a 0 |
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105 | * @return the factorial of i |
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106 | */ |
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107 | static int Faculty (const int i); |
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108 | |
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109 | /** |
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110 | * A method for iterating through all possible subsets of \c k rows and |
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111 | * \c k columns inside a pre-defined submatrix of a pre-defined matrix.<br> |
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112 | * The method will set \c _rowKey and \c columnKey to represent the |
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113 | * next possible subsets of \c k rows and columns inside the submatrix |
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114 | * determined by \c _globalRowKey and \c _globalColumnKey.<br> |
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115 | * When first called, this method will just shift \c _rowKey and |
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116 | * \c _columnKey to point to the first sensible choices. Every subsequent |
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117 | * call will move to the next \c _columnKey until there is no next. |
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118 | * In this situation, a next \c _rowKey will be set, and \c _columnKey |
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119 | * again to the first possible choice.<br> |
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120 | * Finally, in case there is also no next \c _rowkey, the method returns |
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121 | * \c false. (Otherwise \c true is returned.) |
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122 | * @param k the size of the minor / all minors of interest |
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123 | * @return true iff there is a next possible choice of rows and columns |
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124 | */ |
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125 | bool setNextKeys (const int k); |
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126 | |
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127 | /** |
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128 | * private store for the rows and columns of the container minor within |
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129 | * the underlying matrix; |
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130 | * \c _container will be used to fix a submatrix (e.g. 40 x 50) of a |
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131 | * larger matrix (e.g. 70 x 100). This is useful when we would like to |
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132 | * compute all minors of a given size (e.g. 4 x 4) inside such a |
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133 | * pre-defined submatrix. |
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134 | */ |
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135 | MinorKey _container; |
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136 | |
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137 | /** |
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138 | * private store for the number of rows in the container minor; |
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139 | * This is set by MinorProcessor::defineSubMatrix (const int, const int*, |
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140 | * const int, const int*). |
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141 | */ |
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142 | int _containerRows; |
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143 | |
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144 | /** |
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145 | * private store for the number of columns in the container minor; |
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146 | * This is set by MinorProcessor::defineSubMatrix (const int, const int*, |
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147 | * const int, const int*). |
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148 | */ |
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149 | int _containerColumns; |
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150 | |
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151 | /** |
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152 | * private store for the rows and columns of the minor of interest; |
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153 | * Usually, this minor will encode subsets of the rows and columns in |
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154 | * _container. |
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155 | */ |
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156 | MinorKey _minor; |
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157 | |
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158 | /** |
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159 | * private store for the dimension of the minor(s) of interest |
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160 | */ |
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161 | int _minorSize; |
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162 | |
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163 | /** |
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164 | * private store for the number of rows in the underlying matrix |
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165 | */ |
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166 | int _rows; |
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167 | |
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168 | /** |
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169 | * private store for the number of columns in the underlying matrix |
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170 | */ |
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171 | int _columns; |
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172 | |
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173 | /** |
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174 | * A method for identifying the row or column with the most zeros.<br> |
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175 | * Using Laplace's Theorem, a minor can more efficiently be computed when |
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176 | * developing along this best line. |
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177 | * The returned index \c bestIndex is 0-based within the pre-defined |
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178 | * matrix. If some row has the most zeros, then the (0-based) row index is |
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179 | * returned. If, contrarywise, some column has the most zeros, then |
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180 | * <c>x = - 1 - c</c> where \c c is the column index, is returned. |
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181 | * (Note that in this case \c c can be reconstructed by computing |
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182 | * <c>c = - 1 - x</c>.) |
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183 | * @param k the size of the minor / all minors of interest |
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184 | * @param mk the representation of rows and columns of the minor of |
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185 | * interest |
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186 | * @return an int encoding which row or column has the most zeros |
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187 | */ |
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188 | int getBestLine (const int k, const MinorKey& mk) const; |
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189 | |
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190 | /** |
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191 | * A method for testing whether a matrix entry is zero. |
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192 | * @param absoluteRowIndex the absolute (zero-based) row index |
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193 | * @param absoluteColumnIndex the absolute (zero-based) column index |
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194 | * @return true iff the specified matrix entry is zero |
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195 | */ |
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196 | virtual bool isEntryZero (const int absoluteRowIndex, |
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197 | const int absoluteColumnIndex) const; |
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198 | public: |
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199 | /** |
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200 | * The default constructor |
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201 | */ |
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202 | MinorProcessor (); |
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203 | |
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204 | /** |
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205 | * A destructor for deleting an instance. We must make this destructor |
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206 | * virtual so that destructors of all derived classes will automatically |
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207 | * also call the destructor of the base class MinorProcessor. |
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208 | */ |
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209 | virtual ~MinorProcessor (); |
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210 | |
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211 | /** |
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212 | * A method for defining a sub-matrix within a pre-defined matrix. |
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213 | * @param numberOfRows the number of rows in the sub-matrix |
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214 | * @param rowIndices an array with the (0-based) indices of rows inside |
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215 | * the pre-defined matrix |
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216 | * @param numberOfColumns the number of columns in the sub-matrix |
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217 | * @param columnIndices an array with the (0-based) indices of columns |
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218 | * inside the pre-defined matrix |
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219 | * @see MinorValue::defineMatrix (const int, const int, const int*) |
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220 | */ |
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221 | void defineSubMatrix (const int numberOfRows, const int* rowIndices, |
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222 | const int numberOfColumns, const int* columnIndices); |
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223 | |
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224 | /** |
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225 | * Sets the size of the minor(s) of interest.<br> |
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226 | * This method needs to be performed before beginning to compute all minors |
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227 | * of size \a minorSize inside a pre-defined submatrix of an underlying |
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228 | * (also pre-defined) matrix. |
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229 | * @param minorSize the size of the minor(s) of interest |
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230 | * @see MinorValue::defineSubMatrix (const int, const int*, const int, |
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231 | * const int*) |
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232 | */ |
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233 | void setMinorSize (const int minorSize); |
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234 | |
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235 | /** |
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236 | * A method for checking whether there is a next choice of rows and columns |
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237 | * when iterating through all minors of a given size within a pre-defined |
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238 | * sub-matrix of an underlying matrix.<br> |
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239 | * The number of rows and columns has to be set before using |
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240 | * MinorValue::setMinorSize(const int).<br> |
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241 | * After calling MinorValue::hasNextMinor (), the current sets of rows and |
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242 | * columns may be inspected using |
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243 | * MinorValue::getCurrentRowIndices(int* const) const and |
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244 | * MinorValue::getCurrentColumnIndices(int* const) const. |
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245 | * @return true iff there is a next choice of rows and columns |
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246 | * @see MinorProcessor::getMinor (const int, const int*, const int*) |
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247 | * @see MinorValue::getCurrentRowIndices(int* const) const |
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248 | * @see MinorValue::getCurrentColumnIndices(int* const) const |
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249 | */ |
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250 | bool hasNextMinor (); |
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251 | |
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252 | /** |
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253 | * A method for obtaining the current set of rows corresponding to the |
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254 | * current minor when iterating through all minors of a given size within |
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255 | * a pre-defined sub-matrix of an underlying matrix.<br> |
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256 | * This method should only be called after MinorProcessor::hasNextMinor () |
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257 | * had been called and yielded \c true.<br> |
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258 | * The user of this method needs to know the number of rows in order to |
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259 | * know which entries of the newly filled \c target will be valid. |
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260 | * @param target an int array to be filled with the row indices |
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261 | * @see MinorProcessor::hasNextMinor () |
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262 | */ |
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263 | void getCurrentRowIndices (int* const target) const; |
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264 | |
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265 | /** |
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266 | * A method for obtaining the current set of columns corresponding to the |
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267 | * current minor when iterating through all minors of a given size within |
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268 | * a pre-defined sub-matrix of an underlying matrix.<br> |
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269 | * This method should only be called after MinorProcessor::hasNextMinor () |
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270 | * had been called and yielded \c true.<br> |
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271 | * The user of this method needs to know the number of columns in order to |
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272 | * know which entries of the newly filled \c target will be valid. |
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273 | * @param target an int array to be filled with the column indices |
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274 | * @see MinorProcessor::hasNextMinor () |
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275 | */ |
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276 | void getCurrentColumnIndices (int* const target) const; |
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277 | |
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278 | /** |
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279 | * A method for providing a printable version of the represented |
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280 | * MinorProcessor. |
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281 | * @return a printable version of the given instance as instance of class |
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282 | * string |
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283 | */ |
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284 | virtual std::string toString () const; |
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285 | |
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286 | /** |
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287 | * A method for printing a string representation of the given |
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288 | * MinorProcessor to std::cout. |
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289 | */ |
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290 | void print () const; |
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291 | }; |
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292 | |
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293 | /*! \class IntMinorProcessor |
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294 | \brief Class IntMinorProcessor is derived from class MinorProcessor. |
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295 | |
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296 | This class implements the special case of integer matrices. |
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297 | \author Frank Seelisch, http://www.mathematik.uni-kl.de/~seelisch |
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298 | */ |
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299 | class IntMinorProcessor : public MinorProcessor |
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300 | { |
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301 | private: |
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302 | /** |
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303 | * private store for integer matrix entries |
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304 | */ |
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305 | int* _intMatrix; |
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306 | |
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307 | /** |
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308 | * A method for retrieving the matrix entry. |
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309 | * @param rowIndex the absolute (zero-based) row index |
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310 | * @param columnIndex the absolute (zero-based) column index |
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311 | * @return the specified matrix entry |
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312 | */ |
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313 | int getEntry (const int rowIndex, const int columnIndex) const; |
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314 | |
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315 | /** |
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316 | * A method for computing the value of a minor, using a cache.<br> |
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317 | * The sub-matrix is specified by \c mk. Computation works recursively |
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318 | * using Laplace's Theorem. We always develop along the row or column with |
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319 | * the most zeros; see |
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320 | * MinorProcessor::getBestLine (const int k, const MinorKey& mk). |
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321 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
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322 | * all results will be reduced w.r.t. to this basis. Moreover, if the given |
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323 | * characteristic is non-zero, all results will be computed modulo this |
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324 | * characteristic. |
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325 | * @param k the number of rows and columns in the minor to be computed |
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326 | * @param mk the representation of rows and columns of the minor to be |
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327 | * computed |
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328 | * @param multipleMinors decides whether we compute just one or all minors |
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329 | * of a specified size |
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330 | * @param c a cache to be used for caching reusable sub-minors |
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331 | * @param characteristic 0 or the characteristic of the underlying |
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332 | * coefficient ring/field |
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333 | * @param iSB NULL or a standard basis |
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334 | * @return an instance of MinorValue representing the value of the |
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335 | * corresponding minor |
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336 | * @see MinorProcessor::getMinorPrivateLaplace (const int k, |
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337 | const MinorKey& mk, |
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338 | const int characteristic, |
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339 | const ideal& iSB) |
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340 | */ |
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341 | IntMinorValue getMinorPrivateLaplace (const int k, const MinorKey& mk, |
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342 | const bool multipleMinors, |
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343 | Cache<MinorKey, IntMinorValue>& c, |
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344 | int characteristic, |
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345 | const ideal& iSB); |
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346 | |
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347 | /** |
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348 | * A method for computing the value of a minor, without using a cache.<br> |
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349 | * The sub-matrix is specified by \c mk. Computation works recursively |
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350 | * using Laplace's Theorem. We always develop along the row or column with |
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351 | * the most zeros; see |
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352 | * MinorProcessor::getBestLine (const int k, const MinorKey& mk). |
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353 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
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354 | * all results will be reduced w.r.t. to this basis. Moreover, if the given |
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355 | * characteristic is non-zero, all results will be computed modulo this |
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356 | * characteristic. |
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357 | * @param k the number of rows and columns in the minor to be computed |
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358 | * @param mk the representation of rows and columns of the minor to be |
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359 | * computed |
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360 | * @param characteristic 0 or the characteristic of the underlying |
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361 | * coefficient ring/field |
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362 | * @param iSB NULL or a standard basis |
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363 | * @return an instance of MinorValue representing the value of the |
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364 | * corresponding minor |
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365 | * @see MinorProcessor::getMinorPrivateLaplace (const int k, |
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366 | const MinorKey& mk, |
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367 | const bool multipleMinors, |
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368 | Cache<MinorKey, |
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369 | IntMinorValue>& c, |
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370 | int characteristic, |
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371 | const ideal& iSB) |
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372 | */ |
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373 | IntMinorValue getMinorPrivateLaplace (const int k, const MinorKey& mk, |
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374 | const int characteristic, |
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375 | const ideal& iSB); |
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376 | |
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377 | /** |
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378 | * A method for computing the value of a minor using Bareiss's |
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379 | * algorithm.<br> |
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380 | * The sub-matrix is specified by \c mk. |
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381 | * If an ideal is given, it is assumed to be a standard basis. In this |
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382 | * case, all results will be reduced w.r.t. to this basis. Moreover, if the |
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383 | * given characteristic is non-zero, all results will be computed modulo |
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384 | * this characteristic. |
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385 | * @param k the number of rows and columns in the minor to be computed |
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386 | * @param mk the representation of rows and columns of the minor to be |
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387 | * computed |
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388 | * @param characteristic 0 or the characteristic of the underlying |
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389 | * coefficient ring/field |
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390 | * @param iSB NULL or a standard basis |
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391 | * @return an instance of MinorValue representing the value of the |
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392 | * corresponding minor |
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393 | * @see MinorProcessor::getMinorPrivateLaplace (const int k, |
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394 | const MinorKey& mk, |
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395 | const int characteristic, |
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396 | const ideal& iSB) |
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397 | */ |
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398 | IntMinorValue getMinorPrivateBareiss (const int k, const MinorKey& mk, |
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399 | const int characteristic, |
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400 | const ideal& iSB); |
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401 | protected: |
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402 | /** |
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403 | * A method for testing whether a matrix entry is zero. |
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404 | * @param absoluteRowIndex the absolute (zero-based) row index |
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405 | * @param absoluteColumnIndex the absolute (zero-based) column index |
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406 | * @return true iff the specified matrix entry is zero |
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407 | */ |
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408 | bool isEntryZero (const int absoluteRowIndex, |
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409 | const int absoluteColumnIndex) const; |
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410 | public: |
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411 | /** |
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412 | * A constructor for creating an instance. |
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413 | */ |
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414 | IntMinorProcessor (); |
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415 | |
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416 | /** |
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417 | * A destructor for deleting an instance. |
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418 | */ |
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419 | ~IntMinorProcessor (); |
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420 | |
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421 | /** |
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422 | * A method for defining a matrix with integer entries. |
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423 | * @param numberOfRows the number of rows |
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424 | * @param numberOfColumns the number of columns |
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425 | * @param matrix the matrix entries in a linear array, i.e., from left to |
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426 | * right and top to bottom |
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427 | * @see MinorValue::defineSubMatrix (const int, const int*, const int, |
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428 | * const int*) |
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429 | */ |
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430 | void defineMatrix (const int numberOfRows, const int numberOfColumns, |
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431 | const int* matrix); |
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432 | |
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433 | /** |
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434 | * A method for computing the value of a minor without using a cache.<br> |
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435 | * The sub-matrix is determined by \c rowIndices and \c columnIndices. |
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436 | * Computation works either by Laplace's algorithm or by Bareiss's |
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437 | * algorithm.<br> |
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438 | * If an ideal is given, it is assumed to be a standard basis. In this |
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439 | * case, all results will be reduced w.r.t. to this basis. Moreover, if the |
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440 | * given characteristic is non-zero, all results will be computed modulo |
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441 | * this characteristic. |
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442 | * @param dimension the size of the minor to be computed |
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443 | * @param rowIndices 0-based indices of the rows of the minor |
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444 | * @param columnIndices 0-based indices of the column of the minor |
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445 | * @param characteristic 0 or the characteristic of the underlying |
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446 | * coefficient ring/field |
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447 | * @param iSB NULL or a standard basis |
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448 | * @param algorithm either "Bareiss" or "Laplace" |
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449 | * @return an instance of MinorValue representing the value of the |
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450 | * corresponding minor |
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451 | * @see MinorProcessor::getMinor (const int dimension, |
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452 | const int* rowIndices, |
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453 | const int* columnIndices, |
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454 | Cache<MinorKey, IntMinorValue>& c, |
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455 | const int characteristic, |
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456 | const ideal& iSB) |
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457 | */ |
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458 | IntMinorValue getMinor (const int dimension, const int* rowIndices, |
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459 | const int* columnIndices, |
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460 | const int characteristic, const ideal& iSB, |
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461 | const char* algorithm); |
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462 | |
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463 | /** |
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464 | * A method for computing the value of a minor using a cache.<br> |
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465 | * The sub-matrix is determined by \c rowIndices and \c columnIndices. |
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466 | * Computation works by Laplace's algorithm together with caching of |
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467 | * subdeterminants.<br> |
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468 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
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469 | * all results will be reduced w.r.t. to this basis. Moreover, if the given |
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470 | * characteristic is non-zero, all results will be computed modulo this |
---|
471 | * characteristic. |
---|
472 | * @param dimension the size of the minor to be computed |
---|
473 | * @param rowIndices 0-based indices of the rows of the minor |
---|
474 | * @param columnIndices 0-based indices of the column of the minor |
---|
475 | * @param c the cache for storing subdeterminants |
---|
476 | * @param characteristic 0 or the characteristic of the underlying |
---|
477 | * coefficient ring/field |
---|
478 | * @param iSB NULL or a standard basis |
---|
479 | * @return an instance of MinorValue representing the value of the |
---|
480 | * corresponding minor |
---|
481 | * @see MinorProcessor::getMinor (const int dimension, |
---|
482 | const int* rowIndices, |
---|
483 | const int* columnIndices, |
---|
484 | const int characteristic, |
---|
485 | const ideal& iSB, |
---|
486 | const char* algorithm) |
---|
487 | */ |
---|
488 | IntMinorValue getMinor (const int dimension, const int* rowIndices, |
---|
489 | const int* columnIndices, |
---|
490 | Cache<MinorKey, IntMinorValue>& c, |
---|
491 | const int characteristic, const ideal& iSB); |
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492 | |
---|
493 | /** |
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494 | * A method for obtaining the next minor when iterating |
---|
495 | * through all minors of a given size within a pre-defined sub-matrix of an |
---|
496 | * underlying matrix.<br> |
---|
497 | * This method should only be called after MinorProcessor::hasNextMinor () |
---|
498 | * had been called and yielded \c true.<br> |
---|
499 | * Computation works by Laplace's algorithm (without using a cache) or by |
---|
500 | * Bareiss's algorithm.<br> |
---|
501 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
---|
502 | * all results will be reduced w.r.t. to this basis. Moreover, if the given |
---|
503 | * characteristic is non-zero, all results will be computed modulo this |
---|
504 | * characteristic. |
---|
505 | * @param characteristic 0 or the characteristic of the underlying |
---|
506 | * coefficient ring/field |
---|
507 | * @param iSB NULL or a standard basis |
---|
508 | * @param algorithm either "Bareiss" or "Laplace" |
---|
509 | * @return the next minor |
---|
510 | * @see IntMinorValue::getNextMinor (Cache<MinorKey, IntMinorValue>& c, |
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511 | * const int characteristic, |
---|
512 | * const ideal& iSB) |
---|
513 | */ |
---|
514 | IntMinorValue getNextMinor (const int characteristic, const ideal& iSB, |
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515 | const char* algorithm); |
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516 | |
---|
517 | /** |
---|
518 | * A method for obtaining the next minor when iterating |
---|
519 | * through all minors of a given size within a pre-defined sub-matrix of an |
---|
520 | * underlying matrix.<br> |
---|
521 | * This method should only be called after MinorProcessor::hasNextMinor () |
---|
522 | * had been called and yielded \c true.<br> |
---|
523 | * Computation works using the cache \a c which may already contain useful |
---|
524 | * results from previous calls of |
---|
525 | * IntMinorValue::getNextMinor (Cache<MinorKey, IntMinorValue>& c, |
---|
526 | const int characteristic, |
---|
527 | const ideal& iSB). |
---|
528 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
---|
529 | * all results will be reduced w.r.t. to this basis. Moreover, if the given |
---|
530 | * characteristic is non-zero, all results will be computed modulo this |
---|
531 | * characteristic. |
---|
532 | * @param c the cache |
---|
533 | * @param characteristic 0 or the characteristic of the underlying |
---|
534 | * coefficient ring/field |
---|
535 | * @param iSB NULL or a standard basis |
---|
536 | * @return the next minor |
---|
537 | * @see IntMinorValue::getNextMinor (const int characteristic, |
---|
538 | * const ideal& iSB, |
---|
539 | * const char* algorithm) |
---|
540 | */ |
---|
541 | IntMinorValue getNextMinor (Cache<MinorKey, IntMinorValue>& c, |
---|
542 | const int characteristic, |
---|
543 | const ideal& iSB); |
---|
544 | |
---|
545 | /** |
---|
546 | * A method for providing a printable version of the represented |
---|
547 | * MinorProcessor. |
---|
548 | * @return a printable version of the given instance as instance of class |
---|
549 | * string |
---|
550 | */ |
---|
551 | std::string toString () const; |
---|
552 | }; |
---|
553 | |
---|
554 | /*! \class PolyMinorProcessor |
---|
555 | \brief Class PolyMinorProcessor is derived from class MinorProcessor. |
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556 | |
---|
557 | This class implements the special case of polynomial matrices. |
---|
558 | \author Frank Seelisch, http://www.mathematik.uni-kl.de/~seelisch |
---|
559 | */ |
---|
560 | class PolyMinorProcessor : public MinorProcessor |
---|
561 | { |
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562 | private: |
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563 | /** |
---|
564 | * private store for polynomial matrix entries |
---|
565 | */ |
---|
566 | poly* _polyMatrix; |
---|
567 | |
---|
568 | /** |
---|
569 | * A method for retrieving the matrix entry. |
---|
570 | * @param rowIndex the absolute (zero-based) row index |
---|
571 | * @param columnIndex the absolute (zero-based) column index |
---|
572 | * @return the specified matrix entry |
---|
573 | */ |
---|
574 | poly getEntry (const int rowIndex, const int columnIndex) const; |
---|
575 | |
---|
576 | /** |
---|
577 | * A method for computing the value of a minor, using a cache.<br> |
---|
578 | * The sub-matrix is specified by \c mk. Computation works recursively |
---|
579 | * using Laplace's Theorem. We always develop along the row or column with |
---|
580 | * the most zeros; see |
---|
581 | * MinorProcessor::getBestLine (const int k, const MinorKey& mk). |
---|
582 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
---|
583 | * all results will be reduced w.r.t. to this basis. |
---|
584 | * @param k the number of rows and columns in the minor to be computed |
---|
585 | * @param mk the representation of rows and columns of the minor to be |
---|
586 | * computed |
---|
587 | * @param multipleMinors decides whether we compute just one or all minors |
---|
588 | * of a specified size |
---|
589 | * @param c a cache to be used for caching reusable sub-minors |
---|
590 | * @param iSB NULL or a standard basis |
---|
591 | * @return an instance of MinorValue representing the value of the |
---|
592 | * corresponding minor |
---|
593 | * @see MinorProcessor::getMinorPrivateLaplace (const int k, |
---|
594 | * const MinorKey& mk, |
---|
595 | * const ideal& iSB) |
---|
596 | */ |
---|
597 | PolyMinorValue getMinorPrivateLaplace (const int k, const MinorKey& mk, |
---|
598 | const bool multipleMinors, |
---|
599 | Cache<MinorKey, PolyMinorValue>& c, |
---|
600 | const ideal& iSB); |
---|
601 | |
---|
602 | /** |
---|
603 | * A method for computing the value of a minor, without using a cache.<br> |
---|
604 | * The sub-matrix is specified by \c mk. Computation works recursively |
---|
605 | * using Laplace's Theorem. We always develop along the row or column with |
---|
606 | * the most zeros; see |
---|
607 | * MinorProcessor::getBestLine (const int k, const MinorKey& mk). |
---|
608 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
---|
609 | * all results will be reduced w.r.t. to this basis. |
---|
610 | * @param k the number of rows and columns in the minor to be computed |
---|
611 | * @param mk the representation of rows and columns of the minor to be |
---|
612 | * computed |
---|
613 | * @param iSB NULL or a standard basis |
---|
614 | * @return an instance of MinorValue representing the value of the |
---|
615 | * corresponding minor |
---|
616 | * @see MinorProcessor::getMinorPrivate (const int, const MinorKey&, |
---|
617 | * const bool, |
---|
618 | * Cache<MinorKey, MinorValue>&) |
---|
619 | */ |
---|
620 | PolyMinorValue getMinorPrivateLaplace (const int k, const MinorKey& mk, |
---|
621 | const ideal& iSB); |
---|
622 | |
---|
623 | /** |
---|
624 | * A method for computing the value of a minor, without using a cache.<br> |
---|
625 | * The sub-matrix is specified by \c mk. Computation works |
---|
626 | * using Bareiss's algorithm. |
---|
627 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
---|
628 | * all results will be reduced w.r.t. to this basis. |
---|
629 | * @param k the number of rows and columns in the minor to be computed |
---|
630 | * @param mk the representation of rows and columns of the minor to be |
---|
631 | * computed |
---|
632 | * @param iSB NULL or a standard basis |
---|
633 | * @return an instance of MinorValue representing the value of the |
---|
634 | * corresponding minor |
---|
635 | * @see MinorProcessor::getMinorPrivateLaplace (const int k, |
---|
636 | * const MinorKey& mk, |
---|
637 | * const ideal& iSB) |
---|
638 | */ |
---|
639 | PolyMinorValue getMinorPrivateBareiss (const int k, const MinorKey& mk, |
---|
640 | const ideal& iSB); |
---|
641 | protected: |
---|
642 | /** |
---|
643 | * A method for testing whether a matrix entry is zero. |
---|
644 | * @param absoluteRowIndex the absolute (zero-based) row index |
---|
645 | * @param absoluteColumnIndex the absolute (zero-based) column index |
---|
646 | * @return true iff the specified matrix entry is zero |
---|
647 | */ |
---|
648 | bool isEntryZero (const int absoluteRowIndex, |
---|
649 | const int absoluteColumnIndex) const; |
---|
650 | public: |
---|
651 | /** |
---|
652 | * A constructor for creating an instance. |
---|
653 | */ |
---|
654 | PolyMinorProcessor (); |
---|
655 | |
---|
656 | /** |
---|
657 | * A destructor for deleting an instance. |
---|
658 | */ |
---|
659 | ~PolyMinorProcessor (); |
---|
660 | |
---|
661 | /** |
---|
662 | * A method for defining a matrix with polynomial entries. |
---|
663 | * @param numberOfRows the number of rows |
---|
664 | * @param numberOfColumns the number of columns |
---|
665 | * @param polyMatrix the matrix entries in a linear array, i.e., from left |
---|
666 | * to right and top to bottom |
---|
667 | * @see MinorValue::defineSubMatrix (const int, const int*, const int, |
---|
668 | * const int*) |
---|
669 | */ |
---|
670 | void defineMatrix (const int numberOfRows, const int numberOfColumns, |
---|
671 | const poly* polyMatrix); |
---|
672 | |
---|
673 | /** |
---|
674 | * A method for computing the value of a minor, without using a cache.<br> |
---|
675 | * The sub-matrix is determined by \c rowIndices and \c columnIndices. |
---|
676 | * Computation works either by Laplace's algorithm or by Bareiss's |
---|
677 | * algorithm.<br> |
---|
678 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
---|
679 | * all results will be reduced w.r.t. to this basis. |
---|
680 | * @param dimension the size of the minor to be computed |
---|
681 | * @param rowIndices 0-based indices of the rows of the minor |
---|
682 | * @param columnIndices 0-based indices of the column of the minor |
---|
683 | * @param algorithm either "Laplace" or "Bareiss" |
---|
684 | * @param iSB NULL or a standard basis |
---|
685 | * @return an instance of MinorValue representing the value of the |
---|
686 | * corresponding minor |
---|
687 | * @see MinorProcessor::getMinor (const int dimension, |
---|
688 | * const int* rowIndices, |
---|
689 | * const int* columnIndices, |
---|
690 | * Cache<MinorKey, PolyMinorValue>& c, |
---|
691 | * const ideal& iSB) |
---|
692 | */ |
---|
693 | PolyMinorValue getMinor (const int dimension, const int* rowIndices, |
---|
694 | const int* columnIndices, const char* algorithm, |
---|
695 | const ideal& iSB); |
---|
696 | |
---|
697 | /** |
---|
698 | * A method for computing the value of a minor, using a cache.<br> |
---|
699 | * The sub-matrix is determined by \c rowIndices and \c columnIndices. |
---|
700 | * Computation works recursively using Laplace's Theorem. We always develop |
---|
701 | * along the row or column with most zeros; see |
---|
702 | * MinorProcessor::getBestLine (const int, const int, const int). |
---|
703 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
---|
704 | * all results will be reduced w.r.t. to this basis. |
---|
705 | * @param dimension the size of the minor to be computed |
---|
706 | * @param rowIndices 0-based indices of the rows of the minor |
---|
707 | * @param columnIndices 0-based indices of the column of the minor |
---|
708 | * @param c a cache to be used for caching reusable sub-minors |
---|
709 | * @param iSB NULL or a standard basis |
---|
710 | * @return an instance of MinorValue representing the value of the |
---|
711 | * corresponding minor |
---|
712 | * @see MinorProcessor::(const int dimension, const int* rowIndices, |
---|
713 | * const int* columnIndices, const char* algorithm, |
---|
714 | * const ideal& iSB) |
---|
715 | */ |
---|
716 | PolyMinorValue getMinor (const int dimension, const int* rowIndices, |
---|
717 | const int* columnIndices, |
---|
718 | Cache<MinorKey, PolyMinorValue>& c, |
---|
719 | const ideal& iSB); |
---|
720 | |
---|
721 | /** |
---|
722 | * A method for obtaining the next minor when iterating |
---|
723 | * through all minors of a given size within a pre-defined sub-matrix of an |
---|
724 | * underlying matrix.<br> |
---|
725 | * This method should only be called after MinorProcessor::hasNextMinor () |
---|
726 | * had been called and yielded \c true.<br> |
---|
727 | * Computation works either by Laplace's algorithm (without using a cache) |
---|
728 | * or by Bareiss's algorithm.<br> |
---|
729 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
---|
730 | * all results will be reduced w.r.t. to this basis. |
---|
731 | * @param algorithm either "Laplace" or "Bareiss" |
---|
732 | * @param iSB NULL or a standard basis |
---|
733 | * @return true iff there is a next choice of rows and columns |
---|
734 | * @see PolyMinorValue::getNextMinor (Cache<MinorKey, PolyMinorValue>& c, |
---|
735 | * const ideal& iSB) |
---|
736 | */ |
---|
737 | PolyMinorValue getNextMinor (const char* algorithm, const ideal& iSB); |
---|
738 | |
---|
739 | /** |
---|
740 | * A method for obtaining the next minor when iterating |
---|
741 | * through all minors of a given size within a pre-defined sub-matrix of an |
---|
742 | * underlying matrix.<br> |
---|
743 | * This method should only be called after MinorProcessor::hasNextMinor () |
---|
744 | * had been called and yielded \c true.<br> |
---|
745 | * Computation works using Laplace's algorithm and a cache \a c which may |
---|
746 | * already contain useful results from previous calls of |
---|
747 | * PolyMinorValue::getNextMinor (Cache<MinorKey, PolyMinorValue>& c, |
---|
748 | * const ideal& iSB). |
---|
749 | * If an ideal is given, it is assumed to be a standard basis. In this case, |
---|
750 | * all results will be reduced w.r.t. to this basis. |
---|
751 | * @param iSB NULL or a standard basis |
---|
752 | * @return the next minor |
---|
753 | * @see PolyMinorValue::getNextMinor (const char* algorithm, |
---|
754 | * const ideal& iSB) |
---|
755 | */ |
---|
756 | PolyMinorValue getNextMinor (Cache<MinorKey, PolyMinorValue>& c, |
---|
757 | const ideal& iSB); |
---|
758 | |
---|
759 | /** |
---|
760 | * A method for providing a printable version of the represented |
---|
761 | * MinorProcessor. |
---|
762 | * @return a printable version of the given instance as instance of class |
---|
763 | * string |
---|
764 | */ |
---|
765 | std::string toString () const; |
---|
766 | }; |
---|
767 | |
---|
768 | #endif |
---|
769 | /* MINOR_PROCESSOR_H */ |
---|