1 | #ifndef MINOR_PROCESSOR_H |
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2 | #define MINOR_PROCESSOR_H |
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3 | |
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4 | #ifdef HAVE_MINOR |
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5 | |
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6 | #include <Cache.h> |
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7 | #include <Minor.h> |
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8 | #include <assert.h> |
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9 | #include <string> |
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10 | |
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11 | /*! \class MinorProcessor |
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12 | \brief Class MinorProcessor implements the key methods for computing one or all sub-determinantes of |
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13 | a given size in a pre-defined matrix; either without cache or using a cache. |
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14 | |
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15 | After defining the entire matrix (e.g. 10 x 14) using<br> |
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16 | MinorProcessor::defineMatrix (const int, const int, const int*),<br> |
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17 | the user may do two different things:<br> |
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18 | 1. He/she can simply compute a minor in this matrix using<br> |
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19 | MinorProcessor::getMinor (const int, const int*, const int*, Cache<MinorKey, MinorValue>&), or<br> |
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20 | MinorProcessor::getMinor (const int, const int*, const int*);<br> |
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21 | depending on whether a cache shall or shall not be used, respectively.<br> |
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22 | In this first alternative, the user simply provides all row and column indices of the minor. |
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23 | 2. He/she may define a smaller sub-matrix (e.g. 8 x 7) using |
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24 | MinorValue::defineSubMatrix (const int, const int*, const int, const int*). |
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25 | Afterwards, he/she may compute all minors of an even smaller size (e.g. 5 x 5) that consist exclusively of rows and |
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26 | columns of this (8 x 7) sub-matrix (inside the entire 10 x 14 matrix).<br> |
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27 | The implementation at hand eases the iteration over all such minors. Also in the |
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28 | second case there are both implementations, i.e., with and without the usage of a cache.<br><br> |
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29 | MinorProcessor makes use of MinorKey, MinorValue, and Cache. Therefore, it only works for matrices with integer |
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30 | entries. But the implementation of all mentioned classes (MinorKey, MinorValue, and MinorProcessor) is in this |
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31 | respect generic enough to quickly replace integer matrix entries by any other kind of objects (which only need |
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32 | to implement binary addition and multiplication).<br> |
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33 | Elements of any ring, such as polynomial rings, are canonical choices for such objects. |
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34 | \author Frank Seelisch, http://www.mathematik.uni-kl.de/~seelisch |
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35 | */ |
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36 | class MinorProcessor { |
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37 | protected: |
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38 | /** |
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39 | * A static method for computing the maximum number of retrievals of a minor.<br> |
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40 | * More concretely, we are given a matrix of size \c rows x \c columns. We furthermore assume that |
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41 | * we have - as part of this matrix - a minor of size \c containerMinorSize x \c containerMinorSize. |
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42 | * Now we are interested in the number of times a minor of yet smaller size \c minorSize x \c minorSize |
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43 | * will be needed when we compute the containerMinor by Laplace's Theorem.<br> |
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44 | * The method returns the combinatorial results for both cases: containerMinor is fixed within the |
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45 | * matrix (<c>multipleMinors == false</c>), or it can vary inside the matrix (<c>multipleMinors == true</c>).<br> |
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46 | * The notion is here that we want to cache the small minor of size \c minorSize x \c minorSize, i.e. |
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47 | * compute it just once. |
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48 | * @param rows the number of rows of the underlying matrix |
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49 | * @param columns the number of columns of the underlying matrix |
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50 | * @param containerMinorSize the size of the container minor |
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51 | * @param minorSize the size of the small minor (which may be retrieved multiple times) |
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52 | * @param multipleMinors decides whether containerMinor is fixed within the underlying matrix or not |
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53 | * @return the number of times, the small minor will be needed when computing one or all containerMinors |
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54 | */ |
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55 | static int NumberOfRetrievals (const int rows, const int columns, const int containerMinorSize, |
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56 | const int minorSize, const bool multipleMinors); |
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57 | /** |
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58 | * A static method for computing the binomial coefficient i over j. |
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59 | * \par Assert |
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60 | * The method checks whether <em>i >= j >= 0</em>. |
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61 | * @param i a positive integer greater than or equal to \a j |
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62 | * @param j a positive integer less than or equal to \a i, and greater than or equal to \e 0. |
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63 | * @return the binomial coefficient i over j |
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64 | */ |
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65 | static int IOverJ (const int i, const int j); |
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66 | |
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67 | /** |
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68 | * A static method for computing the factorial of i. |
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69 | * \par Assert |
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70 | * The method checks whether <em>i >= 0</em>. |
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71 | * @param i an integer greater than or equal to \a 0 |
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72 | * @return the factorial of i |
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73 | */ |
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74 | static int Faculty (const int i); |
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75 | |
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76 | /** |
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77 | * A method for iterating through all possible subsets of \c k rows and \c k columns inside a pre-defined |
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78 | * submatrix of a pre-defined matrix.<br> |
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79 | * The method will set \c _rowKey and \c columnKey to represent the |
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80 | * next possbile subsets of \c k rows and columns inside the submatrix |
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81 | * determined by \c _globalRowKey and \c _globalColumnKey.<br> |
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82 | * When first called, this method will just shift \c _rowKey and \c _columnKey to point to the first |
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83 | * sensible choices. Every subsequent call will move to the next \c _columnKey until there is no next. |
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84 | * In this situation, a next \c _rowKey will be set, and \c _columnKey again to the first possible choice.<br> |
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85 | * Finally, in case there is also no next \c _rowkey, the method returns \c false. (Otherwise \c true is returned.) |
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86 | * @param k the size of the minor / all minors of interest |
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87 | * @return true iff there is a next possible choice of rows and columns |
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88 | */ |
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89 | bool setNextKeys (const int k); |
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90 | |
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91 | /** |
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92 | * private store for the rows and columns of the container minor within the underlying matrix; |
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93 | * \c _container will be used to fix a submatrix (e.g. 40 x 50) of a larger matrix (e.g. 70 x 100). |
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94 | * This is usefull when we would like to compute all minors of a given size (e.g. 4 x 4) inside |
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95 | * such a pre-defined submatrix. |
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96 | */ |
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97 | MinorKey _container; |
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98 | |
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99 | /** |
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100 | * private store for the number of rows in the container minor; |
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101 | * This is set by MinorProcessor::defineSubMatrix (const int, const int*, const int, const int*). |
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102 | */ |
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103 | int _containerRows; |
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104 | |
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105 | /** |
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106 | * private store for the number of columns in the container minor; |
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107 | * This is set by MinorProcessor::defineSubMatrix (const int, const int*, const int, const int*). |
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108 | */ |
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109 | int _containerColumns; |
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110 | |
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111 | /** |
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112 | * private store for the rows and columns of the minor of interest; |
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113 | * Usually, this minor will encode subsets of the rows and columns in _container. |
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114 | */ |
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115 | MinorKey _minor; |
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116 | |
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117 | /** |
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118 | * private store for the dimension of the minor(s) of interest |
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119 | */ |
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120 | int _minorSize; |
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121 | |
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122 | /** |
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123 | * private store for the number of rows in the underlying matrix |
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124 | */ |
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125 | int _rows; |
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126 | |
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127 | /** |
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128 | * private store for the number of column in the underlying matrix |
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129 | */ |
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130 | int _columns; |
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131 | |
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132 | /** |
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133 | * A method for identifying the row or column with the most zeros.<br> |
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134 | * Using Laplace's Theorem, a minor can more efficiently be computed when developing along this best line. |
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135 | * The returned index \c bestIndex is 0-based within the pre-defined matrix. If some row has the most zeros, |
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136 | * then the (0-based) row index is returned. If, contrarywise, some column has the most zeros, then |
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137 | * <c>x = - 1 - c</c> where \c c is the column index, is returned. (Note that in this case \c c can be |
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138 | * reconstructed by computing <c>c = - 1 - x</c>.) |
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139 | * @param k the size of the minor / all minors of interest |
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140 | * @param mk the representation of rows and columns of the minor of interest |
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141 | * @return an int encoding which row or column has the most zeros |
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142 | */ |
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143 | int getBestLine (const int k, const MinorKey& mk) const; |
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144 | |
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145 | virtual bool isEntryZero (const int absoluteRowIndex, const int absoluteColumnIndex) const; |
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146 | public: |
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147 | MinorProcessor (); |
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148 | /** |
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149 | * A method for defining a sub-matrix within a pre-defined matrix. |
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150 | * @param numberOfRows the number of rows in the sub-matrix |
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151 | * @param rowIndices an array with the (0-based) indices of rows inside the pre-defined matrix |
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152 | * @param numberOfColumns the number of columns in the sub-matrix |
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153 | * @param columnIndices an array with the (0-based) indices of columns inside the pre-defined matrix |
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154 | * @see MinorValue::defineMatrix (const int, const int, const int*) |
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155 | */ |
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156 | void defineSubMatrix (const int numberOfRows, const int* rowIndices, |
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157 | const int numberOfColumns, const int* columnIndices); |
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158 | |
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159 | /** |
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160 | * Sets the size of the minor(s) of interest.<br> |
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161 | * This method needs to be performed before beginning to compute all minors of size \a minorSize |
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162 | * inside a pre-defined submatrix of an underlying (also pre-defined) matrix. |
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163 | * @param minorSize the size of the minor(s) of interest |
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164 | * @see MinorValue::defineSubMatrix (const int, const int*, const int, const int*) |
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165 | */ |
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166 | void setMinorSize (const int minorSize); |
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167 | |
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168 | /** |
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169 | * A method for checking whether there is a next choice of rows and columns when iterating |
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170 | * through all minors of a given size within a pre-defined sub-matrix of an underlying matrix.<br> |
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171 | * The number of rows and columns has to be set before using |
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172 | * MinorValue::setMinorSize(const int).<br> |
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173 | * After calling MinorValue::hasNextMinor (), the current sets of rows and columns may be |
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174 | * inspected using MinorValue::getCurrentRowIndices(int* const) const and |
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175 | * MinorValue::getCurrentColumnIndices(int* const) const. |
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176 | * @return true iff there is a next choice of rows and columns |
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177 | * @see MinorProcessor::getMinor (const int, const int*, const int*) |
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178 | * @see MinorValue::getCurrentRowIndices(int* const) const |
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179 | * @see MinorValue::getCurrentColumnIndices(int* const) const |
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180 | */ |
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181 | bool hasNextMinor (); |
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182 | |
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183 | /** |
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184 | * A method for obtaining the current set of rows corresponding to the current minor when iterating |
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185 | * through all minors of a given size within a pre-defined sub-matrix of an underlying matrix.<br> |
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186 | * This method should only be called after MinorProcessor::hasNextMinor () had been called and yielded |
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187 | * \c true.<br> |
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188 | * The user of this method needs to know the number of rows in order to know which entries of the |
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189 | * newly filled \c target will be valid. |
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190 | * @param target an int array to be filled with the row indices |
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191 | * @see MinorProcessor::hasNextMinor () |
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192 | */ |
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193 | void getCurrentRowIndices (int* const target) const; |
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194 | |
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195 | /** |
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196 | * A method for obtaining the current set of columns corresponding to the current minor when iterating |
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197 | * through all minors of a given size within a pre-defined sub-matrix of an underlying matrix.<br> |
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198 | * This method should only be called after MinorProcessor::hasNextMinor () had been called and yielded |
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199 | * \c true.<br> |
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200 | * The user of this method needs to know the number of columns in order to know which entries of the |
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201 | * newly filled \c target will be valid. |
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202 | * @param target an int array to be filled with the column indices |
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203 | * @see MinorProcessor::hasNextMinor () |
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204 | */ |
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205 | void getCurrentColumnIndices (int* const target) const; |
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206 | |
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207 | /** |
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208 | * A method for providing a printable version of the represented MinorProcessor. |
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209 | * @return a printable version of the given instance as instance of class string |
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210 | */ |
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211 | virtual string toString () const; |
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212 | |
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213 | /** |
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214 | * A method for printing a string representation of the given MinorProcessor to std::cout. |
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215 | */ |
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216 | void print () const; |
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217 | }; |
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218 | |
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219 | class IntMinorProcessor : public MinorProcessor { |
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220 | private: |
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221 | /** |
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222 | * private store for integer matrix entries; \c _matrix[r][c] is the entry in row \c r and column \c c |
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223 | */ |
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224 | int** _matrix; |
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225 | |
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226 | /** |
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227 | * A method for computing the value of a minor, using a cache.<br> |
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228 | * The sub-matrix is specified by \c mk. Computation works recursively |
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229 | * using Laplace's Theorem. We always develop along the row or column with the most zeros; see |
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230 | * MinorProcessor::getBestLine (const int k, const MinorKey& mk). |
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231 | * @param k the number of rows and columns in the minor to be comuted |
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232 | * @param mk the representation of rows and columns of the minor to be comuted |
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233 | * @param multipleMinors decides whether we compute just one or all minors of a specified size |
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234 | * @param c a cache to be used for caching reusable sub-minors |
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235 | * @return an instance of MinorValue representing the value of the corresponding minor |
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236 | * @see MinorProcessor::getMinorPrivate (const int, const MinorKey&) |
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237 | */ |
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238 | IntMinorValue getMinorPrivate (const int k, const MinorKey& mk, |
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239 | const bool multipleMinors, |
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240 | Cache<MinorKey, IntMinorValue>& c, |
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241 | int characteristic); |
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242 | |
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243 | /** |
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244 | * A method for computing the value of a minor, without using a cache.<br> |
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245 | * The sub-matrix is specified by \c mk. Computation works recursively |
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246 | * using Laplace's Theorem. We always develop along the row or column with the most zeros; see |
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247 | * MinorProcessor::getBestLine (const int k, const MinorKey& mk). |
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248 | * @param k the number of rows and columns in the minor to be comuted |
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249 | * @param mk the representation of rows and columns of the minor to be comuted |
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250 | * @return an instance of MinorValue representing the value of the corresponding minor |
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251 | * @see MinorProcessor::getMinorPrivate (const int, const MinorKey&, const bool, Cache<MinorKey, MinorValue>&) |
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252 | */ |
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253 | IntMinorValue getMinorPrivate (const int k, const MinorKey& mk, int characteristic); |
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254 | protected: |
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255 | bool isEntryZero (const int absoluteRowIndex, const int absoluteColumnIndex) const; |
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256 | public: |
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257 | /** |
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258 | * A constructor for creating an instance. |
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259 | */ |
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260 | IntMinorProcessor (); |
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261 | |
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262 | /** |
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263 | * A destructor for deleting an instance. |
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264 | */ |
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265 | ~IntMinorProcessor (); |
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266 | |
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267 | /** |
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268 | * A method for defining a matrix with integer entries. |
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269 | * @param numberOfRows the number of rows |
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270 | * @param numberOfColumns the number of columns |
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271 | * @param matrix the matrix entries in a linear array, i.e., from left to right and top to bottom |
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272 | * @see MinorValue::defineSubMatrix (const int, const int*, const int, const int*) |
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273 | */ |
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274 | void defineMatrix (const int numberOfRows, const int numberOfColumns, const int* matrix); |
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275 | |
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276 | /** |
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277 | * A method for computing the value of a minor, without using a cache.<br> |
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278 | * The sub-matrix is determined by \c rowIndices and \c columnIndices. Computation works recursively |
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279 | * using Laplace's Theorem. We always develop along the row or column with most zeros; see |
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280 | * MinorProcessor::getBestLine (const int, const int, const int). |
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281 | * @param dimension the size of the minor to be computed |
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282 | * @param rowIndices 0-based indices of the rows of the minor |
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283 | * @param columnIndices 0-based indices of the column of the minor |
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284 | * @return an instance of MinorValue representing the value of the corresponding minor |
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285 | * @see MinorProcessor::getMinor (const int, const int*, const int*, Cache<MinorKey, MinorValue>&) |
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286 | */ |
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287 | IntMinorValue getMinor (const int dimension, const int* rowIndices, const int* columnIndices, const int characteristic); |
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288 | |
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289 | /** |
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290 | * A method for computing the value of a minor, using a cache.<br> |
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291 | * The sub-matrix is determined by \c rowIndices and \c columnIndices. Computation works recursively |
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292 | * using Laplace's Theorem. We always develop along the row or column with most zeros; see |
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293 | * MinorProcessor::getBestLine (const int, const int, const int). |
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294 | * @param dimension the size of the minor to be computed |
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295 | * @param rowIndices 0-based indices of the rows of the minor |
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296 | * @param columnIndices 0-based indices of the column of the minor |
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297 | * @param c a cache to be used for caching reusable sub-minors |
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298 | * @return an instance of MinorValue representing the value of the corresponding minor |
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299 | * @see MinorProcessor::getMinor (const int, const int*, const int*) |
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300 | */ |
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301 | IntMinorValue getMinor (const int dimension, const int* rowIndices, const int* columnIndices, |
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302 | Cache<MinorKey, IntMinorValue>& c, const int characteristic); |
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303 | |
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304 | /** |
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305 | * A method for obtaining the next minor when iterating |
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306 | * through all minors of a given size within a pre-defined sub-matrix of an underlying matrix.<br> |
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307 | * This method should only be called after MinorProcessor::hasNextMinor () had been called and yielded |
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308 | * \c true.<br> |
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309 | * Computation works without using a cache. |
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310 | * @return true iff there is a next choice of rows and columns |
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311 | * @see MinorProcessor::getMinor (const int, const int*, const int*) |
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312 | * @see MinorProcessor::hasNextMinor () |
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313 | */ |
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314 | IntMinorValue getNextMinor (const int characteristic); |
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315 | |
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316 | /** |
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317 | * A method for obtaining the next minor when iterating |
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318 | * through all minors of a given size within a pre-defined sub-matrix of an underlying matrix.<br> |
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319 | * This method should only be called after MinorProcessor::hasNextMinor () had been called and yielded |
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320 | * \c true.<br> |
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321 | * Computation works using the cache \a c which may already contain useful results from previous |
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322 | * calls of MinorValue::getNextMinor (Cache<MinorKey, MinorValue>&). |
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323 | * @return the next minor |
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324 | * @see MinorProcessor::getMinor (const int, const int*, const int*) |
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325 | * @see MinorProcessor::hasNextMinor () |
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326 | */ |
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327 | IntMinorValue getNextMinor (Cache<MinorKey, IntMinorValue>& c, const int characteristic); |
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328 | |
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329 | /** |
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330 | * A method for providing a printable version of the represented MinorProcessor. |
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331 | * @return a printable version of the given instance as instance of class string |
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332 | */ |
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333 | string toString () const; |
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334 | }; |
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335 | |
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336 | class PolyMinorProcessor : public MinorProcessor { |
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337 | private: |
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338 | /** |
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339 | * private store for polynomial matrix entries; \c _matrix[r][c] is the entry in row \c r and column \c c |
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340 | */ |
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341 | poly** _polyMatrix; |
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342 | |
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343 | /** |
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344 | * A method for computing the value of a minor, using a cache.<br> |
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345 | * The sub-matrix is specified by \c mk. Computation works recursively |
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346 | * using Laplace's Theorem. We always develop along the row or column with the most zeros; see |
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347 | * MinorProcessor::getBestLine (const int k, const MinorKey& mk). |
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348 | * @param k the number of rows and columns in the minor to be comuted |
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349 | * @param mk the representation of rows and columns of the minor to be comuted |
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350 | * @param multipleMinors decides whether we compute just one or all minors of a specified size |
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351 | * @param c a cache to be used for caching reusable sub-minors |
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352 | * @return an instance of MinorValue representing the value of the corresponding minor |
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353 | * @see MinorProcessor::getMinorPrivate (const int, const MinorKey&) |
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354 | */ |
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355 | PolyMinorValue getMinorPrivate (const int k, const MinorKey& mk, |
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356 | const bool multipleMinors, |
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357 | Cache<MinorKey, PolyMinorValue>& c); |
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358 | |
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359 | /** |
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360 | * A method for computing the value of a minor, without using a cache.<br> |
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361 | * The sub-matrix is specified by \c mk. Computation works recursively |
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362 | * using Laplace's Theorem. We always develop along the row or column with the most zeros; see |
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363 | * MinorProcessor::getBestLine (const int k, const MinorKey& mk). |
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364 | * @param k the number of rows and columns in the minor to be comuted |
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365 | * @param mk the representation of rows and columns of the minor to be comuted |
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366 | * @return an instance of MinorValue representing the value of the corresponding minor |
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367 | * @see MinorProcessor::getMinorPrivate (const int, const MinorKey&, const bool, Cache<MinorKey, MinorValue>&) |
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368 | */ |
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369 | PolyMinorValue getMinorPrivate (const int k, const MinorKey& mk); |
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370 | protected: |
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371 | bool isEntryZero (const int absoluteRowIndex, const int absoluteColumnIndex) const; |
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372 | public: |
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373 | /** |
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374 | * A constructor for creating an instance. |
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375 | */ |
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376 | PolyMinorProcessor (); |
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377 | |
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378 | /** |
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379 | * A destructor for deleting an instance. |
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380 | */ |
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381 | ~PolyMinorProcessor (); |
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382 | |
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383 | /** |
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384 | * A method for defining a matrix with integer entries. |
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385 | * @param numberOfRows the number of rows |
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386 | * @param numberOfColumns the number of columns |
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387 | * @param matrix the matrix entries in a linear array, i.e., from left to right and top to bottom |
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388 | * @see MinorValue::defineSubMatrix (const int, const int*, const int, const int*) |
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389 | */ |
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390 | void defineMatrix (const int numberOfRows, const int numberOfColumns, const poly* polyMatrix); |
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391 | |
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392 | /** |
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393 | * A method for computing the value of a minor, without using a cache.<br> |
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394 | * The sub-matrix is determined by \c rowIndices and \c columnIndices. Computation works recursively |
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395 | * using Laplace's Theorem. We always develop along the row or column with most zeros; see |
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396 | * MinorProcessor::getBestLine (const int, const int, const int). |
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397 | * @param dimension the size of the minor to be computed |
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398 | * @param rowIndices 0-based indices of the rows of the minor |
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399 | * @param columnIndices 0-based indices of the column of the minor |
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400 | * @return an instance of MinorValue representing the value of the corresponding minor |
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401 | * @see MinorProcessor::getMinor (const int, const int*, const int*, Cache<MinorKey, MinorValue>&) |
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402 | */ |
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403 | PolyMinorValue getMinor (const int dimension, const int* rowIndices, const int* columnIndices); |
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404 | |
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405 | /** |
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406 | * A method for computing the value of a minor, using a cache.<br> |
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407 | * The sub-matrix is determined by \c rowIndices and \c columnIndices. Computation works recursively |
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408 | * using Laplace's Theorem. We always develop along the row or column with most zeros; see |
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409 | * MinorProcessor::getBestLine (const int, const int, const int). |
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410 | * @param dimension the size of the minor to be computed |
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411 | * @param rowIndices 0-based indices of the rows of the minor |
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412 | * @param columnIndices 0-based indices of the column of the minor |
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413 | * @param c a cache to be used for caching reusable sub-minors |
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414 | * @return an instance of MinorValue representing the value of the corresponding minor |
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415 | * @see MinorProcessor::getMinor (const int, const int*, const int*) |
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416 | */ |
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417 | PolyMinorValue getMinor (const int dimension, const int* rowIndices, const int* columnIndices, |
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418 | Cache<MinorKey, PolyMinorValue>& c); |
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419 | |
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420 | /** |
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421 | * A method for obtaining the next minor when iterating |
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422 | * through all minors of a given size within a pre-defined sub-matrix of an underlying matrix.<br> |
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423 | * This method should only be called after MinorProcessor::hasNextMinor () had been called and yielded |
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424 | * \c true.<br> |
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425 | * Computation works without using a cache. |
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426 | * @return true iff there is a next choice of rows and columns |
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427 | * @see MinorProcessor::getMinor (const int, const int*, const int*) |
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428 | * @see MinorProcessor::hasNextMinor () |
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429 | */ |
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430 | PolyMinorValue getNextMinor (); |
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431 | |
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432 | /** |
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433 | * A method for obtaining the next minor when iterating |
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434 | * through all minors of a given size within a pre-defined sub-matrix of an underlying matrix.<br> |
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435 | * This method should only be called after MinorProcessor::hasNextMinor () had been called and yielded |
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436 | * \c true.<br> |
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437 | * Computation works using the cache \a c which may already contain useful results from previous |
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438 | * calls of MinorValue::getNextMinor (Cache<MinorKey, MinorValue>&). |
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439 | * @return the next minor |
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440 | * @see MinorProcessor::getMinor (const int, const int*, const int*) |
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441 | * @see MinorProcessor::hasNextMinor () |
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442 | */ |
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443 | PolyMinorValue getNextMinor (Cache<MinorKey, PolyMinorValue>& c); |
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444 | |
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445 | /** |
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446 | * A method for providing a printable version of the represented MinorProcessor. |
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447 | * @return a printable version of the given instance as instance of class string |
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448 | */ |
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449 | string toString () const; |
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450 | }; |
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451 | |
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452 | #endif // HAVE_MINOR |
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453 | |
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454 | #endif |
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455 | /* MINOR_PROCESSOR_H */ |
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