[16f511] | 1 | #ifdef HAVE_CONFIG_H |
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[ba5e9e] | 2 | #include "singularconfig.h" |
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[16f511] | 3 | #endif /* HAVE_CONFIG_H */ |
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[b1dfaf] | 4 | #include <kernel/mod2.h> |
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[308a766] | 5 | |
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| 6 | #include "MinorProcessor.h" |
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| 7 | |
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| 8 | #include <polys/kbuckets.h> |
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| 9 | |
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[599326] | 10 | #include <kernel/structs.h> |
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[737a68] | 11 | #include <kernel/polys.h> |
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[599326] | 12 | #include <kernel/febase.h> |
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| 13 | #include <kernel/kstd1.h> |
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[308a766] | 14 | |
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| 15 | #include <kernel/ideals.h> |
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| 16 | |
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| 17 | using namespace std; |
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[f0fd47] | 18 | |
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[5c44339] | 19 | #ifdef COUNT_AND_PRINT_OPERATIONS |
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| 20 | long addsPoly = 0; /* for the number of additions of two polynomials */ |
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| 21 | long multsPoly = 0; /* for the number of multiplications of two polynomials */ |
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| 22 | long addsPolyForDiv = 0; /* for the number of additions of two polynomials for |
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| 23 | polynomial division part */ |
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| 24 | long multsPolyForDiv = 0; /* for the number of multiplications of two polynomials |
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| 25 | for polynomial division part */ |
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| 26 | long multsMon = 0; /* for the number of multiplications of two monomials */ |
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| 27 | long multsMonForDiv = 0; /* for the number of m-m-multiplications for polynomial |
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| 28 | division part */ |
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| 29 | long savedMultsMFD = 0; /* number of m-m-multiplications that could be saved |
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| 30 | when polynomial division would be optimal |
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| 31 | (if p / t1 = t2 + ..., then t1 * t2 = LT(p), i.e., |
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| 32 | this multiplication need not be performed which |
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| 33 | would save one m-m-multiplication) */ |
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| 34 | long divsMon = 0; /* for the number of divisions of two monomials; |
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| 35 | these are all guaranteed to work, i.e., m1/m2 only |
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| 36 | when exponentVector(m1) >= exponentVector(m2) */ |
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| 37 | void printCounters (char* prefix, bool resetToZero) |
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| 38 | { |
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| 39 | printf("%s [p+p(div) | p*p(div) | m*m(div, -save) | m/m ]", prefix); |
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| 40 | printf(" = [%ld(%ld) | %ld(%ld) | %ld(%d, -%ld) | %ld]\n", |
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| 41 | addsPoly, addsPolyForDiv, multsPoly, multsPolyForDiv, |
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| 42 | multsMon, multsMonForDiv, savedMultsMFD, divsMon); |
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| 43 | if (resetToZero) |
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| 44 | { |
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| 45 | multsMon = 0; addsPoly = 0; multsPoly = 0; divsMon = 0; |
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| 46 | savedMultsMFD = 0; multsMonForDiv = 0; addsPolyForDiv = 0; |
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| 47 | multsPolyForDiv = 0; |
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| 48 | } |
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| 49 | } |
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| 50 | #endif |
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| 51 | /* COUNT_AND_PRINT_OPERATIONS */ |
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| 52 | |
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[f0fd47] | 53 | void MinorProcessor::print() const |
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| 54 | { |
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| 55 | PrintS(this->toString().c_str()); |
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| 56 | } |
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| 57 | |
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| 58 | int MinorProcessor::getBestLine (const int k, const MinorKey& mk) const |
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| 59 | { |
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| 60 | /* This method identifies the row or column with the most zeros. |
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| 61 | The returned index (bestIndex) is absolute within the pre- |
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| 62 | defined matrix. |
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| 63 | If some row has the most zeros, then the absolute (0-based) |
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| 64 | row index is returned. |
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| 65 | If, contrariwise, some column has the most zeros, then -1 minus |
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| 66 | the absolute (0-based) column index is returned. */ |
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| 67 | int numberOfZeros = 0; |
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| 68 | int bestIndex = 100000; /* We start with an invalid row/column index. */ |
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| 69 | int maxNumberOfZeros = -1; /* We update this variable whenever we find |
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| 70 | a new so-far optimal row or column. */ |
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| 71 | for (int r = 0; r < k; r++) |
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| 72 | { |
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| 73 | /* iterate through all k rows of the momentary minor */ |
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| 74 | int absoluteR = mk.getAbsoluteRowIndex(r); |
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| 75 | numberOfZeros = 0; |
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| 76 | for (int c = 0; c < k; c++) |
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| 77 | { |
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| 78 | int absoluteC = mk.getAbsoluteColumnIndex(c); |
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| 79 | if (isEntryZero(absoluteR, absoluteC)) numberOfZeros++; |
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| 80 | } |
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| 81 | if (numberOfZeros > maxNumberOfZeros) |
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| 82 | { |
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| 83 | /* We found a new best line which is a row. */ |
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| 84 | bestIndex = absoluteR; |
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| 85 | maxNumberOfZeros = numberOfZeros; |
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| 86 | } |
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| 87 | }; |
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| 88 | for (int c = 0; c < k; c++) |
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| 89 | { |
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| 90 | int absoluteC = mk.getAbsoluteColumnIndex(c); |
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| 91 | numberOfZeros = 0; |
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| 92 | for (int r = 0; r < k; r++) |
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| 93 | { |
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| 94 | int absoluteR = mk.getAbsoluteRowIndex(r); |
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| 95 | if (isEntryZero(absoluteR, absoluteC)) numberOfZeros++; |
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| 96 | } |
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| 97 | if (numberOfZeros > maxNumberOfZeros) |
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| 98 | { |
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| 99 | /* We found a new best line which is a column. So we transform |
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| 100 | the return value. Note that we can easily retrieve absoluteC |
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| 101 | from bestLine: absoluteC = - 1 - bestLine. */ |
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| 102 | bestIndex = - absoluteC - 1; |
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| 103 | maxNumberOfZeros = numberOfZeros; |
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| 104 | } |
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| 105 | }; |
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| 106 | return bestIndex; |
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| 107 | } |
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| 108 | |
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| 109 | void MinorProcessor::setMinorSize(const int minorSize) |
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| 110 | { |
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| 111 | _minorSize = minorSize; |
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| 112 | _minor.reset(); |
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| 113 | } |
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| 114 | |
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| 115 | bool MinorProcessor::hasNextMinor() |
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| 116 | { |
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| 117 | return setNextKeys(_minorSize); |
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| 118 | } |
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| 119 | |
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| 120 | void MinorProcessor::getCurrentRowIndices(int* const target) const |
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| 121 | { |
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| 122 | return _minor.getAbsoluteRowIndices(target); |
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| 123 | } |
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| 124 | |
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| 125 | void MinorProcessor::getCurrentColumnIndices(int* const target) const |
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| 126 | { |
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| 127 | return _minor.getAbsoluteColumnIndices(target); |
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| 128 | } |
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| 129 | |
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| 130 | void MinorProcessor::defineSubMatrix(const int numberOfRows, |
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| 131 | const int* rowIndices, |
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| 132 | const int numberOfColumns, |
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| 133 | const int* columnIndices) |
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| 134 | { |
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| 135 | /* The method assumes ascending row and column indices in the |
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| 136 | two argument arrays. These indices are understood to be zero-based. |
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| 137 | The method will set the two arrays of ints in _container. |
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| 138 | Example: The indices 0, 2, 3, 7 will be converted to an array with |
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| 139 | one int representing the binary number 10001101 |
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| 140 | (check bits from right to left). */ |
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| 141 | |
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| 142 | _containerRows = numberOfRows; |
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| 143 | int highestRowIndex = rowIndices[numberOfRows - 1]; |
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| 144 | int rowBlockCount = (highestRowIndex / 32) + 1; |
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[5f4463] | 145 | unsigned int *rowBlocks=new unsigned int[rowBlockCount]; |
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[f0fd47] | 146 | for (int i = 0; i < rowBlockCount; i++) rowBlocks[i] = 0; |
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| 147 | for (int i = 0; i < numberOfRows; i++) |
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| 148 | { |
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| 149 | int blockIndex = rowIndices[i] / 32; |
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| 150 | int offset = rowIndices[i] % 32; |
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| 151 | rowBlocks[blockIndex] += (1 << offset); |
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| 152 | } |
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| 153 | |
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| 154 | _containerColumns = numberOfColumns; |
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| 155 | int highestColumnIndex = columnIndices[numberOfColumns - 1]; |
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| 156 | int columnBlockCount = (highestColumnIndex / 32) + 1; |
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[5f4463] | 157 | unsigned *columnBlocks=new unsigned[columnBlockCount]; |
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[f0fd47] | 158 | for (int i = 0; i < columnBlockCount; i++) columnBlocks[i] = 0; |
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| 159 | for (int i = 0; i < numberOfColumns; i++) |
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| 160 | { |
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| 161 | int blockIndex = columnIndices[i] / 32; |
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| 162 | int offset = columnIndices[i] % 32; |
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| 163 | columnBlocks[blockIndex] += (1 << offset); |
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| 164 | } |
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| 165 | |
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| 166 | _container.set(rowBlockCount, rowBlocks, columnBlockCount, columnBlocks); |
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[5f4463] | 167 | delete[] columnBlocks; |
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| 168 | delete[] rowBlocks; |
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[f0fd47] | 169 | } |
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| 170 | |
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| 171 | bool MinorProcessor::setNextKeys(const int k) |
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[29c136] | 172 | { |
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[f0fd47] | 173 | /* This method moves _minor to the next valid (k x k)-minor within |
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| 174 | _container. It returns true iff this is successful, i.e. iff |
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| 175 | _minor did not already encode the terminal (k x k)-minor. */ |
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| 176 | if (_minor.compare(MinorKey(0, 0, 0, 0)) == 0) |
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| 177 | { |
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| 178 | /* This means that we haven't started yet. Thus, we are about |
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| 179 | to compute the first (k x k)-minor. */ |
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| 180 | _minor.selectFirstRows(k, _container); |
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| 181 | _minor.selectFirstColumns(k, _container); |
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| 182 | return true; |
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| 183 | } |
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| 184 | else if (_minor.selectNextColumns(k, _container)) |
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| 185 | { |
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| 186 | /* Here we were able to pick a next subset of columns |
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| 187 | within the same subset of rows. */ |
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| 188 | return true; |
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| 189 | } |
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| 190 | else if (_minor.selectNextRows(k, _container)) |
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| 191 | { |
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| 192 | /* Here we were not able to pick a next subset of columns |
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| 193 | within the same subset of rows. But we could pick a next |
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| 194 | subset of rows. We must hence reset the subset of columns: */ |
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| 195 | _minor.selectFirstColumns(k, _container); |
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| 196 | return true; |
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| 197 | } |
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| 198 | else |
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| 199 | { |
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| 200 | /* We were neither able to pick a next subset |
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| 201 | of columns nor of rows. I.e., we have iterated through |
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| 202 | all sensible choices of subsets of rows and columns. */ |
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| 203 | return false; |
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| 204 | } |
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| 205 | } |
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| 206 | |
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[2e4ec14] | 207 | bool MinorProcessor::isEntryZero (const int /*absoluteRowIndex*/, |
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| 208 | const int /*absoluteColumnIndex*/) const |
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[f0fd47] | 209 | { |
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| 210 | assume(false); |
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| 211 | return false; |
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| 212 | } |
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| 213 | |
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| 214 | string MinorProcessor::toString () const |
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| 215 | { |
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| 216 | assume(false); |
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| 217 | return ""; |
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| 218 | } |
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| 219 | |
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| 220 | int MinorProcessor::IOverJ(const int i, const int j) |
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| 221 | { |
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| 222 | /* This is a non-recursive implementation. */ |
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[308a766] | 223 | assume( (i >= 0) && (j >= 0) && (i >= j)); |
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[f0fd47] | 224 | if (j == 0 || i == j) return 1; |
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| 225 | int result = 1; |
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| 226 | for (int k = i - j + 1; k <= i; k++) result *= k; |
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| 227 | /* Now, result = (i - j + 1) * ... * i. */ |
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| 228 | for (int k = 2; k <= j; k++) result /= k; |
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| 229 | /* Now, result = (i - j + 1) * ... * i / 1 / 2 ... |
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| 230 | ... / j = i! / j! / (i - j)!. */ |
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| 231 | return result; |
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| 232 | } |
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| 233 | |
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| 234 | int MinorProcessor::Faculty(const int i) |
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| 235 | { |
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| 236 | /* This is a non-recursive implementation. */ |
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[308a766] | 237 | assume(i >= 0); |
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[f0fd47] | 238 | int result = 1; |
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| 239 | for (int j = 1; j <= i; j++) result *= j; |
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| 240 | // Now, result = 1 * 2 * ... * i = i! |
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| 241 | return result; |
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| 242 | } |
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| 243 | |
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| 244 | int MinorProcessor::NumberOfRetrievals (const int rows, const int columns, |
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| 245 | const int containerMinorSize, |
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| 246 | const int minorSize, |
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| 247 | const bool multipleMinors) |
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| 248 | { |
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| 249 | /* This method computes the number of potential retrievals |
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| 250 | of a single minor when computing all minors of a given size |
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| 251 | within a matrix of given size. */ |
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| 252 | int result = 0; |
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| 253 | if (multipleMinors) |
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| 254 | { |
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| 255 | /* Here, we would like to compute all minors of size |
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| 256 | containerMinorSize x containerMinorSize in a matrix |
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| 257 | of size rows x columns. |
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| 258 | Then, we need to retrieve any minor of size |
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| 259 | minorSize x minorSize exactly n times, where n is as |
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| 260 | follows: */ |
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| 261 | result = IOverJ(rows - minorSize, containerMinorSize - minorSize) |
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| 262 | * IOverJ(columns - minorSize, containerMinorSize - minorSize) |
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| 263 | * Faculty(containerMinorSize - minorSize); |
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| 264 | } |
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| 265 | else |
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| 266 | { |
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| 267 | /* Here, we would like to compute just one minor of size |
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| 268 | containerMinorSize x containerMinorSize. Then, we need |
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| 269 | to retrieve any minor of size minorSize x minorSize exactly |
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| 270 | (containerMinorSize - minorSize)! times: */ |
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| 271 | result = Faculty(containerMinorSize - minorSize); |
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| 272 | } |
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| 273 | return result; |
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| 274 | } |
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| 275 | |
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| 276 | MinorProcessor::MinorProcessor () |
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| 277 | { |
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| 278 | _container = MinorKey(0, 0, 0, 0); |
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| 279 | _minor = MinorKey(0, 0, 0, 0); |
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| 280 | _containerRows = 0; |
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| 281 | _containerColumns = 0; |
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| 282 | _minorSize = 0; |
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| 283 | _rows = 0; |
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| 284 | _columns = 0; |
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| 285 | } |
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| 286 | |
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[d2ea299] | 287 | MinorProcessor::~MinorProcessor () { } |
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| 288 | |
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[f0fd47] | 289 | IntMinorProcessor::IntMinorProcessor () |
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| 290 | { |
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| 291 | _intMatrix = 0; |
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| 292 | } |
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| 293 | |
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| 294 | string IntMinorProcessor::toString () const |
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| 295 | { |
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| 296 | char h[32]; |
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| 297 | string t = ""; |
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| 298 | string s = "IntMinorProcessor:"; |
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| 299 | s += "\n matrix: "; |
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| 300 | sprintf(h, "%d", _rows); s += h; |
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| 301 | s += " x "; |
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| 302 | sprintf(h, "%d", _columns); s += h; |
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| 303 | for (int r = 0; r < _rows; r++) |
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| 304 | { |
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| 305 | s += "\n "; |
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| 306 | for (int c = 0; c < _columns; c++) |
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| 307 | { |
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| 308 | sprintf(h, "%d", getEntry(r, c)); t = h; |
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| 309 | for (int k = 0; k < int(4 - strlen(h)); k++) s += " "; |
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| 310 | s += t; |
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| 311 | } |
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| 312 | } |
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| 313 | int myIndexArray[500]; |
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| 314 | s += "\n considered submatrix has row indices: "; |
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| 315 | _container.getAbsoluteRowIndices(myIndexArray); |
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| 316 | for (int k = 0; k < _containerRows; k++) |
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| 317 | { |
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| 318 | if (k != 0) s += ", "; |
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| 319 | sprintf(h, "%d", myIndexArray[k]); s += h; |
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| 320 | } |
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| 321 | s += " (first row of matrix has index 0)"; |
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| 322 | s += "\n considered submatrix has column indices: "; |
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| 323 | _container.getAbsoluteColumnIndices(myIndexArray); |
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| 324 | for (int k = 0; k < _containerColumns; k++) |
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| 325 | { |
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| 326 | if (k != 0) s += ", "; |
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| 327 | sprintf(h, "%d", myIndexArray[k]); s += h; |
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| 328 | } |
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| 329 | s += " (first column of matrix has index 0)"; |
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| 330 | s += "\n size of considered minor(s): "; |
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| 331 | sprintf(h, "%d", _minorSize); s += h; |
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| 332 | s += "x"; |
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| 333 | s += h; |
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| 334 | return s; |
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| 335 | } |
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| 336 | |
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| 337 | IntMinorProcessor::~IntMinorProcessor() |
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| 338 | { |
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| 339 | /* free memory of _intMatrix */ |
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| 340 | delete [] _intMatrix; _intMatrix = 0; |
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| 341 | } |
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| 342 | |
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| 343 | bool IntMinorProcessor::isEntryZero (const int absoluteRowIndex, |
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| 344 | const int absoluteColumnIndex) const |
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| 345 | { |
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| 346 | return getEntry(absoluteRowIndex, absoluteColumnIndex) == 0; |
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| 347 | } |
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| 348 | |
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| 349 | void IntMinorProcessor::defineMatrix (const int numberOfRows, |
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| 350 | const int numberOfColumns, |
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| 351 | const int* matrix) |
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| 352 | { |
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| 353 | /* free memory of _intMatrix */ |
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| 354 | delete [] _intMatrix; _intMatrix = 0; |
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| 355 | |
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| 356 | _rows = numberOfRows; |
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| 357 | _columns = numberOfColumns; |
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| 358 | |
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| 359 | /* allocate memory for new entries in _intMatrix */ |
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| 360 | int n = _rows * _columns; |
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| 361 | _intMatrix = new int[n]; |
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| 362 | |
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| 363 | /* copying values from one-dimensional method |
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| 364 | parameter "matrix" */ |
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| 365 | for (int i = 0; i < n; i++) |
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| 366 | _intMatrix[i] = matrix[i]; |
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| 367 | } |
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| 368 | |
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| 369 | IntMinorValue IntMinorProcessor::getMinor(const int dimension, |
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| 370 | const int* rowIndices, |
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| 371 | const int* columnIndices, |
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| 372 | Cache<MinorKey, IntMinorValue>& c, |
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| 373 | const int characteristic, |
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| 374 | const ideal& iSB) |
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| 375 | { |
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| 376 | defineSubMatrix(dimension, rowIndices, dimension, columnIndices); |
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| 377 | _minorSize = dimension; |
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| 378 | /* call a helper method which recursively computes the minor using the |
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| 379 | cache c: */ |
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| 380 | return getMinorPrivateLaplace(dimension, _container, false, c, |
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| 381 | characteristic, iSB); |
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| 382 | } |
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| 383 | |
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| 384 | IntMinorValue IntMinorProcessor::getMinor(const int dimension, |
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| 385 | const int* rowIndices, |
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| 386 | const int* columnIndices, |
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| 387 | const int characteristic, |
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| 388 | const ideal& iSB, |
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| 389 | const char* algorithm) |
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| 390 | { |
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[089b98] | 391 | defineSubMatrix(dimension, rowIndices, dimension, columnIndices); |
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| 392 | _minorSize = dimension; |
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| 393 | |
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| 394 | /* call a helper method which computes the minor (without a cache): */ |
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| 395 | if (strcmp(algorithm, "Laplace") == 0) |
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| 396 | return getMinorPrivateLaplace(_minorSize, _container, characteristic, |
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| 397 | iSB); |
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| 398 | else if (strcmp(algorithm, "Bareiss") == 0) |
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| 399 | return getMinorPrivateBareiss(_minorSize, _container, characteristic, |
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| 400 | iSB); |
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| 401 | else assume(false); |
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[f0fd47] | 402 | |
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[089b98] | 403 | /* The following code is never reached and just there to make the |
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| 404 | compiler happy: */ |
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| 405 | return IntMinorValue(); |
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[f0fd47] | 406 | } |
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| 407 | |
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| 408 | IntMinorValue IntMinorProcessor::getNextMinor(const int characteristic, |
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| 409 | const ideal& iSB, |
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| 410 | const char* algorithm) |
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| 411 | { |
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[089b98] | 412 | /* call a helper method which computes the minor (without a cache): */ |
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| 413 | if (strcmp(algorithm, "Laplace") == 0) |
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| 414 | return getMinorPrivateLaplace(_minorSize, _minor, characteristic, iSB); |
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| 415 | else if (strcmp(algorithm, "Bareiss") == 0) |
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| 416 | return getMinorPrivateBareiss(_minorSize, _minor, characteristic, iSB); |
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| 417 | else assume(false); |
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[a9c298] | 418 | |
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[089b98] | 419 | /* The following code is never reached and just there to make the |
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| 420 | compiler happy: */ |
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| 421 | return IntMinorValue(); |
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[f0fd47] | 422 | } |
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| 423 | |
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| 424 | IntMinorValue IntMinorProcessor::getNextMinor(Cache<MinorKey, |
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| 425 | IntMinorValue>& c, |
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| 426 | const int characteristic, |
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| 427 | const ideal& iSB) |
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| 428 | { |
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| 429 | /* computation with cache */ |
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| 430 | return getMinorPrivateLaplace(_minorSize, _minor, true, c, characteristic, |
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| 431 | iSB); |
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| 432 | } |
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| 433 | |
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| 434 | /* computes the reduction of an integer i modulo an ideal |
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| 435 | which captures a std basis */ |
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| 436 | int getReduction (const int i, const ideal& iSB) |
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| 437 | { |
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| 438 | if (i == 0) return 0; |
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| 439 | poly f = pISet(i); |
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| 440 | poly g = kNF(iSB, currRing->qideal, f); |
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| 441 | int result = 0; |
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[3d9165] | 442 | if (g != NULL) result = n_Int(pGetCoeff(g), currRing->cf); |
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[f0fd47] | 443 | pDelete(&f); |
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| 444 | pDelete(&g); |
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| 445 | return result; |
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| 446 | } |
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| 447 | |
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| 448 | IntMinorValue IntMinorProcessor::getMinorPrivateLaplace( |
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| 449 | const int k, |
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| 450 | const MinorKey& mk, |
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| 451 | const int characteristic, |
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| 452 | const ideal& iSB) |
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| 453 | { |
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[308a766] | 454 | assume(k > 0); /* k is the minor's dimension; the minor must be at least |
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[f0fd47] | 455 | 1x1 */ |
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| 456 | /* The method works by recursion, and using Lapace's Theorem along the |
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| 457 | row/column with the most zeros. */ |
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| 458 | if (k == 1) |
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| 459 | { |
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| 460 | int e = getEntry(mk.getAbsoluteRowIndex(0), mk.getAbsoluteColumnIndex(0)); |
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| 461 | if (characteristic != 0) e = e % characteristic; |
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| 462 | if (iSB != 0) e = getReduction(e, iSB); |
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| 463 | return IntMinorValue(e, 0, 0, 0, 0, -1, -1); /* "-1" is to signal that any |
---|
| 464 | statistics about the number |
---|
| 465 | of retrievals does not make |
---|
| 466 | sense, as we do not use a |
---|
| 467 | cache. */ |
---|
| 468 | } |
---|
| 469 | else |
---|
| 470 | { |
---|
| 471 | /* Here, the minor must be 2x2 or larger. */ |
---|
| 472 | int b = getBestLine(k, mk); /* row or column with most |
---|
| 473 | zeros */ |
---|
| 474 | int result = 0; /* This will contain the |
---|
| 475 | value of the minor. */ |
---|
| 476 | int s = 0; int m = 0; int as = 0; int am = 0; /* counters for additions and |
---|
| 477 | multiplications, ..."a*" |
---|
| 478 | for accumulated operation |
---|
| 479 | counters */ |
---|
[5c44339] | 480 | bool hadNonZeroEntry = false; |
---|
[f0fd47] | 481 | if (b >= 0) |
---|
| 482 | { |
---|
| 483 | /* This means that the best line is the row with absolute (0-based) |
---|
| 484 | index b. |
---|
| 485 | Using Laplace, the sign of the contributing minors must be iterating; |
---|
| 486 | the initial sign depends on the relative index of b in minorRowKey: */ |
---|
| 487 | int sign = (mk.getRelativeRowIndex(b) % 2 == 0 ? 1 : -1); |
---|
| 488 | for (int c = 0; c < k; c++) /* This iterates over all involved columns. */ |
---|
| 489 | { |
---|
| 490 | int absoluteC = mk.getAbsoluteColumnIndex(c); |
---|
| 491 | if (getEntry(b, absoluteC) != 0) /* Only then do we have to consider |
---|
| 492 | this sub-determinante. */ |
---|
| 493 | { |
---|
[5c44339] | 494 | hadNonZeroEntry = true; |
---|
[f0fd47] | 495 | /* Next MinorKey is mk with row b and column absoluteC omitted: */ |
---|
| 496 | MinorKey subMk = mk.getSubMinorKey(b, absoluteC); |
---|
| 497 | IntMinorValue mv = getMinorPrivateLaplace(k - 1, subMk, |
---|
| 498 | characteristic, iSB); /* recursive call */ |
---|
| 499 | m += mv.getMultiplications(); |
---|
| 500 | s += mv.getAdditions(); |
---|
| 501 | am += mv.getAccumulatedMultiplications(); |
---|
| 502 | as += mv.getAccumulatedAdditions(); |
---|
| 503 | /* adding sub-determinante times matrix entry |
---|
| 504 | times appropriate sign: */ |
---|
| 505 | result += sign * mv.getResult() * getEntry(b, absoluteC); |
---|
| 506 | |
---|
| 507 | if (characteristic != 0) result = result % characteristic; |
---|
| 508 | s++; m++; as++, am++; /* This is for the last addition and |
---|
| 509 | multiplication. */ |
---|
| 510 | } |
---|
| 511 | sign = - sign; /* alternating the sign */ |
---|
| 512 | } |
---|
| 513 | } |
---|
| 514 | else |
---|
| 515 | { |
---|
| 516 | b = - b - 1; |
---|
| 517 | /* This means that the best line is the column with absolute (0-based) |
---|
| 518 | index b. |
---|
| 519 | Using Laplace, the sign of the contributing minors must be iterating; |
---|
| 520 | the initial sign depends on the relative index of b in |
---|
| 521 | minorColumnKey: */ |
---|
| 522 | int sign = (mk.getRelativeColumnIndex(b) % 2 == 0 ? 1 : -1); |
---|
| 523 | for (int r = 0; r < k; r++) /* This iterates over all involved rows. */ |
---|
| 524 | { |
---|
| 525 | int absoluteR = mk.getAbsoluteRowIndex(r); |
---|
| 526 | if (getEntry(absoluteR, b) != 0) /* Only then do we have to consider |
---|
| 527 | this sub-determinante. */ |
---|
| 528 | { |
---|
[5c44339] | 529 | hadNonZeroEntry = true; |
---|
[f0fd47] | 530 | /* Next MinorKey is mk with row absoluteR and column b omitted. */ |
---|
| 531 | MinorKey subMk = mk.getSubMinorKey(absoluteR, b); |
---|
| 532 | IntMinorValue mv = getMinorPrivateLaplace(k - 1, subMk, characteristic, iSB); /* recursive call */ |
---|
| 533 | m += mv.getMultiplications(); |
---|
| 534 | s += mv.getAdditions(); |
---|
| 535 | am += mv.getAccumulatedMultiplications(); |
---|
| 536 | as += mv.getAccumulatedAdditions(); |
---|
| 537 | /* adding sub-determinante times matrix entry |
---|
| 538 | times appropriate sign: */ |
---|
| 539 | result += sign * mv.getResult() * getEntry(absoluteR, b); |
---|
| 540 | if (characteristic != 0) result = result % characteristic; |
---|
| 541 | s++; m++; as++, am++; /* This is for the last addition and |
---|
| 542 | multiplication. */ |
---|
| 543 | } |
---|
| 544 | sign = - sign; /* alternating the sign */ |
---|
| 545 | } |
---|
| 546 | } |
---|
[5c44339] | 547 | if (hadNonZeroEntry) |
---|
| 548 | { |
---|
[f0fd47] | 549 | s--; as--; /* first addition was 0 + ..., so we do not count it */ |
---|
[5c44339] | 550 | } |
---|
| 551 | if (s < 0) s = 0; /* may happen when all subminors are zero and no |
---|
| 552 | addition needs to be performed */ |
---|
| 553 | if (as < 0) as = 0; /* may happen when all subminors are zero and no |
---|
[f0fd47] | 554 | addition needs to be performed */ |
---|
[5c44339] | 555 | if (iSB != 0) result = getReduction(result, iSB); |
---|
| 556 | IntMinorValue newMV(result, m, s, am, as, -1, -1); |
---|
| 557 | /* "-1" is to signal that any statistics about the number of retrievals |
---|
| 558 | does not make sense, as we do not use a cache. */ |
---|
| 559 | return newMV; |
---|
[f0fd47] | 560 | } |
---|
| 561 | } |
---|
| 562 | |
---|
| 563 | /* This method can only be used in the case of coefficients |
---|
| 564 | coming from a field or at least from an integral domain. */ |
---|
| 565 | IntMinorValue IntMinorProcessor::getMinorPrivateBareiss( |
---|
| 566 | const int k, |
---|
| 567 | const MinorKey& mk, |
---|
| 568 | const int characteristic, |
---|
| 569 | const ideal& iSB) |
---|
| 570 | { |
---|
[308a766] | 571 | assume(k > 0); /* k is the minor's dimension; the minor must be at least |
---|
[f0fd47] | 572 | 1x1 */ |
---|
[5f4463] | 573 | int *theRows=new int[k]; mk.getAbsoluteRowIndices(theRows); |
---|
| 574 | int *theColumns=new int[k]; mk.getAbsoluteColumnIndices(theColumns); |
---|
[f0fd47] | 575 | /* the next line provides the return value for the case k = 1 */ |
---|
| 576 | int e = getEntry(theRows[0], theColumns[0]); |
---|
| 577 | if (characteristic != 0) e = e % characteristic; |
---|
| 578 | if (iSB != 0) e = getReduction(e, iSB); |
---|
| 579 | IntMinorValue mv(e, 0, 0, 0, 0, -1, -1); |
---|
| 580 | if (k > 1) |
---|
| 581 | { |
---|
| 582 | /* the matrix to perform Bareiss with */ |
---|
[5f4463] | 583 | long *tempMatrix=new long[k * k]; |
---|
[f0fd47] | 584 | /* copy correct set of entries from _intMatrix to tempMatrix */ |
---|
| 585 | int i = 0; |
---|
| 586 | for (int r = 0; r < k; r++) |
---|
| 587 | for (int c = 0; c < k; c++) |
---|
| 588 | { |
---|
| 589 | e = getEntry(theRows[r], theColumns[c]); |
---|
| 590 | if (characteristic != 0) e = e % characteristic; |
---|
| 591 | tempMatrix[i++] = e; |
---|
| 592 | } |
---|
| 593 | /* Bareiss algorithm operating on tempMatrix which is at least 2x2 */ |
---|
| 594 | int sign = 1; /* This will store the correct sign resulting |
---|
| 595 | from permuting the rows of tempMatrix. */ |
---|
[5f4463] | 596 | int *rowPermutation=new int[k]; |
---|
| 597 | /* This is for storing the permutation of rows |
---|
| 598 | resulting from searching for a non-zero |
---|
| 599 | pivot element. */ |
---|
[f0fd47] | 600 | for (int i = 0; i < k; i++) rowPermutation[i] = i; |
---|
| 601 | int divisor = 1; /* the Bareiss divisor */ |
---|
| 602 | for (int r = 0; r <= k - 2; r++) |
---|
| 603 | { |
---|
| 604 | /* look for a non-zero entry in column r: */ |
---|
| 605 | int i = r; |
---|
| 606 | while ((i < k) && (tempMatrix[rowPermutation[i] * k + r] == 0)) |
---|
| 607 | i++; |
---|
| 608 | if (i == k) |
---|
| 609 | /* There is no non-zero entry; hence the minor is zero. */ |
---|
| 610 | return IntMinorValue(0, 0, 0, 0, 0, -1, -1); |
---|
| 611 | if (i != r) |
---|
| 612 | { |
---|
| 613 | /* We swap the rows with indices r and i: */ |
---|
| 614 | int j = rowPermutation[i]; |
---|
| 615 | rowPermutation[i] = rowPermutation[r]; |
---|
| 616 | rowPermutation[r] = j; |
---|
| 617 | /* Now we know that tempMatrix[rowPermutation[r] * k + r] is not zero. |
---|
| 618 | But carefull; we have to negate the sign, as there is always an odd |
---|
| 619 | number of row transpositions to swap two given rows of a matrix. */ |
---|
| 620 | sign = -sign; |
---|
| 621 | } |
---|
| 622 | if (r >= 1) divisor = tempMatrix[rowPermutation[r - 1] * k + r - 1]; |
---|
| 623 | for (int rr = r + 1; rr < k; rr++) |
---|
| 624 | for (int cc = r + 1; cc < k; cc++) |
---|
| 625 | { |
---|
| 626 | e = rowPermutation[rr] * k + cc; |
---|
| 627 | /* Attention: The following may cause an overflow and |
---|
| 628 | thus a wrong result: */ |
---|
| 629 | tempMatrix[e] = tempMatrix[e] * tempMatrix[rowPermutation[r] * k + r] |
---|
| 630 | - tempMatrix[rowPermutation[r] * k + cc] |
---|
| 631 | * tempMatrix[rowPermutation[rr] * k + r]; |
---|
| 632 | /* The following is, by theory, always a division without |
---|
| 633 | remainder: */ |
---|
| 634 | tempMatrix[e] = tempMatrix[e] / divisor; |
---|
| 635 | if (characteristic != 0) |
---|
| 636 | tempMatrix[e] = tempMatrix[e] % characteristic; |
---|
| 637 | } |
---|
[5f4463] | 638 | delete[] rowPermutation; |
---|
| 639 | delete[] tempMatrix; |
---|
[f0fd47] | 640 | } |
---|
| 641 | int theValue = sign * tempMatrix[rowPermutation[k - 1] * k + k - 1]; |
---|
| 642 | if (iSB != 0) theValue = getReduction(theValue, iSB); |
---|
| 643 | mv = IntMinorValue(theValue, 0, 0, 0, 0, -1, -1); |
---|
| 644 | } |
---|
[5f4463] | 645 | delete [] theRows; |
---|
| 646 | delete [] theColumns; |
---|
[f0fd47] | 647 | return mv; |
---|
| 648 | } |
---|
| 649 | |
---|
| 650 | int IntMinorProcessor::getEntry (const int rowIndex, |
---|
| 651 | const int columnIndex) const |
---|
| 652 | { |
---|
| 653 | return _intMatrix[rowIndex * _columns + columnIndex]; |
---|
| 654 | } |
---|
| 655 | |
---|
| 656 | IntMinorValue IntMinorProcessor::getMinorPrivateLaplace( |
---|
| 657 | const int k, const MinorKey& mk, |
---|
| 658 | const bool multipleMinors, |
---|
| 659 | Cache<MinorKey, IntMinorValue>& cch, |
---|
| 660 | const int characteristic, const ideal& iSB) |
---|
| 661 | { |
---|
[308a766] | 662 | assume(k > 0); /* k is the minor's dimension; the minor must be at least |
---|
[f0fd47] | 663 | 1x1 */ |
---|
| 664 | /* The method works by recursion, and using Lapace's Theorem along |
---|
| 665 | the row/column with the most zeros. */ |
---|
| 666 | if (k == 1) |
---|
| 667 | { |
---|
| 668 | int e = getEntry(mk.getAbsoluteRowIndex(0), mk.getAbsoluteColumnIndex(0)); |
---|
| 669 | if (characteristic != 0) e = e % characteristic; |
---|
| 670 | if (iSB != 0) e = getReduction(e, iSB); |
---|
| 671 | return IntMinorValue(e, 0, 0, 0, 0, -1, -1); |
---|
| 672 | /* we set "-1" as, for k == 1, we do not have any cache retrievals */ |
---|
| 673 | } |
---|
| 674 | else |
---|
| 675 | { |
---|
| 676 | int b = getBestLine(k, mk); /* row or column with |
---|
| 677 | most zeros */ |
---|
| 678 | int result = 0; /* This will contain the |
---|
| 679 | value of the minor. */ |
---|
| 680 | int s = 0; int m = 0; int as = 0; int am = 0; /* counters for additions |
---|
| 681 | and multiplications, |
---|
| 682 | ..."a*" for |
---|
| 683 | accumulated operation |
---|
| 684 | counters */ |
---|
| 685 | IntMinorValue mv(0, 0, 0, 0, 0, 0, 0); /* for storing all |
---|
| 686 | intermediate minors */ |
---|
[5c44339] | 687 | bool hadNonZeroEntry = false; |
---|
[f0fd47] | 688 | if (b >= 0) |
---|
| 689 | { |
---|
| 690 | /* This means that the best line is the row with absolute (0-based) |
---|
| 691 | index b. |
---|
| 692 | Using Laplace, the sign of the contributing minors must be |
---|
| 693 | iterating; the initial sign depends on the relative index of b |
---|
| 694 | in minorRowKey: */ |
---|
| 695 | int sign = (mk.getRelativeRowIndex(b) % 2 == 0 ? 1 : -1); |
---|
| 696 | for (int c = 0; c < k; c++) /* This iterates over all involved |
---|
| 697 | columns. */ |
---|
| 698 | { |
---|
| 699 | int absoluteC = mk.getAbsoluteColumnIndex(c); |
---|
| 700 | if (getEntry(b, absoluteC) != 0) /* Only then do we have to consider |
---|
| 701 | this sub-determinante. */ |
---|
| 702 | { |
---|
[5c44339] | 703 | hadNonZeroEntry = true; |
---|
[f0fd47] | 704 | /* Next MinorKey is mk with row b and column absoluteC omitted. */ |
---|
| 705 | MinorKey subMk = mk.getSubMinorKey(b, absoluteC); |
---|
| 706 | if (cch.hasKey(subMk)) |
---|
| 707 | { /* trying to find the result in the cache */ |
---|
| 708 | mv = cch.getValue(subMk); |
---|
| 709 | mv.incrementRetrievals(); /* once more, we made use of the cached |
---|
| 710 | value for key mk */ |
---|
| 711 | cch.put(subMk, mv); /* We need to do this with "put", as the |
---|
| 712 | (altered) number of retrievals may have |
---|
| 713 | an impact on the internal ordering among |
---|
| 714 | the cached entries. */ |
---|
| 715 | } |
---|
| 716 | else |
---|
| 717 | { |
---|
| 718 | mv = getMinorPrivateLaplace(k - 1, subMk, multipleMinors, cch, |
---|
| 719 | characteristic, iSB); /* recursive call */ |
---|
| 720 | /* As this minor was not in the cache, we count the additions |
---|
| 721 | and multiplications that we needed to perform in the |
---|
| 722 | recursive call: */ |
---|
| 723 | m += mv.getMultiplications(); |
---|
| 724 | s += mv.getAdditions(); |
---|
| 725 | } |
---|
| 726 | /* In any case, we count all nested operations in the accumulative |
---|
| 727 | counters: */ |
---|
| 728 | am += mv.getAccumulatedMultiplications(); |
---|
| 729 | as += mv.getAccumulatedAdditions(); |
---|
| 730 | /* adding sub-determinante times matrix entry times appropriate |
---|
| 731 | sign */ |
---|
| 732 | result += sign * mv.getResult() * getEntry(b, absoluteC); |
---|
| 733 | if (characteristic != 0) result = result % characteristic; |
---|
| 734 | s++; m++; as++; am++; /* This is for the last addition and |
---|
| 735 | multiplication. */ |
---|
| 736 | } |
---|
| 737 | sign = - sign; /* alternating the sign */ |
---|
| 738 | } |
---|
| 739 | } |
---|
| 740 | else |
---|
| 741 | { |
---|
| 742 | b = - b - 1; |
---|
| 743 | /* This means that the best line is the column with absolute (0-based) |
---|
| 744 | index b. |
---|
| 745 | Using Laplace, the sign of the contributing minors must be iterating; |
---|
| 746 | the initial sign depends on the relative index of b in |
---|
| 747 | minorColumnKey: */ |
---|
| 748 | int sign = (mk.getRelativeColumnIndex(b) % 2 == 0 ? 1 : -1); |
---|
| 749 | for (int r = 0; r < k; r++) /* This iterates over all involved rows. */ |
---|
| 750 | { |
---|
| 751 | int absoluteR = mk.getAbsoluteRowIndex(r); |
---|
| 752 | if (getEntry(absoluteR, b) != 0) /* Only then do we have to consider |
---|
| 753 | this sub-determinante. */ |
---|
| 754 | { |
---|
[5c44339] | 755 | hadNonZeroEntry = true; |
---|
[f0fd47] | 756 | /* Next MinorKey is mk with row absoluteR and column b omitted. */ |
---|
| 757 | MinorKey subMk = mk.getSubMinorKey(absoluteR, b); |
---|
| 758 | if (cch.hasKey(subMk)) |
---|
| 759 | { /* trying to find the result in the cache */ |
---|
| 760 | mv = cch.getValue(subMk); |
---|
| 761 | mv.incrementRetrievals(); /* once more, we made use of the cached |
---|
| 762 | value for key mk */ |
---|
| 763 | cch.put(subMk, mv); /* We need to do this with "put", as the |
---|
| 764 | (altered) number of retrievals may have an |
---|
| 765 | impact on the internal ordering among the |
---|
| 766 | cached entries. */ |
---|
| 767 | } |
---|
| 768 | else |
---|
| 769 | { |
---|
| 770 | mv = getMinorPrivateLaplace(k - 1, subMk, multipleMinors, cch, characteristic, iSB); /* recursive call */ |
---|
| 771 | /* As this minor was not in the cache, we count the additions and |
---|
| 772 | multiplications that we needed to do in the recursive call: */ |
---|
| 773 | m += mv.getMultiplications(); |
---|
| 774 | s += mv.getAdditions(); |
---|
| 775 | } |
---|
| 776 | /* In any case, we count all nested operations in the accumulative |
---|
| 777 | counters: */ |
---|
| 778 | am += mv.getAccumulatedMultiplications(); |
---|
| 779 | as += mv.getAccumulatedAdditions(); |
---|
| 780 | /* adding sub-determinante times matrix entry times appropriate |
---|
| 781 | sign: */ |
---|
| 782 | result += sign * mv.getResult() * getEntry(absoluteR, b); |
---|
| 783 | if (characteristic != 0) result = result % characteristic; |
---|
| 784 | s++; m++; as++; am++; /* This is for the last addition and |
---|
| 785 | multiplication. */ |
---|
| 786 | } |
---|
| 787 | sign = - sign; /* alternating the sign */ |
---|
| 788 | } |
---|
| 789 | } |
---|
| 790 | /* Let's cache the newly computed minor: */ |
---|
| 791 | int potentialRetrievals = NumberOfRetrievals(_containerRows, |
---|
| 792 | _containerColumns, |
---|
| 793 | _minorSize, k, |
---|
| 794 | multipleMinors); |
---|
[5c44339] | 795 | if (hadNonZeroEntry) |
---|
| 796 | { |
---|
| 797 | s--; as--; /* first addition was 0 + ..., so we do not count it */ |
---|
| 798 | } |
---|
[f0fd47] | 799 | if (s < 0) s = 0; /* may happen when all subminors are zero and no |
---|
| 800 | addition needs to be performed */ |
---|
| 801 | if (as < 0) as = 0; /* may happen when all subminors are zero and no |
---|
| 802 | addition needs to be performed */ |
---|
| 803 | if (iSB != 0) result = getReduction(result, iSB); |
---|
| 804 | IntMinorValue newMV(result, m, s, am, as, 1, potentialRetrievals); |
---|
| 805 | cch.put(mk, newMV); /* Here's the actual put inside the cache. */ |
---|
| 806 | return newMV; |
---|
| 807 | } |
---|
| 808 | } |
---|
| 809 | |
---|
| 810 | PolyMinorProcessor::PolyMinorProcessor () |
---|
| 811 | { |
---|
| 812 | _polyMatrix = 0; |
---|
| 813 | } |
---|
| 814 | |
---|
| 815 | poly PolyMinorProcessor::getEntry (const int rowIndex, |
---|
| 816 | const int columnIndex) const |
---|
| 817 | { |
---|
| 818 | return _polyMatrix[rowIndex * _columns + columnIndex]; |
---|
| 819 | } |
---|
| 820 | |
---|
| 821 | bool PolyMinorProcessor::isEntryZero (const int absoluteRowIndex, |
---|
| 822 | const int absoluteColumnIndex) const |
---|
| 823 | { |
---|
| 824 | return getEntry(absoluteRowIndex, absoluteColumnIndex) == NULL; |
---|
| 825 | } |
---|
| 826 | |
---|
| 827 | string PolyMinorProcessor::toString () const |
---|
| 828 | { |
---|
| 829 | char h[32]; |
---|
| 830 | string t = ""; |
---|
| 831 | string s = "PolyMinorProcessor:"; |
---|
| 832 | s += "\n matrix: "; |
---|
| 833 | sprintf(h, "%d", _rows); s += h; |
---|
| 834 | s += " x "; |
---|
| 835 | sprintf(h, "%d", _columns); s += h; |
---|
| 836 | int myIndexArray[500]; |
---|
| 837 | s += "\n considered submatrix has row indices: "; |
---|
| 838 | _container.getAbsoluteRowIndices(myIndexArray); |
---|
| 839 | for (int k = 0; k < _containerRows; k++) |
---|
| 840 | { |
---|
| 841 | if (k != 0) s += ", "; |
---|
| 842 | sprintf(h, "%d", myIndexArray[k]); s += h; |
---|
| 843 | } |
---|
| 844 | s += " (first row of matrix has index 0)"; |
---|
| 845 | s += "\n considered submatrix has column indices: "; |
---|
| 846 | _container.getAbsoluteColumnIndices(myIndexArray); |
---|
| 847 | for (int k = 0; k < _containerColumns; k++) |
---|
| 848 | { |
---|
| 849 | if (k != 0) s += ", "; |
---|
| 850 | sprintf(h, "%d", myIndexArray[k]); s += h; |
---|
| 851 | } |
---|
| 852 | s += " (first column of matrix has index 0)"; |
---|
| 853 | s += "\n size of considered minor(s): "; |
---|
| 854 | sprintf(h, "%d", _minorSize); s += h; |
---|
| 855 | s += "x"; |
---|
| 856 | s += h; |
---|
| 857 | return s; |
---|
| 858 | } |
---|
| 859 | |
---|
| 860 | PolyMinorProcessor::~PolyMinorProcessor() |
---|
| 861 | { |
---|
| 862 | /* free memory of _polyMatrix */ |
---|
| 863 | int n = _rows * _columns; |
---|
| 864 | for (int i = 0; i < n; i++) |
---|
| 865 | p_Delete(&_polyMatrix[i], currRing); |
---|
| 866 | delete [] _polyMatrix; _polyMatrix = 0; |
---|
| 867 | } |
---|
| 868 | |
---|
| 869 | void PolyMinorProcessor::defineMatrix (const int numberOfRows, |
---|
| 870 | const int numberOfColumns, |
---|
| 871 | const poly* polyMatrix) |
---|
| 872 | { |
---|
| 873 | /* free memory of _polyMatrix */ |
---|
| 874 | int n = _rows * _columns; |
---|
| 875 | for (int i = 0; i < n; i++) |
---|
| 876 | p_Delete(&_polyMatrix[i], currRing); |
---|
| 877 | delete [] _polyMatrix; _polyMatrix = 0; |
---|
| 878 | |
---|
| 879 | _rows = numberOfRows; |
---|
| 880 | _columns = numberOfColumns; |
---|
| 881 | n = _rows * _columns; |
---|
| 882 | |
---|
| 883 | /* allocate memory for new entries in _polyMatrix */ |
---|
| 884 | _polyMatrix = new poly[n]; |
---|
| 885 | |
---|
| 886 | /* copying values from one-dimensional method |
---|
| 887 | parameter "polyMatrix" */ |
---|
| 888 | for (int i = 0; i < n; i++) |
---|
| 889 | _polyMatrix[i] = pCopy(polyMatrix[i]); |
---|
| 890 | } |
---|
| 891 | |
---|
| 892 | PolyMinorValue PolyMinorProcessor::getMinor(const int dimension, |
---|
| 893 | const int* rowIndices, |
---|
| 894 | const int* columnIndices, |
---|
| 895 | Cache<MinorKey, PolyMinorValue>& c, |
---|
| 896 | const ideal& iSB) |
---|
| 897 | { |
---|
| 898 | defineSubMatrix(dimension, rowIndices, dimension, columnIndices); |
---|
| 899 | _minorSize = dimension; |
---|
| 900 | /* call a helper method which recursively computes the minor using the cache |
---|
| 901 | c: */ |
---|
| 902 | return getMinorPrivateLaplace(dimension, _container, false, c, iSB); |
---|
| 903 | } |
---|
| 904 | |
---|
| 905 | PolyMinorValue PolyMinorProcessor::getMinor(const int dimension, |
---|
| 906 | const int* rowIndices, |
---|
| 907 | const int* columnIndices, |
---|
| 908 | const char* algorithm, |
---|
| 909 | const ideal& iSB) |
---|
| 910 | { |
---|
| 911 | defineSubMatrix(dimension, rowIndices, dimension, columnIndices); |
---|
| 912 | _minorSize = dimension; |
---|
| 913 | /* call a helper method which computes the minor (without using a cache): */ |
---|
| 914 | if (strcmp(algorithm, "Laplace") == 0) |
---|
| 915 | return getMinorPrivateLaplace(_minorSize, _container, iSB); |
---|
| 916 | else if (strcmp(algorithm, "Bareiss") == 0) |
---|
| 917 | return getMinorPrivateBareiss(_minorSize, _container, iSB); |
---|
| 918 | else assume(false); |
---|
[089b98] | 919 | |
---|
| 920 | /* The following code is never reached and just there to make the |
---|
| 921 | compiler happy: */ |
---|
| 922 | return PolyMinorValue(); |
---|
[f0fd47] | 923 | } |
---|
| 924 | |
---|
[d2ea299] | 925 | PolyMinorValue PolyMinorProcessor::getNextMinor(const char* algorithm, |
---|
[f0fd47] | 926 | const ideal& iSB) |
---|
| 927 | { |
---|
[089b98] | 928 | /* call a helper method which computes the minor (without using a |
---|
| 929 | cache): */ |
---|
| 930 | if (strcmp(algorithm, "Laplace") == 0) |
---|
| 931 | return getMinorPrivateLaplace(_minorSize, _minor, iSB); |
---|
| 932 | else if (strcmp(algorithm, "Bareiss") == 0) |
---|
| 933 | return getMinorPrivateBareiss(_minorSize, _minor, iSB); |
---|
| 934 | else assume(false); |
---|
[a9c298] | 935 | |
---|
[089b98] | 936 | /* The following code is never reached and just there to make the |
---|
| 937 | compiler happy: */ |
---|
| 938 | return PolyMinorValue(); |
---|
[f0fd47] | 939 | } |
---|
| 940 | |
---|
| 941 | PolyMinorValue PolyMinorProcessor::getNextMinor(Cache<MinorKey, |
---|
| 942 | PolyMinorValue>& c, |
---|
| 943 | const ideal& iSB) |
---|
| 944 | { |
---|
| 945 | /* computation with cache */ |
---|
| 946 | return getMinorPrivateLaplace(_minorSize, _minor, true, c, iSB); |
---|
| 947 | } |
---|
| 948 | |
---|
| 949 | /* assumes that all entries in polyMatrix are already reduced w.r.t. iSB */ |
---|
| 950 | PolyMinorValue PolyMinorProcessor::getMinorPrivateLaplace(const int k, |
---|
| 951 | const MinorKey& mk, |
---|
| 952 | const ideal& iSB) |
---|
| 953 | { |
---|
[308a766] | 954 | assume(k > 0); /* k is the minor's dimension; the minor must be at least |
---|
[f0fd47] | 955 | 1x1 */ |
---|
| 956 | /* The method works by recursion, and using Lapace's Theorem along the |
---|
| 957 | row/column with the most zeros. */ |
---|
| 958 | if (k == 1) |
---|
| 959 | { |
---|
| 960 | PolyMinorValue pmv(getEntry(mk.getAbsoluteRowIndex(0), |
---|
| 961 | mk.getAbsoluteColumnIndex(0)), |
---|
| 962 | 0, 0, 0, 0, -1, -1); |
---|
| 963 | /* "-1" is to signal that any statistics about the number of retrievals |
---|
| 964 | does not make sense, as we do not use a cache. */ |
---|
| 965 | return pmv; |
---|
| 966 | } |
---|
| 967 | else |
---|
| 968 | { |
---|
| 969 | /* Here, the minor must be 2x2 or larger. */ |
---|
| 970 | int b = getBestLine(k, mk); /* row or column with most |
---|
| 971 | zeros */ |
---|
| 972 | poly result = NULL; /* This will contain the |
---|
| 973 | value of the minor. */ |
---|
| 974 | int s = 0; int m = 0; int as = 0; int am = 0; /* counters for additions |
---|
| 975 | and multiplications, |
---|
| 976 | ..."a*" for accumulated |
---|
| 977 | operation counters */ |
---|
[5c44339] | 978 | bool hadNonZeroEntry = false; |
---|
[f0fd47] | 979 | if (b >= 0) |
---|
| 980 | { |
---|
| 981 | /* This means that the best line is the row with absolute (0-based) |
---|
| 982 | index b. |
---|
| 983 | Using Laplace, the sign of the contributing minors must be iterating; |
---|
| 984 | the initial sign depends on the relative index of b in minorRowKey: */ |
---|
| 985 | int sign = (mk.getRelativeRowIndex(b) % 2 == 0 ? 1 : -1); |
---|
| 986 | poly signPoly = NULL; |
---|
| 987 | for (int c = 0; c < k; c++) /* This iterates over all involved columns. */ |
---|
| 988 | { |
---|
| 989 | int absoluteC = mk.getAbsoluteColumnIndex(c); |
---|
| 990 | if (!isEntryZero(b, absoluteC)) /* Only then do we have to consider |
---|
| 991 | this sub-determinante. */ |
---|
| 992 | { |
---|
[5c44339] | 993 | hadNonZeroEntry = true; |
---|
[f0fd47] | 994 | /* Next MinorKey is mk with row b and column absoluteC omitted. */ |
---|
| 995 | MinorKey subMk = mk.getSubMinorKey(b, absoluteC); |
---|
| 996 | /* recursive call: */ |
---|
| 997 | PolyMinorValue mv = getMinorPrivateLaplace(k - 1, subMk, iSB); |
---|
| 998 | m += mv.getMultiplications(); |
---|
| 999 | s += mv.getAdditions(); |
---|
| 1000 | am += mv.getAccumulatedMultiplications(); |
---|
| 1001 | as += mv.getAccumulatedAdditions(); |
---|
| 1002 | pDelete(&signPoly); |
---|
| 1003 | signPoly = pISet(sign); |
---|
| 1004 | poly temp = pp_Mult_qq(mv.getResult(), getEntry(b, absoluteC), |
---|
| 1005 | currRing); |
---|
| 1006 | temp = p_Mult_q(signPoly, temp, currRing); |
---|
| 1007 | result = p_Add_q(result, temp, currRing); |
---|
[5c44339] | 1008 | #ifdef COUNT_AND_PRINT_OPERATIONS |
---|
| 1009 | multsPoly++; |
---|
| 1010 | addsPoly++; |
---|
| 1011 | multsMon += pLength(mv.getResult()) * pLength(getEntry(b, absoluteC)); |
---|
| 1012 | #endif |
---|
[f0fd47] | 1013 | signPoly = NULL; |
---|
| 1014 | s++; m++; as++, am++; /* This is for the addition and multiplication |
---|
| 1015 | in the previous lines of code. */ |
---|
| 1016 | } |
---|
| 1017 | sign = - sign; /* alternating the sign */ |
---|
| 1018 | } |
---|
| 1019 | } |
---|
| 1020 | else |
---|
| 1021 | { |
---|
| 1022 | b = - b - 1; |
---|
| 1023 | /* This means that the best line is the column with absolute (0-based) |
---|
| 1024 | index b. |
---|
| 1025 | Using Laplace, the sign of the contributing minors must be iterating; |
---|
| 1026 | the initial sign depends on the relative index of b in |
---|
| 1027 | minorColumnKey: */ |
---|
| 1028 | int sign = (mk.getRelativeColumnIndex(b) % 2 == 0 ? 1 : -1); |
---|
| 1029 | poly signPoly = NULL; |
---|
| 1030 | for (int r = 0; r < k; r++) /* This iterates over all involved rows. */ |
---|
| 1031 | { |
---|
| 1032 | int absoluteR = mk.getAbsoluteRowIndex(r); |
---|
| 1033 | if (!isEntryZero(absoluteR, b)) /* Only then do we have to consider |
---|
| 1034 | this sub-determinante. */ |
---|
| 1035 | { |
---|
[5c44339] | 1036 | hadNonZeroEntry = true; |
---|
[f0fd47] | 1037 | /* This is mk with row absoluteR and column b omitted. */ |
---|
| 1038 | MinorKey subMk = mk.getSubMinorKey(absoluteR, b); |
---|
| 1039 | /* recursive call: */ |
---|
| 1040 | PolyMinorValue mv = getMinorPrivateLaplace(k - 1, subMk, iSB); |
---|
| 1041 | m += mv.getMultiplications(); |
---|
| 1042 | s += mv.getAdditions(); |
---|
| 1043 | am += mv.getAccumulatedMultiplications(); |
---|
| 1044 | as += mv.getAccumulatedAdditions(); |
---|
| 1045 | pDelete(&signPoly); |
---|
| 1046 | signPoly = pISet(sign); |
---|
| 1047 | poly temp = pp_Mult_qq(mv.getResult(), getEntry(absoluteR, b), |
---|
| 1048 | currRing); |
---|
| 1049 | temp = p_Mult_q(signPoly, temp, currRing); |
---|
| 1050 | result = p_Add_q(result, temp, currRing); |
---|
[5c44339] | 1051 | #ifdef COUNT_AND_PRINT_OPERATIONS |
---|
| 1052 | multsPoly++; |
---|
| 1053 | addsPoly++; |
---|
| 1054 | multsMon += pLength(mv.getResult()) * pLength(getEntry(absoluteR, b)); |
---|
| 1055 | #endif |
---|
[f0fd47] | 1056 | signPoly = NULL; |
---|
| 1057 | s++; m++; as++, am++; /* This is for the addition and multiplication |
---|
| 1058 | in the previous lines of code. */ |
---|
| 1059 | } |
---|
| 1060 | sign = - sign; /* alternating the sign */ |
---|
| 1061 | } |
---|
| 1062 | } |
---|
[5c44339] | 1063 | if (hadNonZeroEntry) |
---|
| 1064 | { |
---|
| 1065 | s--; as--; /* first addition was 0 + ..., so we do not count it */ |
---|
| 1066 | #ifdef COUNT_AND_PRINT_OPERATIONS |
---|
| 1067 | addsPoly--; |
---|
| 1068 | #endif |
---|
| 1069 | } |
---|
[f0fd47] | 1070 | if (s < 0) s = 0; /* may happen when all subminors are zero and no |
---|
| 1071 | addition needs to be performed */ |
---|
| 1072 | if (as < 0) as = 0; /* may happen when all subminors are zero and no |
---|
| 1073 | addition needs to be performed */ |
---|
| 1074 | if (iSB != 0) result = kNF(iSB, currRing->qideal, result); |
---|
| 1075 | PolyMinorValue newMV(result, m, s, am, as, -1, -1); |
---|
| 1076 | /* "-1" is to signal that any statistics about the number of retrievals |
---|
| 1077 | does not make sense, as we do not use a cache. */ |
---|
| 1078 | pDelete(&result); |
---|
| 1079 | return newMV; |
---|
| 1080 | } |
---|
| 1081 | } |
---|
| 1082 | |
---|
| 1083 | /* assumes that all entries in polyMatrix are already reduced w.r.t. iSB */ |
---|
| 1084 | PolyMinorValue PolyMinorProcessor::getMinorPrivateLaplace( |
---|
| 1085 | const int k, |
---|
| 1086 | const MinorKey& mk, |
---|
| 1087 | const bool multipleMinors, |
---|
| 1088 | Cache<MinorKey, PolyMinorValue>& cch, |
---|
| 1089 | const ideal& iSB) |
---|
| 1090 | { |
---|
[308a766] | 1091 | assume(k > 0); /* k is the minor's dimension; the minor must be at least |
---|
[f0fd47] | 1092 | 1x1 */ |
---|
| 1093 | /* The method works by recursion, and using Lapace's Theorem along |
---|
| 1094 | the row/column with the most zeros. */ |
---|
| 1095 | if (k == 1) |
---|
| 1096 | { |
---|
| 1097 | PolyMinorValue pmv(getEntry(mk.getAbsoluteRowIndex(0), |
---|
| 1098 | mk.getAbsoluteColumnIndex(0)), |
---|
| 1099 | 0, 0, 0, 0, -1, -1); |
---|
| 1100 | /* we set "-1" as, for k == 1, we do not have any cache retrievals */ |
---|
| 1101 | return pmv; |
---|
| 1102 | } |
---|
| 1103 | else |
---|
| 1104 | { |
---|
| 1105 | int b = getBestLine(k, mk); /* row or column with most |
---|
| 1106 | zeros */ |
---|
| 1107 | poly result = NULL; /* This will contain the |
---|
| 1108 | value of the minor. */ |
---|
| 1109 | int s = 0; int m = 0; int as = 0; int am = 0; /* counters for additions |
---|
| 1110 | and multiplications, |
---|
| 1111 | ..."a*" for accumulated |
---|
| 1112 | operation counters */ |
---|
[5c44339] | 1113 | bool hadNonZeroEntry = false; |
---|
[f0fd47] | 1114 | if (b >= 0) |
---|
| 1115 | { |
---|
| 1116 | /* This means that the best line is the row with absolute (0-based) |
---|
| 1117 | index b. |
---|
| 1118 | Using Laplace, the sign of the contributing minors must be iterating; |
---|
| 1119 | the initial sign depends on the relative index of b in |
---|
| 1120 | minorRowKey: */ |
---|
| 1121 | int sign = (mk.getRelativeRowIndex(b) % 2 == 0 ? 1 : -1); |
---|
| 1122 | poly signPoly = NULL; |
---|
| 1123 | for (int c = 0; c < k; c++) /* This iterates over all involved columns. */ |
---|
| 1124 | { |
---|
| 1125 | int absoluteC = mk.getAbsoluteColumnIndex(c); |
---|
| 1126 | if (!isEntryZero(b, absoluteC)) /* Only then do we have to consider |
---|
| 1127 | this sub-determinante. */ |
---|
| 1128 | { |
---|
[5c44339] | 1129 | hadNonZeroEntry = true; |
---|
[f0fd47] | 1130 | PolyMinorValue mv; /* for storing all intermediate minors */ |
---|
| 1131 | /* Next MinorKey is mk with row b and column absoluteC omitted. */ |
---|
| 1132 | MinorKey subMk = mk.getSubMinorKey(b, absoluteC); |
---|
| 1133 | if (cch.hasKey(subMk)) |
---|
| 1134 | { /* trying to find the result in the cache */ |
---|
| 1135 | mv = cch.getValue(subMk); |
---|
| 1136 | mv.incrementRetrievals(); /* once more, we made use of the cached |
---|
| 1137 | value for key mk */ |
---|
| 1138 | cch.put(subMk, mv); /* We need to do this with "put", as the |
---|
| 1139 | (altered) number of retrievals may have an |
---|
| 1140 | impact on the internal ordering among cache |
---|
| 1141 | entries. */ |
---|
| 1142 | } |
---|
| 1143 | else |
---|
| 1144 | { |
---|
| 1145 | /* recursive call: */ |
---|
| 1146 | mv = getMinorPrivateLaplace(k - 1, subMk, multipleMinors, cch, |
---|
| 1147 | iSB); |
---|
| 1148 | /* As this minor was not in the cache, we count the additions and |
---|
| 1149 | multiplications that we needed to do in the recursive call: */ |
---|
| 1150 | m += mv.getMultiplications(); |
---|
| 1151 | s += mv.getAdditions(); |
---|
| 1152 | } |
---|
| 1153 | /* In any case, we count all nested operations in the accumulative |
---|
| 1154 | counters: */ |
---|
| 1155 | am += mv.getAccumulatedMultiplications(); |
---|
| 1156 | as += mv.getAccumulatedAdditions(); |
---|
| 1157 | pDelete(&signPoly); |
---|
| 1158 | signPoly = pISet(sign); |
---|
| 1159 | poly temp = pp_Mult_qq(mv.getResult(), getEntry(b, absoluteC), |
---|
| 1160 | currRing); |
---|
| 1161 | temp = p_Mult_q(signPoly, temp, currRing); |
---|
| 1162 | result = p_Add_q(result, temp, currRing); |
---|
[5c44339] | 1163 | #ifdef COUNT_AND_PRINT_OPERATIONS |
---|
| 1164 | multsPoly++; |
---|
| 1165 | addsPoly++; |
---|
| 1166 | multsMon += pLength(mv.getResult()) * pLength(getEntry(b, absoluteC)); |
---|
| 1167 | #endif |
---|
[f0fd47] | 1168 | signPoly = NULL; |
---|
| 1169 | s++; m++; as++; am++; /* This is for the addition and multiplication |
---|
| 1170 | in the previous lines of code. */ |
---|
| 1171 | } |
---|
| 1172 | sign = - sign; /* alternating the sign */ |
---|
| 1173 | } |
---|
| 1174 | } |
---|
| 1175 | else |
---|
| 1176 | { |
---|
| 1177 | b = - b - 1; |
---|
| 1178 | /* This means that the best line is the column with absolute (0-based) |
---|
| 1179 | index b. |
---|
| 1180 | Using Laplace, the sign of the contributing minors must be iterating; |
---|
| 1181 | the initial sign depends on the relative index of b in |
---|
| 1182 | minorColumnKey: */ |
---|
| 1183 | int sign = (mk.getRelativeColumnIndex(b) % 2 == 0 ? 1 : -1); |
---|
| 1184 | poly signPoly = NULL; |
---|
| 1185 | for (int r = 0; r < k; r++) /* This iterates over all involved rows. */ |
---|
| 1186 | { |
---|
| 1187 | int absoluteR = mk.getAbsoluteRowIndex(r); |
---|
| 1188 | if (!isEntryZero(absoluteR, b)) /* Only then do we have to consider |
---|
| 1189 | this sub-determinante. */ |
---|
| 1190 | { |
---|
[5c44339] | 1191 | hadNonZeroEntry = true; |
---|
[f0fd47] | 1192 | PolyMinorValue mv; /* for storing all intermediate minors */ |
---|
| 1193 | /* Next MinorKey is mk with row absoluteR and column b omitted. */ |
---|
| 1194 | MinorKey subMk = mk.getSubMinorKey(absoluteR, b); |
---|
| 1195 | if (cch.hasKey(subMk)) |
---|
| 1196 | { /* trying to find the result in the cache */ |
---|
| 1197 | mv = cch.getValue(subMk); |
---|
| 1198 | mv.incrementRetrievals(); /* once more, we made use of the cached |
---|
| 1199 | value for key mk */ |
---|
| 1200 | cch.put(subMk, mv); /* We need to do this with "put", as the |
---|
| 1201 | (altered) number of retrievals may have an |
---|
| 1202 | impact on the internal ordering among the |
---|
| 1203 | cached entries. */ |
---|
| 1204 | } |
---|
| 1205 | else |
---|
| 1206 | { |
---|
| 1207 | mv = getMinorPrivateLaplace(k - 1, subMk, multipleMinors, cch, |
---|
| 1208 | iSB); /* recursive call */ |
---|
| 1209 | /* As this minor was not in the cache, we count the additions and |
---|
| 1210 | multiplications that we needed to do in the recursive call: */ |
---|
| 1211 | m += mv.getMultiplications(); |
---|
| 1212 | s += mv.getAdditions(); |
---|
| 1213 | } |
---|
| 1214 | /* In any case, we count all nested operations in the accumulative |
---|
| 1215 | counters: */ |
---|
| 1216 | am += mv.getAccumulatedMultiplications(); |
---|
| 1217 | as += mv.getAccumulatedAdditions(); |
---|
| 1218 | pDelete(&signPoly); |
---|
| 1219 | signPoly = pISet(sign); |
---|
| 1220 | poly temp = pp_Mult_qq(mv.getResult(), getEntry(absoluteR, b), |
---|
| 1221 | currRing); |
---|
| 1222 | temp = p_Mult_q(signPoly, temp, currRing); |
---|
| 1223 | result = p_Add_q(result, temp, currRing); |
---|
[5c44339] | 1224 | #ifdef COUNT_AND_PRINT_OPERATIONS |
---|
| 1225 | multsPoly++; |
---|
| 1226 | addsPoly++; |
---|
| 1227 | multsMon += pLength(mv.getResult()) * pLength(getEntry(absoluteR, b)); |
---|
| 1228 | #endif |
---|
[f0fd47] | 1229 | signPoly = NULL; |
---|
| 1230 | s++; m++; as++; am++; /* This is for the addition and multiplication |
---|
| 1231 | in the previous lines of code. */ |
---|
| 1232 | } |
---|
| 1233 | sign = - sign; /* alternating the sign */ |
---|
| 1234 | } |
---|
| 1235 | } |
---|
| 1236 | /* Let's cache the newly computed minor: */ |
---|
| 1237 | int potentialRetrievals = NumberOfRetrievals(_containerRows, |
---|
| 1238 | _containerColumns, |
---|
| 1239 | _minorSize, |
---|
| 1240 | k, |
---|
| 1241 | multipleMinors); |
---|
[5c44339] | 1242 | if (hadNonZeroEntry) |
---|
| 1243 | { |
---|
| 1244 | s--; as--; /* first addition was 0 + ..., so we do not count it */ |
---|
| 1245 | #ifdef COUNT_AND_PRINT_OPERATIONS |
---|
| 1246 | addsPoly--; |
---|
| 1247 | #endif |
---|
| 1248 | } |
---|
[f0fd47] | 1249 | if (s < 0) s = 0; /* may happen when all subminors are zero and no |
---|
| 1250 | addition needs to be performed */ |
---|
| 1251 | if (as < 0) as = 0; /* may happen when all subminors are zero and no |
---|
| 1252 | addition needs to be performed */ |
---|
| 1253 | if (iSB != 0) result = kNF(iSB, currRing->qideal, result); |
---|
| 1254 | PolyMinorValue newMV(result, m, s, am, as, 1, potentialRetrievals); |
---|
| 1255 | pDelete(&result); result = NULL; |
---|
| 1256 | cch.put(mk, newMV); /* Here's the actual put inside the cache. */ |
---|
| 1257 | return newMV; |
---|
| 1258 | } |
---|
| 1259 | } |
---|
| 1260 | |
---|
| 1261 | /* This can only be used in the case of coefficients coming from a field |
---|
| 1262 | or at least an integral domain. */ |
---|
| 1263 | void addOperationBucket(poly& f1, poly& f2, kBucket_pt& bucket) |
---|
| 1264 | { |
---|
| 1265 | /* fills all terms of f1 * f2 into the bucket */ |
---|
| 1266 | poly a = f1; poly b = f2; |
---|
| 1267 | int aLen = pLength(a); int bLen = pLength(b); |
---|
| 1268 | if (aLen > bLen) |
---|
| 1269 | { |
---|
| 1270 | b = f1; a = f2; bLen = aLen; |
---|
| 1271 | } |
---|
| 1272 | pNormalize(b); |
---|
| 1273 | |
---|
| 1274 | while (a != NULL) |
---|
| 1275 | { |
---|
| 1276 | /* The next line actually uses only LT(a): */ |
---|
| 1277 | kBucket_Plus_mm_Mult_pp(bucket, a, b, bLen); |
---|
| 1278 | a = pNext(a); |
---|
| 1279 | } |
---|
| 1280 | } |
---|
| 1281 | |
---|
| 1282 | /* computes the polynomial (p1 * p2 - p3 * p4) and puts result into p1; |
---|
| 1283 | the method destroys the old value of p1; |
---|
| 1284 | p2, p3, and p4 may be pNormalize-d but must, apart from that, |
---|
| 1285 | not be changed; |
---|
[5c44339] | 1286 | This can only be used in the case of coefficients coming from a field |
---|
| 1287 | or at least an integral domain. */ |
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[f0fd47] | 1288 | void elimOperationBucketNoDiv(poly &p1, poly &p2, poly &p3, poly &p4) |
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| 1289 | { |
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[5c44339] | 1290 | #ifdef COUNT_AND_PRINT_OPERATIONS |
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| 1291 | if ((pLength(p1) != 0) && (pLength(p2) != 0)) |
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| 1292 | { |
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| 1293 | multsPoly++; |
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| 1294 | multsMon += pLength(p1) * pLength(p2); |
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| 1295 | } |
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| 1296 | if ((pLength(p3) != 0) && (pLength(p4) != 0)) |
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| 1297 | { |
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| 1298 | multsPoly++; |
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| 1299 | multsMon += pLength(p3) * pLength(p4); |
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| 1300 | } |
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| 1301 | if ((pLength(p1) != 0) && (pLength(p2) != 0) && |
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| 1302 | (pLength(p3) != 0) && (pLength(p4) != 0)) |
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| 1303 | addsPoly++; |
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| 1304 | #endif |
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[3d9165] | 1305 | kBucket_pt myBucket = kBucketCreate(currRing); |
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[f0fd47] | 1306 | addOperationBucket(p1, p2, myBucket); |
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| 1307 | poly p3Neg = pNeg(pCopy(p3)); |
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| 1308 | addOperationBucket(p3Neg, p4, myBucket); |
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| 1309 | pDelete(&p3Neg); |
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| 1310 | pDelete(&p1); |
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| 1311 | p1 = kBucketClear(myBucket); |
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| 1312 | kBucketDestroy(&myBucket); |
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| 1313 | } |
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| 1314 | |
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| 1315 | /* computes the polynomial (p1 * p2 - p3 * p4) / p5 and puts result into p1; |
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| 1316 | the method destroys the old value of p1; |
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| 1317 | p2, p3, p4, and p5 may be pNormalize-d but must, apart from that, |
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| 1318 | not be changed; |
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| 1319 | c5 is assumed to be the leading coefficient of p5; |
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| 1320 | p5Len is assumed to be the length of p5; |
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[5c44339] | 1321 | This can only be used in the case of coefficients coming from a field |
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| 1322 | or at least an integral domain. */ |
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[f0fd47] | 1323 | void elimOperationBucket(poly &p1, poly &p2, poly &p3, poly &p4, poly &p5, |
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| 1324 | number &c5, int p5Len) |
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| 1325 | { |
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[5c44339] | 1326 | #ifdef COUNT_AND_PRINT_OPERATIONS |
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| 1327 | if ((pLength(p1) != 0) && (pLength(p2) != 0)) |
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| 1328 | { |
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| 1329 | multsPoly++; |
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| 1330 | multsMon += pLength(p1) * pLength(p2); |
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| 1331 | } |
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| 1332 | if ((pLength(p3) != 0) && (pLength(p4) != 0)) |
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| 1333 | { |
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| 1334 | multsPoly++; |
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| 1335 | multsMon += pLength(p3) * pLength(p4); |
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| 1336 | } |
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| 1337 | if ((pLength(p1) != 0) && (pLength(p2) != 0) && |
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| 1338 | (pLength(p3) != 0) && (pLength(p4) != 0)) |
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| 1339 | addsPoly++; |
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| 1340 | #endif |
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[3d9165] | 1341 | kBucket_pt myBucket = kBucketCreate(currRing); |
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[f0fd47] | 1342 | addOperationBucket(p1, p2, myBucket); |
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| 1343 | poly p3Neg = pNeg(pCopy(p3)); |
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| 1344 | addOperationBucket(p3Neg, p4, myBucket); |
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| 1345 | pDelete(&p3Neg); |
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| 1346 | |
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| 1347 | /* Now, myBucket contains all terms of p1 * p2 - p3 * p4. |
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| 1348 | Now we need to perform the polynomial division myBucket / p5 |
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| 1349 | which is known to work without remainder: */ |
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| 1350 | pDelete(&p1); poly helperPoly = NULL; |
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| 1351 | |
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| 1352 | poly bucketLm = pCopy(kBucketGetLm(myBucket)); |
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| 1353 | while (bucketLm != NULL) |
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| 1354 | { |
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| 1355 | /* divide bucketLm by the leading term of p5 and put result into bucketLm; |
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| 1356 | we start with the coefficients; |
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| 1357 | note that bucketLm will always represent a term */ |
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| 1358 | number coeff = nDiv(pGetCoeff(bucketLm), c5); |
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| 1359 | nNormalize(coeff); |
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| 1360 | pSetCoeff(bucketLm, coeff); |
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| 1361 | /* subtract exponent vector of p5 from that of quotient; modifies |
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| 1362 | quotient */ |
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| 1363 | p_ExpVectorSub(bucketLm, p5, currRing); |
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[5c44339] | 1364 | #ifdef COUNT_AND_PRINT_OPERATIONS |
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| 1365 | divsMon++; |
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| 1366 | multsMonForDiv += p5Len; |
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| 1367 | multsMon += p5Len; |
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| 1368 | savedMultsMFD++; |
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| 1369 | multsPoly++; |
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| 1370 | multsPolyForDiv++; |
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| 1371 | addsPoly++; |
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| 1372 | addsPolyForDiv++; |
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| 1373 | #endif |
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[f0fd47] | 1374 | kBucket_Minus_m_Mult_p(myBucket, bucketLm, p5, &p5Len); |
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| 1375 | /* The following lines make bucketLm the new leading term of p1, |
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| 1376 | i.e., put bucketLm in front of everything which is already in p1. |
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| 1377 | Thus, after the while loop, we need to revert p1. */ |
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| 1378 | helperPoly = bucketLm; |
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| 1379 | helperPoly->next = p1; |
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| 1380 | p1 = helperPoly; |
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| 1381 | |
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| 1382 | bucketLm = pCopy(kBucketGetLm(myBucket)); |
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| 1383 | } |
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| 1384 | p1 = pReverse(p1); |
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| 1385 | kBucketDestroy(&myBucket); |
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| 1386 | } |
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| 1387 | |
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| 1388 | /* assumes that all entries in polyMatrix are already reduced w.r.t. iSB |
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| 1389 | This can only be used in the case of coefficients coming from a field!!! */ |
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| 1390 | PolyMinorValue PolyMinorProcessor::getMinorPrivateBareiss(const int k, |
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| 1391 | const MinorKey& mk, |
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| 1392 | const ideal& iSB) |
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| 1393 | { |
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[308a766] | 1394 | assume(k > 0); /* k is the minor's dimension; the minor must be at least |
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[f0fd47] | 1395 | 1x1 */ |
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[5f4463] | 1396 | int *theRows=new int[k]; mk.getAbsoluteRowIndices(theRows); |
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| 1397 | int *theColumns=new int[k]; mk.getAbsoluteColumnIndices(theColumns); |
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[f0fd47] | 1398 | if (k == 1) |
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[5f4463] | 1399 | { |
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| 1400 | PolyMinorValue tmp=PolyMinorValue(getEntry(theRows[0], theColumns[0]), |
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[f0fd47] | 1401 | 0, 0, 0, 0, -1, -1); |
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[5f4463] | 1402 | delete[] theColumns; |
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| 1403 | delete[] theRows; |
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| 1404 | return tmp; |
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| 1405 | } |
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[f0fd47] | 1406 | else /* k > 0 */ |
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| 1407 | { |
---|
| 1408 | /* the matrix to perform Bareiss with */ |
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| 1409 | poly* tempMatrix = (poly*)omAlloc(k * k * sizeof(poly)); |
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| 1410 | /* copy correct set of entries from _polyMatrix to tempMatrix */ |
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| 1411 | int i = 0; |
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| 1412 | for (int r = 0; r < k; r++) |
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| 1413 | for (int c = 0; c < k; c++) |
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| 1414 | tempMatrix[i++] = pCopy(getEntry(theRows[r], theColumns[c])); |
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| 1415 | |
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| 1416 | /* Bareiss algorithm operating on tempMatrix which is at least 2x2 */ |
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| 1417 | int sign = 1; /* This will store the correct sign resulting from |
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| 1418 | permuting the rows of tempMatrix. */ |
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[5f4463] | 1419 | int *rowPermutation=new int[k]; /* This is for storing the permutation of rows |
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[f0fd47] | 1420 | resulting from searching for a non-zero pivot |
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| 1421 | element. */ |
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| 1422 | for (int i = 0; i < k; i++) rowPermutation[i] = i; |
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| 1423 | poly divisor = NULL; |
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| 1424 | int divisorLength = 0; |
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| 1425 | number divisorLC; |
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| 1426 | for (int r = 0; r <= k - 2; r++) |
---|
| 1427 | { |
---|
| 1428 | /* look for a non-zero entry in column r, rows = r .. (k - 1) |
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| 1429 | s.t. the polynomial has least complexity: */ |
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| 1430 | int minComplexity = -1; int complexity = 0; int bestRow = -1; |
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| 1431 | poly pp = NULL; |
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| 1432 | for (int i = r; i < k; i++) |
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| 1433 | { |
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| 1434 | pp = tempMatrix[rowPermutation[i] * k + r]; |
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| 1435 | if (pp != NULL) |
---|
| 1436 | { |
---|
| 1437 | if (minComplexity == -1) |
---|
| 1438 | { |
---|
| 1439 | minComplexity = pSize(pp); |
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| 1440 | bestRow = i; |
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| 1441 | } |
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| 1442 | else |
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| 1443 | { |
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| 1444 | complexity = 0; |
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| 1445 | while ((pp != NULL) && (complexity < minComplexity)) |
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[a9c298] | 1446 | { |
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[f0fd47] | 1447 | complexity += nSize(pGetCoeff(pp)); pp = pNext(pp); |
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| 1448 | } |
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| 1449 | if (complexity < minComplexity) |
---|
| 1450 | { |
---|
| 1451 | minComplexity = complexity; |
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| 1452 | bestRow = i; |
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| 1453 | } |
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| 1454 | } |
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| 1455 | if (minComplexity <= 1) break; /* terminate the search */ |
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| 1456 | } |
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| 1457 | } |
---|
| 1458 | if (bestRow == -1) |
---|
| 1459 | { |
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| 1460 | /* There is no non-zero entry; hence the minor is zero. */ |
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| 1461 | for (int i = 0; i < k * k; i++) pDelete(&tempMatrix[i]); |
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| 1462 | return PolyMinorValue(NULL, 0, 0, 0, 0, -1, -1); |
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| 1463 | } |
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| 1464 | pNormalize(tempMatrix[rowPermutation[bestRow] * k + r]); |
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| 1465 | if (bestRow != r) |
---|
| 1466 | { |
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| 1467 | /* We swap the rows with indices r and i: */ |
---|
| 1468 | int j = rowPermutation[bestRow]; |
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| 1469 | rowPermutation[bestRow] = rowPermutation[r]; |
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| 1470 | rowPermutation[r] = j; |
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| 1471 | /* Now we know that tempMatrix[rowPermutation[r] * k + r] is not zero. |
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| 1472 | But carefull; we have to negate the sign, as there is always an odd |
---|
| 1473 | number of row transpositions to swap two given rows of a matrix. */ |
---|
| 1474 | sign = -sign; |
---|
| 1475 | } |
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[5c44339] | 1476 | #if (defined COUNT_AND_PRINT_OPERATIONS) && (COUNT_AND_PRINT_OPERATIONS > 2) |
---|
| 1477 | poly w = NULL; int wl = 0; |
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| 1478 | printf("matrix after %d steps:\n", r); |
---|
| 1479 | for (int u = 0; u < k; u++) |
---|
| 1480 | { |
---|
| 1481 | for (int v = 0; v < k; v++) |
---|
| 1482 | { |
---|
| 1483 | if ((v < r) && (u > v)) |
---|
| 1484 | wl = 0; |
---|
| 1485 | else |
---|
| 1486 | { |
---|
| 1487 | w = tempMatrix[rowPermutation[u] * k + v]; |
---|
| 1488 | wl = pLength(w); |
---|
| 1489 | } |
---|
| 1490 | printf("%5d ", wl); |
---|
| 1491 | } |
---|
| 1492 | printf("\n"); |
---|
| 1493 | } |
---|
| 1494 | printCounters ("", false); |
---|
| 1495 | #endif |
---|
[f0fd47] | 1496 | if (r != 0) |
---|
| 1497 | { |
---|
| 1498 | divisor = tempMatrix[rowPermutation[r - 1] * k + r - 1]; |
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| 1499 | pNormalize(divisor); |
---|
| 1500 | divisorLength = pLength(divisor); |
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| 1501 | divisorLC = pGetCoeff(divisor); |
---|
| 1502 | } |
---|
| 1503 | for (int rr = r + 1; rr < k; rr++) |
---|
| 1504 | for (int cc = r + 1; cc < k; cc++) |
---|
| 1505 | { |
---|
| 1506 | if (r == 0) |
---|
| 1507 | elimOperationBucketNoDiv(tempMatrix[rowPermutation[rr] * k + cc], |
---|
| 1508 | tempMatrix[rowPermutation[r] * k + r], |
---|
| 1509 | tempMatrix[rowPermutation[r] * k + cc], |
---|
| 1510 | tempMatrix[rowPermutation[rr] * k + r]); |
---|
| 1511 | else |
---|
| 1512 | elimOperationBucket(tempMatrix[rowPermutation[rr] * k + cc], |
---|
| 1513 | tempMatrix[rowPermutation[r] * k + r], |
---|
| 1514 | tempMatrix[rowPermutation[r] * k + cc], |
---|
| 1515 | tempMatrix[rowPermutation[rr] * k + r], |
---|
| 1516 | divisor, divisorLC, divisorLength); |
---|
| 1517 | } |
---|
| 1518 | } |
---|
[5c44339] | 1519 | #if (defined COUNT_AND_PRINT_OPERATIONS) && (COUNT_AND_PRINT_OPERATIONS > 2) |
---|
| 1520 | poly w = NULL; int wl = 0; |
---|
| 1521 | printf("matrix after %d steps:\n", k - 1); |
---|
| 1522 | for (int u = 0; u < k; u++) |
---|
| 1523 | { |
---|
| 1524 | for (int v = 0; v < k; v++) |
---|
| 1525 | { |
---|
| 1526 | if ((v < k - 1) && (u > v)) |
---|
| 1527 | wl = 0; |
---|
| 1528 | else |
---|
| 1529 | { |
---|
| 1530 | w = tempMatrix[rowPermutation[u] * k + v]; |
---|
| 1531 | wl = pLength(w); |
---|
| 1532 | } |
---|
| 1533 | printf("%5d ", wl); |
---|
| 1534 | } |
---|
| 1535 | printf("\n"); |
---|
| 1536 | } |
---|
| 1537 | #endif |
---|
[f0fd47] | 1538 | poly result = tempMatrix[rowPermutation[k - 1] * k + k - 1]; |
---|
| 1539 | if (sign == -1) result = pNeg(result); |
---|
| 1540 | if (iSB != 0) result = kNF(iSB, currRing->qideal, result); |
---|
| 1541 | PolyMinorValue mv(result, 0, 0, 0, 0, -1, -1); |
---|
| 1542 | for (int i = 0; i < k * k; i++) pDelete(&tempMatrix[i]); |
---|
| 1543 | omFreeSize(tempMatrix, k * k * sizeof(poly)); |
---|
[5f4463] | 1544 | delete[] rowPermutation; |
---|
| 1545 | delete[] theColumns; |
---|
| 1546 | delete[] theRows; |
---|
[f0fd47] | 1547 | return mv; |
---|
| 1548 | } |
---|
| 1549 | } |
---|
| 1550 | |
---|