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|---|---|---|---|
| 1 | #include "khruev_a_gauss_jordan/seq/include/ops_seq.hpp" | ||
| 2 | |||
| 3 | #include <algorithm> | ||
| 4 | #include <cmath> | ||
| 5 | #include <cstddef> | ||
| 6 | #include <utility> | ||
| 7 | #include <vector> | ||
| 8 | |||
| 9 | #include "khruev_a_gauss_jordan/common/include/common.hpp" | ||
| 10 | |||
| 11 | namespace khruev_a_gauss_jordan { | ||
| 12 | |||
| 13 | namespace { | ||
| 14 | |||
| 15 | constexpr double kTol = 1e-10; | ||
| 16 | |||
| 17 | bool NearZero(double x) { | ||
| 18 |
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672 | return std::fabs(x) < kTol; |
| 19 | } | ||
| 20 | |||
| 21 | int SelectPivot(const std::vector<std::vector<double>> &a, int start_row, int col) { | ||
| 22 | int best = -1; | ||
| 23 | double max_val = 0.0; | ||
| 24 | |||
| 25 |
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352 | for (int i = start_row; std::cmp_less(i, static_cast<int>(a.size())); ++i) { |
| 26 |
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224 | double v = std::fabs(a[i][col]); |
| 27 |
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224 | if (v > max_val) { |
| 28 | max_val = v; | ||
| 29 | best = i; | ||
| 30 | } | ||
| 31 | } | ||
| 32 |
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128 | return (max_val > kTol) ? best : -1; |
| 33 | } | ||
| 34 | |||
| 35 | void Normalize(std::vector<double> &row, int pivot_col) { | ||
| 36 | 128 | double p = row[pivot_col]; | |
| 37 |
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128 | if (NearZero(p)) { |
| 38 | return; | ||
| 39 | } | ||
| 40 |
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576 | for (double &x : row) { |
| 41 | 448 | x /= p; | |
| 42 | } | ||
| 43 | } | ||
| 44 | |||
| 45 | void Eliminate(std::vector<double> &row, const std::vector<double> &pivot, double factor) { | ||
| 46 |
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240 | for (size_t j = 0; j < row.size(); ++j) { |
| 47 | 184 | row[j] -= factor * pivot[j]; | |
| 48 | } | ||
| 49 | } | ||
| 50 | |||
| 51 | bool RowIsZero(const std::vector<double> &row, int until) { | ||
| 52 |
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448 | for (int j = 0; j < until; ++j) { |
| 53 |
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448 | if (!NearZero(row[j])) { |
| 54 | return false; | ||
| 55 | } | ||
| 56 | } | ||
| 57 | return true; | ||
| 58 | } | ||
| 59 | |||
| 60 | } // namespace | ||
| 61 | |||
| 62 |
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56 | KhruevAGaussJordanSEQ::KhruevAGaussJordanSEQ(const InType &in) { |
| 63 | SetTypeOfTask(GetStaticTypeOfTask()); | ||
| 64 |
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56 | InType tmp(in); |
| 65 | GetInput().swap(tmp); | ||
| 66 | 56 | } | |
| 67 | |||
| 68 |
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56 | bool KhruevAGaussJordanSEQ::ValidationImpl() { |
| 69 |
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56 | if (GetInput().empty()) { |
| 70 | return true; | ||
| 71 | } | ||
| 72 | |||
| 73 | size_t cols = GetInput()[0].size(); | ||
| 74 |
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184 | for (const auto &r : GetInput()) { |
| 75 |
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128 | if (r.size() != cols) { |
| 76 | return false; | ||
| 77 | } | ||
| 78 | } | ||
| 79 | |||
| 80 |
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56 | return GetOutput().empty() && cols > 0; |
| 81 | } | ||
| 82 | |||
| 83 |
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56 | bool KhruevAGaussJordanSEQ::PreProcessingImpl() { |
| 84 | GetOutput().clear(); | ||
| 85 | 56 | return true; | |
| 86 | } | ||
| 87 | |||
| 88 | 56 | void KhruevAGaussJordanSEQ::ToReducedForm(std::vector<std::vector<double>> &a) { | |
| 89 | 56 | int n = static_cast<int>(a.size()); | |
| 90 | 56 | int m = static_cast<int>(a[0].size()); | |
| 91 | |||
| 92 | int row = 0; | ||
| 93 |
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184 | for (int col = 0; col < m - 1 && row < n; ++col) { |
| 94 | int pivot = 0; | ||
| 95 | pivot = SelectPivot(a, row, col); | ||
| 96 |
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128 | if (pivot == -1) { |
| 97 | ✗ | continue; | |
| 98 | } | ||
| 99 | |||
| 100 |
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128 | std::swap(a[row], a[pivot]); |
| 101 | Normalize(a[row], col); | ||
| 102 | |||
| 103 |
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448 | for (int i = 0; i < n; ++i) { |
| 104 |
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320 | if (i == row) { |
| 105 | 128 | continue; | |
| 106 | } | ||
| 107 |
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192 | double factor = a[i][col]; |
| 108 |
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192 | if (!NearZero(factor)) { |
| 109 | Eliminate(a[i], a[row], factor); | ||
| 110 | } | ||
| 111 | } | ||
| 112 | 128 | ++row; | |
| 113 | } | ||
| 114 | 56 | } | |
| 115 | |||
| 116 | 56 | bool KhruevAGaussJordanSEQ::DetectInconsistency(const std::vector<std::vector<double>> &a) { | |
| 117 | 56 | const int m = static_cast<int>(a[0].size()); | |
| 118 | |||
| 119 | return std::ranges::any_of( | ||
| 120 |
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256 | a, [m](const std::vector<double> &row) { return RowIsZero(row, m - 1) && !NearZero(row[m - 1]); }); |
| 121 | } | ||
| 122 | |||
| 123 | 56 | int KhruevAGaussJordanSEQ::ComputeRank(const std::vector<std::vector<double>> &a) { | |
| 124 | int rank = 0; | ||
| 125 | 56 | int m = static_cast<int>(a[0].size()); | |
| 126 |
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184 | for (const auto &row : a) { |
| 127 |
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256 | if (!RowIsZero(row, m - 1)) { |
| 128 | 128 | ++rank; | |
| 129 | } | ||
| 130 | } | ||
| 131 | 56 | return rank; | |
| 132 | } | ||
| 133 | |||
| 134 | 56 | std::vector<double> KhruevAGaussJordanSEQ::RecoverSolution(const std::vector<std::vector<double>> &a) { | |
| 135 | 56 | int n = static_cast<int>(a.size()); | |
| 136 | 56 | int m = static_cast<int>(a[0].size()); | |
| 137 | |||
| 138 | 56 | std::vector<double> sol(m - 1, 0.0); | |
| 139 |
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184 | for (int i = 0; i < std::min(n, m - 1); ++i) { |
| 140 |
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224 | for (int j = 0; j < m - 1; ++j) { |
| 141 |
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224 | if (!NearZero(a[i][j])) { |
| 142 | 128 | sol[j] = a[i][m - 1]; | |
| 143 | 128 | break; | |
| 144 | } | ||
| 145 | } | ||
| 146 | } | ||
| 147 | 56 | return sol; | |
| 148 | } | ||
| 149 | |||
| 150 |
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56 | bool KhruevAGaussJordanSEQ::RunImpl() { |
| 151 |
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56 | if (GetInput().empty()) { |
| 152 | return true; | ||
| 153 | } | ||
| 154 | 56 | auto a = GetInput(); | |
| 155 | 56 | ToReducedForm(a); | |
| 156 | |||
| 157 |
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56 | if (DetectInconsistency(a)) { |
| 158 | GetOutput().clear(); | ||
| 159 | ✗ | return false; | |
| 160 | } | ||
| 161 | |||
| 162 | int rank = 0; | ||
| 163 |
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56 | rank = ComputeRank(a); |
| 164 |
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56 | if (rank < static_cast<int>(a[0].size()) - 1 && std::cmp_less(rank, static_cast<int>(a.size()))) { |
| 165 | GetOutput().clear(); | ||
| 166 | ✗ | return false; | |
| 167 | } | ||
| 168 | |||
| 169 |
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56 | GetOutput() = RecoverSolution(a); |
| 170 | 56 | return true; | |
| 171 | 56 | } | |
| 172 | |||
| 173 | 56 | bool KhruevAGaussJordanSEQ::PostProcessingImpl() { | |
| 174 | 56 | return true; | |
| 175 | } | ||
| 176 | |||
| 177 | } // namespace khruev_a_gauss_jordan | ||
| 178 |