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include/random_walks/accelerated_billiard_walk_utils.hpp
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| // VolEsti (volume computation and sampling library) | ||
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| // Copyright (c) 2012-2020 Vissarion Fisikopoulos | ||
| // Copyright (c) 2018-2020 Apostolos Chalkis | ||
| // Copyright (c) 2024 Luca Perju | ||
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| // Licensed under GNU LGPL.3, see LICENCE file | ||
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| #ifndef ACCELERATED_BILLIARD_WALK_UTILS_HPP | ||
| #define ACCELERATED_BILLIARD_WALK_UTILS_HPP | ||
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| #include <Eigen/Eigen> | ||
| #include <vector> | ||
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| const double eps = 1e-10; | ||
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| // data structure which maintains the values of (b - Ar)/Av, and can extract the minimum positive value and the facet associated with it | ||
| // vec[i].first contains the value of (b(i) - Ar(i))/Av(i) + moved_dist, where moved_dist is the total distance that the point has travelled so far | ||
| // The heap will only contain the values from vec which are greater than moved_dist (so that they are positive) | ||
| template<typename NT> | ||
| class BoundaryOracleHeap { | ||
| public: | ||
| int n, heap_size; | ||
| std::vector<std::pair<NT, int>> heap; | ||
| std::vector<std::pair<NT, int>> vec; | ||
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| private: | ||
| int siftDown(int index) { | ||
| while((index << 1) + 1 < heap_size) { | ||
| int child = (index << 1) + 1; | ||
| if(child + 1 < heap_size && heap[child + 1].first < heap[child].first - eps) { | ||
| child += 1; | ||
| } | ||
| if(heap[child].first < heap[index].first - eps) | ||
| { | ||
| std::swap(heap[child], heap[index]); | ||
| std::swap(vec[heap[child].second].second, vec[heap[index].second].second); | ||
| index = child; | ||
| } else { | ||
| return index; | ||
| } | ||
| } | ||
| return index; | ||
| } | ||
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| int siftUp(int index) { | ||
| while(index > 0 && heap[(index - 1) >> 1].first - eps > heap[index].first) { | ||
| std::swap(heap[(index - 1) >> 1], heap[index]); | ||
| std::swap(vec[heap[(index - 1) >> 1].second].second, vec[heap[index].second].second); | ||
| index = (index - 1) >> 1; | ||
| } | ||
| return index; | ||
| } | ||
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| // takes the index of a facet, and (in case it is in the heap) removes it from the heap. | ||
| void remove (int index) { | ||
| index = vec[index].second; | ||
| if(index == -1) { | ||
| return; | ||
| } | ||
| std::swap(heap[heap_size - 1], heap[index]); | ||
| std::swap(vec[heap[heap_size - 1].second].second, vec[heap[index].second].second); | ||
| vec[heap[heap_size - 1].second].second = -1; | ||
| heap_size -= 1; | ||
| index = siftDown(index); | ||
| siftUp(index); | ||
| } | ||
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| // inserts a new value into the heap, with its associated facet | ||
| void insert (const std::pair<NT, int> val) { | ||
| vec[val.second].second = heap_size; | ||
| vec[val.second].first = val.first; | ||
| heap[heap_size++] = val; | ||
| siftUp(heap_size - 1); | ||
| } | ||
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| public: | ||
| BoundaryOracleHeap() {} | ||
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| BoundaryOracleHeap(int n) : n(n), heap_size(0) { | ||
| heap.resize(n); | ||
| vec.resize(n); | ||
| } | ||
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| // rebuilds the heap with the existing values from vec | ||
| // O(n) | ||
| void rebuild (const NT &moved_dist) { | ||
| heap_size = 0; | ||
| for(int i = 0; i < n; ++i) { | ||
| vec[i].second = -1; | ||
| if(vec[i].first - eps > moved_dist) { | ||
| vec[i].second = heap_size; | ||
| heap[heap_size++] = {vec[i].first, i}; | ||
| } | ||
| } | ||
| for(int i = heap_size - 1; i >= 0; --i) { | ||
| siftDown(i); | ||
| } | ||
| } | ||
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| // returns (b(i) - Ar(i))/Av(i) + moved_dist | ||
| // O(1) | ||
| NT get_val (const int &index) { | ||
| return vec[index].first; | ||
| } | ||
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| // returns the nearest facet | ||
| // O(1) | ||
| std::pair<NT, int> get_min () { | ||
| return heap[0]; | ||
| } | ||
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| // changes the stored value for a given facet, and updates the heap accordingly | ||
| // O(logn) | ||
| void change_val(const int& index, const NT& new_val, const NT& moved_dist) { | ||
| if(new_val < moved_dist - eps) { | ||
| vec[index].first = new_val; | ||
| remove(index); | ||
| } else { | ||
| if(vec[index].second == -1) { | ||
| insert({new_val, index}); | ||
| } else { | ||
| heap[vec[index].second].first = new_val; | ||
| vec[index].first = new_val; | ||
| siftDown(vec[index].second); | ||
| siftUp(vec[index].second); | ||
| } | ||
| } | ||
| } | ||
| }; | ||
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| #endif |
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