[auto-verifier] docs commit ee6082f

heuristic/exponential_dist_sampler.hpp.md

@@ -0,0 +1,63 @@
+---
+data:
+  _extendedDependsOn: []
+  _extendedRequiredBy: []
+  _extendedVerifiedWith: []
+  _isVerificationFailed: false
+  _pathExtension: hpp
+  _verificationStatusIcon: ':warning:'
+  attributes:
+    links: []
+  bundledCode: "#line 2 \"heuristic/exponential_dist_sampler.hpp\"\n\n#include <cmath>\n\
+    #include <cstdint>\n#include <array>\n\ntemplate <int D> struct ExponentialDistSampler\
+    \ {\n    std::array<double, (1 << D)> minuslogps;\n\n    constexpr ExponentialDistSampler()\
+    \ {\n        for (int i = 0; i < (1 << D); ++i) minuslogps.at(i) = -log((0.5 +\
+    \ i) / (1 << D));\n    }\n\n    double sample(uint32_t random_mask) const {\n\
+    \        return minuslogps.at(random_mask & ((1 << D) - 1));\n    }\n\n    //\
+    \ p ~ U(0, 1) => -log(p) ~ Ex(1)\n    // P[exp(-|dx| / T) >= p] = P[|dx| <= -log(p)\
+    \ * T]\n    bool check_sa(double abs_dx, double T, uint32_t random_mask) const\
+    \ {\n        return abs_dx <= minuslogps.at(random_mask & ((1 << D) - 1)) * T;\n\
+    \    }\n};\n// const ExponentialDistSampler<16> log_ps;\n"
+  code: "#pragma once\n\n#include <cmath>\n#include <cstdint>\n#include <array>\n\n\
+    template <int D> struct ExponentialDistSampler {\n    std::array<double, (1 <<\
+    \ D)> minuslogps;\n\n    constexpr ExponentialDistSampler() {\n        for (int\
+    \ i = 0; i < (1 << D); ++i) minuslogps.at(i) = -log((0.5 + i) / (1 << D));\n \
+    \   }\n\n    double sample(uint32_t random_mask) const {\n        return minuslogps.at(random_mask\
+    \ & ((1 << D) - 1));\n    }\n\n    // p ~ U(0, 1) => -log(p) ~ Ex(1)\n    // P[exp(-|dx|\
+    \ / T) >= p] = P[|dx| <= -log(p) * T]\n    bool check_sa(double abs_dx, double\
+    \ T, uint32_t random_mask) const {\n        return abs_dx <= minuslogps.at(random_mask\
+    \ & ((1 << D) - 1)) * T;\n    }\n};\n// const ExponentialDistSampler<16> log_ps;\n"
+  dependsOn: []
+  isVerificationFile: false
+  path: heuristic/exponential_dist_sampler.hpp
+  requiredBy: []
+  timestamp: '2024-03-01 09:07:31+09:00'
+  verificationStatus: LIBRARY_NO_TESTS
+  verifiedWith: []
+documentation_of: heuristic/exponential_dist_sampler.hpp
+layout: document
+title: "Fast sampler of exponential distribution \uFF08\u9AD8\u901F\u6307\u6570\u5206\
+  \u5E03\u30B5\u30F3\u30D7\u30E9\u30FC\u30FB\u64EC\u4F3C\u713C\u304D\u306A\u307E\u3057\
+  \u6CD5\u306E\u9077\u79FB\u5224\u5B9A\uFF09"
+---
+
+母数 $\lambda = 1$ の指数分布を模擬するサンプラー．
+
+典型的な用途として，擬似焼きなまし法 (simulated annealing, SA) の遷移判定を（指数関数や対数関数の計算を毎回行うことなく）高速に行える．
+
+## 使用方法
+
+```cpp
+constexpr int D = 18;
+const ExponentialDistSampler<D> eds;  // 2^D 個のサンプルを前計算
+
+// 下位 D bit がランダムに分布した mask を与えると x ~ Ex(1) をサンプル
+uint32_t mask;
+double x = eds.sample(mask);
+
+double dx;
+double T;
+
+// コストの変化が abs(dx), 温度 T のとき焼きなまし法の遷移を受理するか確率的に判定
+bool upd = eds.check_sa(abs(dx), T, mask);
+```

index.md

@@ -347,6 +347,13 @@ data:
     - icon: ':heavy_check_mark:'
       path: graph/strongly_connected_components_bitset.hpp
       title: graph/strongly_connected_components_bitset.hpp
+  - name: heuristic
+    pages:
+    - icon: ':warning:'
+      path: heuristic/exponential_dist_sampler.hpp
+      title: "Fast sampler of exponential distribution \uFF08\u9AD8\u901F\u6307\u6570\
+        \u5206\u5E03\u30B5\u30F3\u30D7\u30E9\u30FC\u30FB\u64EC\u4F3C\u713C\u304D\u306A\
+        \u307E\u3057\u6CD5\u306E\u9077\u79FB\u5224\u5B9A\uFF09"
   - name: linear_algebra_matrix
     pages:
     - icon: ':heavy_check_mark:'