std::cauchy_distribution - cppreference.com (original) (raw)
| | | | | ----------------------------------------------------------------- | | ------------- | | template< class RealType = double > class cauchy_distribution; | | (since C++11) |
Produces random numbers according to a Cauchy distribution (also called Lorentz distribution):
\({\small f(x;a,b)={(b\pi{[1+{(\frac{x-a}{b})}^{2}]} })}^{-1}\)f(x; a,b) = ⎛
⎜
⎝bπ ⎡
⎢
⎣1 + ⎛
⎜
⎝⎞
⎟
⎠2
⎤
⎥
⎦⎞
⎟
⎠-1
std::cauchy_distribution satisfies all requirements of RandomNumberDistribution.
Contents
- 1 Template parameters
- 2 Member types
- 3 Member functions
- 4 Non-member functions
- 5 Example
- 6 External links
[edit] Template parameters
| RealType | - | The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double. |
|---|
[edit] Member types
| Member type | Definition |
|---|---|
| result_type (C++11) | RealType |
| param_type (C++11) | the type of the parameter set, see RandomNumberDistribution. |
[edit] Member functions
| (constructor)(C++11) | constructs new distribution (public member function) [edit] |
|---|---|
| reset(C++11) | resets the internal state of the distribution (public member function) [edit] |
| Generation | |
| operator()(C++11) | generates the next random number in the distribution (public member function) [edit] |
| Characteristics | |
| ab(C++11) | returns the distribution parameters (public member function) [edit] |
| param(C++11) | gets or sets the distribution parameter object (public member function) [edit] |
| min(C++11) | returns the minimum potentially generated value (public member function) [edit] |
| max(C++11) | returns the maximum potentially generated value (public member function) [edit] |
[edit] Non-member functions
[edit] Example
#include #include #include #include #include #include #include template void draw_vbars(Seq&& s, const bool DrawMinMax = true) { static_assert(0 < Height and 0 < BarWidth and 0 <= Padding and 0 <= Offset); auto cout_n = [](auto&& v, int n = 1) { while (n-- > 0) std::cout << v; }; const auto [min, max] = std::minmax_element(std::cbegin(s), std::cend(s)); std::vector<std::div_t> qr; for (typedef decltype(*std::cbegin(s)) V; V e : s) qr.push_back(std::div(std::lerp(V(0), 8 * Height, (e - *min) / (*max - min)), 8)); for (auto h{Height}; h-- > 0; cout_n('\n')) { cout_n(' ', Offset); for (auto dv : qr) { const auto q{dv.quot}, r{dv.rem}; unsigned char d[]{0xe2, 0x96, 0x88, 0}; // Full Block: '█' q < h ? d[0] = ' ', d[1] = 0 : q == h ? d[2] -= (7 - r) : 0; cout_n(d, BarWidth), cout_n(' ', Padding); } if (DrawMinMax && Height > 1) Height - 1 == h ? std::cout << "┬ " << *max: h ? std::cout << "│ " : std::cout << "┴ " << *min; } } int main() { std::random_device rd{}; std::mt19937 gen{rd()}; auto cauchy = [&gen](const float x0, const float 𝛾) { std::cauchy_distribution d{x0 / a /, 𝛾 / b /}; const int norm = 1'00'00; const float cutoff = 0.005f; std::map<int, int> hist{}; for (int n = 0; n != norm; ++n) ++hist[std::round(d(gen))]; std::vector bars; std::vector indices; for (auto const& [n, p] : hist) if (float x = p * (1.0 / norm); cutoff < x) { bars.push_back(x); indices.push_back(n); } std::cout << "x₀ = " << x0 << ", 𝛾 = " << 𝛾 << ":\n"; draw_vbars<4,3>(bars); for (int n : indices) std::cout << std::setw(2) << n << " "; std::cout << "\n\n"; }; cauchy(/ x₀ = / -2.0f, / 𝛾 = / 0.50f); cauchy(/ x₀ = / +0.0f, / 𝛾 = */ 1.25f); }
Possible output:
x₀ = -2, 𝛾 = 0.5: ███ ┬ 0.5006 ███ │ ▂▂▂ ███ ▁▁▁ │ ▁▁▁ ▁▁▁ ▁▁▁ ▃▃▃ ███ ███ ███ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.0076 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 x₀ = 0, 𝛾 = 1.25: ███ ┬ 0.2539 ▅▅▅ ███ ▃▃▃ │ ▁▁▁ ███ ███ ███ ▁▁▁ │ ▁▁▁ ▁▁▁ ▁▁▁ ▁▁▁ ▃▃▃ ▅▅▅ ███ ███ ███ ███ ███ ▅▅▅ ▃▃▃ ▂▂▂ ▁▁▁ ▁▁▁ ▁▁▁ ┴ 0.0058 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 9