Difference between revisions of "cpp/numeric/random/extreme value distribution"
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{{cpp/title|extreme_value_distribution}} | {{cpp/title|extreme_value_distribution}} | ||
− | {{cpp/numeric/random/extreme_value_distribution/ | + | {{cpp/numeric/random/extreme_value_distribution/navbar}} |
− | {{ddcl | header=random | | + | {{ddcl|header=random|since=c++11|1= |
template< class RealType = double > | template< class RealType = double > | ||
class extreme_value_distribution; | class extreme_value_distribution; | ||
}} | }} | ||
− | {{ | + | Produces random numbers according to the {{enwiki|Generalized extreme value distribution}} (it is also known as Gumbel Type I, log-Weibull, Fisher-Tippett Type I): |
+ | |||
+ | :{{mathjax-or|1=\({\small p(x;a,b) = \frac{1}{b} \exp{(\frac{a-x}{b}-\exp{(\frac{a-x}{b})})} }\)|2=p(x;a,b) = {{mfrac||1|b}} exp{{mparen|(|)|{{mfrac||a-x|b}} - exp{{mparen|(|)|{{mfrac||a-x|b}}}} }}}} | ||
+ | |||
+ | {{tt|std::extreme_value_distribution}} satisfies all requirements of {{named req|RandomNumberDistribution}}. | ||
+ | |||
+ | ===Template parameters=== | ||
+ | {{par begin}} | ||
+ | {{cpp/numeric/random/param_list|RealType}} | ||
+ | {{par end}} | ||
===Member types=== | ===Member types=== | ||
− | {{ | + | {{dsc begin}} |
− | {{ | + | {{dsc hitem|Member type|Definition}} |
− | {{ | + | {{dsc|{{tt|result_type}} {{mark c++11}}|{{co|RealType}}}} |
− | {{ | + | {{cpp/numeric/random/param_type}} |
− | {{ | + | {{dsc end}} |
===Member functions=== | ===Member functions=== | ||
− | {{ | + | {{dsc begin}} |
− | {{ | + | {{dsc inc|cpp/numeric/random/distribution/dsc constructor|extreme_value_distribution}} |
− | {{ | + | {{dsc inc|cpp/numeric/random/distribution/dsc reset|extreme_value_distribution}} |
− | {{ | + | {{dsc h2|Generation}} |
− | {{ | + | {{dsc inc|cpp/numeric/random/distribution/dsc operator()|extreme_value_distribution}} |
− | {{ | + | {{dsc h2|Characteristics}} |
− | {{ | + | {{dsc inc|cpp/numeric/random/distribution/dsc params|extreme_value_distribution}} |
− | {{ | + | {{dsc inc|cpp/numeric/random/distribution/dsc param|extreme_value_distribution}} |
− | {{ | + | {{dsc inc|cpp/numeric/random/distribution/dsc min|extreme_value_distribution}} |
− | {{ | + | {{dsc inc|cpp/numeric/random/distribution/dsc max|extreme_value_distribution}} |
− | {{ | + | {{dsc end}} |
===Non-member functions=== | ===Non-member functions=== | ||
− | {{ | + | {{dsc begin}} |
− | {{ | + | {{dsc inc|cpp/numeric/random/distribution/dsc operator_cmp|extreme_value_distribution}} |
− | {{ | + | {{dsc inc|cpp/numeric/random/distribution/dsc operator_ltltgtgt|extreme_value_distribution}} |
− | {{ | + | {{dsc end}} |
===Example=== | ===Example=== | ||
{{example | {{example | ||
− | + | |code= | |
− | | output= | + | #include <algorithm> |
+ | #include <cmath> | ||
+ | #include <iomanip> | ||
+ | #include <iostream> | ||
+ | #include <map> | ||
+ | #include <random> | ||
+ | #include <vector> | ||
+ | |||
+ | {{cpp/numeric/draw_vbars}} | ||
+ | |||
+ | int main() | ||
+ | { | ||
+ | std::random_device rd{}; | ||
+ | std::mt19937 gen{rd()}; | ||
+ | |||
+ | std::extreme_value_distribution<> d{-1.618f, 1.618f}; | ||
+ | |||
+ | const int norm = 10'000; | ||
+ | const float cutoff = 0.000'3f; | ||
+ | |||
+ | std::map<int, int> hist{}; | ||
+ | for (int n = 0; n != norm; ++n) | ||
+ | ++hist[std::round(d(gen))]; | ||
+ | |||
+ | std::vector<float> bars; | ||
+ | std::vector<int> indices; | ||
+ | for (const auto& [n, p] : hist) | ||
+ | if (const float x = p * (1.0f / norm); x > cutoff) | ||
+ | { | ||
+ | bars.push_back(x); | ||
+ | indices.push_back(n); | ||
+ | } | ||
+ | |||
+ | draw_vbars<8,4>(bars); | ||
+ | |||
+ | for (int n : indices) | ||
+ | std::cout << ' ' << std::setw(2) << n << " "; | ||
+ | std::cout << '\n'; | ||
+ | } | ||
+ | |p=true | ||
+ | |output=<nowiki/> | ||
+ | ████ ▅▅▅▅ ┬ 0.2186 | ||
+ | ████ ████ │ | ||
+ | ▁▁▁▁ ████ ████ ▇▇▇▇ │ | ||
+ | ████ ████ ████ ████ │ | ||
+ | ████ ████ ████ ████ ▆▆▆▆ │ | ||
+ | ████ ████ ████ ████ ████ ▁▁▁▁ │ | ||
+ | ▄▄▄▄ ████ ████ ████ ████ ████ ████ ▃▃▃▃ │ | ||
+ | ▁▁▁▁ ████ ████ ████ ████ ████ ████ ████ ████ ▆▆▆▆ ▃▃▃▃ ▂▂▂▂ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ ┴ 0.0005 | ||
+ | -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 | ||
}} | }} | ||
===External links=== | ===External links=== | ||
− | [ | + | {{eli|[https://mathworld.wolfram.com/ExtremeValueDistribution.html Weisstein, Eric W. "Extreme Value Distribution."] From MathWorld — A Wolfram Web Resource.}} |
+ | |||
+ | {{langlinks|de|es|fr|it|ja|pt|ru|zh}} |
Latest revision as of 10:40, 17 October 2023
Defined in header <random>
|
||
template< class RealType = double > class extreme_value_distribution; |
(since C++11) | |
Produces random numbers according to the Generalized extreme value distribution (it is also known as Gumbel Type I, log-Weibull, Fisher-Tippett Type I):
- p(x;a,b) =
exp⎛1 b
⎜
⎝
- exp⎛a-x b
⎜
⎝
⎞a-x b
⎟
⎠⎞
⎟
⎠
std::extreme_value_distribution
satisfies all requirements of RandomNumberDistribution.
Contents |
[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
(C++11) |
constructs new distribution (public member function) |
(C++11) |
resets the internal state of the distribution (public member function) |
Generation | |
(C++11) |
generates the next random number in the distribution (public member function) |
Characteristics | |
(C++11) |
returns the distribution parameters (public member function) |
(C++11) |
gets or sets the distribution parameter object (public member function) |
(C++11) |
returns the minimum potentially generated value (public member function) |
(C++11) |
returns the maximum potentially generated value (public member function) |
[edit] Non-member functions
(C++11)(C++11)(removed in C++20) |
compares two distribution objects (function) |
(C++11) |
performs stream input and output on pseudo-random number distribution (function template) |
[edit] Example
Run this code
#include <algorithm> #include <cmath> #include <iomanip> #include <iostream> #include <map> #include <random> #include <vector> template<int Height = 5, int BarWidth = 1, int Padding = 1, int Offset = 0, class Seq> 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()}; std::extreme_value_distribution<> d{-1.618f, 1.618f}; const int norm = 10'000; const float cutoff = 0.000'3f; std::map<int, int> hist{}; for (int n = 0; n != norm; ++n) ++hist[std::round(d(gen))]; std::vector<float> bars; std::vector<int> indices; for (const auto& [n, p] : hist) if (const float x = p * (1.0f / norm); x > cutoff) { bars.push_back(x); indices.push_back(n); } draw_vbars<8,4>(bars); for (int n : indices) std::cout << ' ' << std::setw(2) << n << " "; std::cout << '\n'; }
Possible output:
████ ▅▅▅▅ ┬ 0.2186 ████ ████ │ ▁▁▁▁ ████ ████ ▇▇▇▇ │ ████ ████ ████ ████ │ ████ ████ ████ ████ ▆▆▆▆ │ ████ ████ ████ ████ ████ ▁▁▁▁ │ ▄▄▄▄ ████ ████ ████ ████ ████ ████ ▃▃▃▃ │ ▁▁▁▁ ████ ████ ████ ████ ████ ████ ████ ████ ▆▆▆▆ ▃▃▃▃ ▂▂▂▂ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ ┴ 0.0005 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
[edit] External links
Weisstein, Eric W. "Extreme Value Distribution." From MathWorld — A Wolfram Web Resource. |