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Difference between revisions of "cpp/numeric/random/extreme value distribution"

From cppreference.com
< cpp‎ | numeric‎ | random
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{{cpp/title|extreme_value_distribution}}
 
{{cpp/title|extreme_value_distribution}}
{{cpp/numeric/random/extreme_value_distribution/sidebar}}
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{{cpp/numeric/random/extreme_value_distribution/navbar}}
{{ddcl | header=random | notes={{mark since c++11}} | 1=
+
{{ddcl|header=random|since=c++11|1=
 
template< class RealType = double >
 
template< class RealType = double >
 
class extreme_value_distribution;
 
class extreme_value_distribution;
 
}}
 
}}
  
{{todo}}
+
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===
{{dcl list begin}}
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{{dsc begin}}
{{tdcl list hitem | Member type | Definition}}
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{{dsc hitem|Member type|Definition}}
{{tdcl list item | {{tt|result_type}} | {{c|RealType}}}}
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{{dsc|{{tt|result_type}} {{mark c++11}}|{{co|RealType}}}}
{{tdcl list item | {{tt|param_type}} | the type of the parameter set, unspecified}}
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{{cpp/numeric/random/param_type}}
{{tdcl list end}}
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{{dsc end}}
  
 
===Member functions===
 
===Member functions===
{{dcl list begin}}
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{{dsc begin}}
{{dcl list template | cpp/numeric/random/distribution/dcl list constructor | extreme_value_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc constructor|extreme_value_distribution}}
{{dcl list template | cpp/numeric/random/distribution/dcl list reset | extreme_value_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc reset|extreme_value_distribution}}
  
{{dcl list h2 | Generation}}
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{{dsc h2|Generation}}
{{dcl list template | cpp/numeric/random/distribution/dcl list operator() | extreme_value_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc operator()|extreme_value_distribution}}
  
{{dcl list h2 | Characteristics}}
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{{dsc h2|Characteristics}}
{{dcl list todo}}
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{{dsc inc|cpp/numeric/random/distribution/dsc params|extreme_value_distribution}}
{{dcl list template | cpp/numeric/random/distribution/dcl list param | extreme_value_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc param|extreme_value_distribution}}
{{dcl list template | cpp/numeric/random/distribution/dcl list min | extreme_value_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc min|extreme_value_distribution}}
{{dcl list template | cpp/numeric/random/distribution/dcl list max | extreme_value_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc max|extreme_value_distribution}}
{{dcl list end}}
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{{dsc end}}
  
 
===Non-member functions===
 
===Non-member functions===
{{dcl list begin}}
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{{dsc begin}}
{{dcl list template | cpp/numeric/random/distribution/dcl list operator_cmp | extreme_value_distribution }}
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{{dsc inc|cpp/numeric/random/distribution/dsc operator_cmp|extreme_value_distribution}}
{{dcl list template | cpp/numeric/random/distribution/dcl list operator_ltltgtgt | extreme_value_distribution}}
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{{dsc inc|cpp/numeric/random/distribution/dsc operator_ltltgtgt|extreme_value_distribution}}
{{dcl list end}}
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{{dsc end}}
  
 
===Example===
 
===Example===
 
{{example
 
{{example
| code=
+
|code=
  | output=
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#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===
[http://mathworld.wolfram.com/ExtremeValueDistribution.html Weisstein, Eric W. "Extreme Value Distribution."] From MathWorld--A Wolfram Web Resource.
+
{{eli|[https://mathworld.wolfram.com/ExtremeValueDistribution.html Weisstein, Eric W. "Extreme Value Distribution."] From MathWorld &mdash; 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) =
1
b
exp

a-x
b
- exp

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

constructs new distribution
(public member function) [edit]
(C++11)
resets the internal state of the distribution
(public member function) [edit]
Generation
generates the next random number in the distribution
(public member function) [edit]
Characteristics
(C++11)
returns the distribution parameters
(public member function) [edit]
(C++11)
gets or sets the distribution parameter object
(public member function) [edit]
(C++11)
returns the minimum potentially generated value
(public member function) [edit]
(C++11)
returns the maximum potentially generated value
(public member function) [edit]

[edit] Non-member functions

(C++11)(C++11)(removed in C++20)
compares two distribution objects
(function) [edit]
performs stream input and output on pseudo-random number distribution
(function template) [edit]

[edit] Example

#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.