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

From cppreference.com
< cpp‎ | numeric‎ | random
m (→‎Example: break line)
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         }
 
         }
 
         if (MinMax && Height > 1) {
 
         if (MinMax && Height > 1) {
−
            std::cout << "│";
+
             if (h == Height - 1)
−
             if (h == Height - 1) std::cout << " " << *max;
+
                std::cout << "┬ " << *max;
−
             else if (h == 0) std::cout << " " << *min;
+
             else if (h == 0)
 +
                std::cout << "┴ " << *min;
 +
            else
 +
                std::cout << "│";
 
         }
 
         }
 
         std::cout << '\n';
 
         std::cout << '\n';
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  | p=true
 
  | p=true
 
  | output=<nowiki/>
 
  | output=<nowiki/>
−
               ████ ▂▂▂▂                                                       │ 0.2227
+
               ████ ▅▅▅▅                                                       ┬ 0.2186
 
               ████ ████                                                        │
 
               ████ ████                                                        │
−
              ████ ████ ▆▆▆▆                                                   │
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          ▁▁▁▁ ████ ████ ▇▇▇▇                                                   │
 
           ████ ████ ████ ████                                                  │
 
           ████ ████ ████ ████                                                  │
−
           ████ ████ ████ ████ ▅▅▅▅                                             │
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           ████ ████ ████ ████ ▆▆▆▆                                             │
−
           ████ ████ ████ ████ ████ ▂▂▂▂                                         │
+
           ████ ████ ████ ████ ████ ▁▁▁▁                                         │
−
     ▄▄▄▄ ████ ████ ████ ████ ████ ████ ▂▂▂▂                                   │
+
     ▄▄▄▄ ████ ████ ████ ████ ████ ████ ▃▃▃▃                                   │
−
▁▁▁▁ ████ ████ ████ ████ ████ ████ ████ ████ ▆▆▆▆ ▃▃▃▃ ▂▂▂▂ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ │ 0.0006
+
▁▁▁▁ ████ ████ ████ ████ ████ ████ ████ ████ ▆▆▆▆ ▃▃▃▃ ▂▂▂▂ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ ▁▁▁▁ ┴ 0.0005
−
 
+
 
  -5  -4  -3  -2  -1    0    1    2    3    4    5    6    7    8    9  10
 
  -5  -4  -3  -2  -1    0    1    2    3    4    5    6    7    8    9  10
 
}}
 
}}

Revision as of 22:31, 23 June 2020

 
C++
 
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
(C++17)
(C++17)
Interpolations
(C++20)
(C++20)
Saturation arithmetic
(C++26)
(C++26)
(C++26)
(C++26)
(C++26)

Generic numeric operations
Bit operations
(C++20)    
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++23)
(C++20)
 
Pseudo-random number generation
 
std::extreme_value_distribution
 
Defined in header <random>
template< class RealType = double >
class extreme_value_distribution;
 (since C++11)

Produces random numbers according to the 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

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.

Member types

Member type Definition
result_type RealType
param_type (C++11) the type of the parameter set, see RandomNumberDistribution.

Member functions

(C++11)
 constructs new distribution
(public member function) [edit]
(C++11)
 resets the internal state of the distribution
(public member function) [edit]
Generation
(C++11)
 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]

Non-member functions

(C++11)(C++11)(removed in C++20)
 compares two distribution objects
(function) [edit]
(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,
         bool MinMax = true, class S>
void draw_vbars(S const& s)
{
    static_assert((Height > 0) && (BarWidth > 0) && (Padding >= 0) && (Offset >= 0));
 
    const auto repeat_cout = [](auto const& v, int n)
    {
        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 (float e : s) {
        qr.push_back(std::div(std::lerp(0.f, Height * 8 , (e - *min) / (*max - *min)), 8));
    }
    for (auto h{Height}; h-- > 0 ;) {
        repeat_cout(' ', Offset);
        for (auto [q, r] : qr) {
            char d[] = "█"; // == { 0xe2, 0x96, 0x88, 0 }
            if (q < h) {
                repeat_cout(' ', BarWidth);
            } else {
                if (q == h) {
                    d[2] -= (7 - r);
                }
                repeat_cout(d, BarWidth);
            }
            repeat_cout(' ', Padding);
        }
        if (MinMax && Height > 1) {
            if (h == Height - 1)
                std::cout << "┬ " << *max;
            else if (h == 0)
                std::cout << "┴ " << *min;
            else
                std::cout << "│";
        }
        std::cout << '\n';
    }
}
 
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) {
        float x = p*(1.0f/norm);
        if (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

External links

Weisstein, Eric W. "Extreme Value Distribution." From MathWorld--A Wolfram Web Resource.

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