std::cauchy_distribution

 

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std::cauchy_distribution

Member functions

cauchy_distribution::cauchy_distribution (C++11)

cauchy_distribution::reset (C++11)

Generation

cauchy_distribution::operator() (C++11)

Characteristics

cauchy_distribution::acauchy_distribution::b (C++11)(C++11)

cauchy_distribution::param (C++11)

cauchy_distribution::min (C++11)

cauchy_distribution::max (C++11)

Non-member functions

operator==operator!= (C++11)(C++11)(until C++20)

operator<<operator>> (C++11)(C++11)

 

Defined in header <random>
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 + ⎛
⎜
⎝

x - a

b

⎞
⎟
⎠2
⎤
⎥
⎦⎞
⎟
⎠-1

std::cauchy_distribution satisfies all requirements of RandomNumberDistribution.

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

Member functions

(constructor) (C++11)	constructs new distribution (public member function)
reset (C++11)	resets the internal state of the distribution (public member function)
Generation
operator() (C++11)	generates the next random number in the distribution (public member function)
Characteristics
ab (C++11)	returns the distribution parameters (public member function)
param (C++11)	gets or sets the distribution parameter object (public member function)
min (C++11)	returns the minimum potentially generated value (public member function)
max (C++11)	returns the maximum potentially generated value (public member function)

Non-member functions

operator==operator!= (C++11)(C++11)(removed in C++20)	compares two distribution objects (function)
operator<<operator>> (C++11)	performs stream input and output on pseudo-random number distribution (function template)

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()};
 
    auto cauchy = [&gen](const float x0, const float 𝛾)
    {
        std::cauchy_distribution<float> 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<float> bars;
        std::vector<int> 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

External links

Weisstein, Eric W. "Cauchy Distribution." From MathWorld — A Wolfram Web Resource.