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) =
⎛std::cauchy_distribution satisfies all requirements of RandomNumberDistribution.
| RealType | - | The result type generated by the generator. The effect is undefined if this is not one of float, double, or long double. |
| Member type | Definition |
|---|---|
result_type (C++11) | RealType |
param_type (C++11) | the type of the parameter set, see RandomNumberDistribution. |
|
(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) |
|
(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) |
#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| Weisstein, Eric W. "Cauchy Distribution." From MathWorld — A Wolfram Web Resource. |
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