std::cauchy_distribution
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
|
(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 |
|
| 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) |
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) |
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,
bool DrawMinMax = true, class Sample>
void draw_vbars(Sample const& s) {
static_assert((Height > 0) && (BarWidth > 0) && (Padding >= 0) && (Offset >= 0));
auto cout_n = [](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 ;) {
cout_n(' ', Offset);
for (auto [q, r] : qr) {
char d[] = "█"; // == { 0xe2, 0x96, 0x88, 0 }
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)
h == Height - 1 ? std::cout << "┬ " << *max:
h != 0 ? std::cout << "│"
: std::cout << "┴ " << *min;
cout_n('\n', 1);
}
}
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 (const auto [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.
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https://en.cppreference.com/w/cpp/numeric/random/cauchy_distribution
