std::cauchy_distribution
From cppreference.com
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):
- f(x; a,b) = ⎛
⎜
⎝bπ ⎡
⎢
⎣1 + ⎛
⎜
⎝
⎞x - a b
⎟
⎠2
⎤
⎥
⎦⎞
⎟
⎠-1
std::cauchy_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 longdouble. |
[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
(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) |
[edit]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) |
[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, class Seq>void draw_vbars(Seq&& s, constbool 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;}; constauto[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){constauto q{dv.quot}, r{dv.rem};unsignedchar 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](constfloat x0, constfloat 𝛾){ std::cauchy_distribution<float> d{x0 /* a */, 𝛾 /* b */}; constint norm =1'00'00;constfloat 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(autoconst&[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
[edit]External links
| Weisstein, Eric W. "Cauchy Distribution." From MathWorld — A Wolfram Web Resource. |
