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(C++11)(C++11)(until C++20) | ||||
(C++11)(C++11) |
Defined in header <random> | ||
template<class RealType=double> class cauchy_distribution; | (since C++11) | |
Produces random numbers according to aCauchy distribution (also called Lorentz distribution):
| x - a |
| b |
std::cauchy_distribution satisfies all requirements ofRandomNumberDistribution.
Contents |
| RealType | - | The result type generated by the generator. The effect is undefined if this is not one offloat,double, orlongdouble. |
| Member type | Definition |
result_type(C++11) | RealType |
param_type(C++11) | the type of the parameter set, seeRandomNumberDistribution. |
(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] |
(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] |
#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 and0< BarWidth and0<= Padding and0<= 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
| Weisstein, Eric W. "Cauchy Distribution." From MathWorld — A Wolfram Web Resource. |
