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std::piecewise_linear_distribution

From cppreference.com
< cpp‎ | numeric‎ | random
 
 
Numerics library
 
Pseudo-random number generation
 
 
Defined in header <random>
template< class RealType = double >
class piecewise_linear_distribution;
(since C++11)

std::piecewise_linear_distribution produces random floating-point numbers, which are distributed according to a linear probability density function within each of the several subintervals \(\small{[b_i, b_{i+1})}\)[bi, bi+1). The distribution is such that the probability density at each interval boundary is exactly the predefined value \(\small{p_i}\)pi.

The probability density for any \(\small{ b_i \le x < b_{i+1} }\)bi≤x<bi+1 is \(\small{p_i\frac{b_{i+1}-x}{b_{i+1}-b_i} + p_{i+1}\frac{x-b_i}{b_{i+1}-b_i} }\)pi
bi+1-x
bi+1-bi
+ pi+1
x-bi
bi+1-bi
, where probability densities at interval boundaries \(\small{p_k}\)pk are calculated as \(\small{w_k/S}\)wk/S where \(\small{S}\)S is the sum of all \(\small{\frac{1}{2}(w_k + w_{k+1})(b_{k+1} - b_k)}\)
1
2
(wk+wk+1)(bk+1−bk)
.

The set of interval boundaries \(\small{b_i}\)bi and the set of weights at boundaries \(\small{w_i}\)wi are the parameters of this distribution.

std::piecewise_linear_distribution satisfies all requirements of RandomNumberDistribution.

[edit] 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.

[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

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
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]

[edit] Non-member functions

(C++11)(C++11)(removed in C++20)
compares two distribution objects
(function) [edit]
performs stream input and output on pseudo-random number distribution
(function template) [edit]

[edit] Example

Run this code
#include <iomanip>
#include <iostream>
#include <map>
#include <random>
#include <string>
 
int main()
{
 std::random_device rd;
 std::mt19937 gen{rd()};
 // increase the probability from 0 to 5
 // remain flat from 5 to 10
 // decrease from 10 to 15 at the same rate
 std::vector <double> i{0, 5, 10, 15};
 std::vector <double> w{0, 1, 1, 0};
 std::piecewise_linear_distribution<> d{i.begin(), i.end(), w.begin()};
 
 std::map <int, int> hist;
 for (int n{}; n < 1e4; ++n)
 ++hist[d(gen)];
 
 for (auto [x, y] : hist)
 std::cout << std::setw (2) << std::setfill ('0') << x
 << ' ' << std::string (y / 100, '*') << '\n';
}

Possible output:

00 *
01 ***
02 ****
03 ******
04 *********
05 *********
06 *********
07 **********
08 *********
09 **********
10 *********
11 *******
12 ****
13 ***
14 *
Retrieved from "https://en.cppreference.com/mwiki/index.php?title=cpp/numeric/random/piecewise_linear_distribution&oldid=166819"

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