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std::piecewise_linear_distribution - cppreference.com

std::piecewise_linear_distribution

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

\(\small{ b_i \le x < b_{i+1} }\)biâ¤x<bi+1

\(\small{p_i\frac{b_{i+1}-x}{b_{i+1}-b_i} + p_{i+1}\frac{x-b_i}{b_{i+1}-b_i} }\)pi + pi+1

, 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

\(\small{\frac{1}{2}(w_k + w_{k+1})(b_{k+1} - b_k)}\)(wk+wk+1)(bk+1âbk)

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] resets the internal state of the distribution
(public member function) [edit] Generation generates the next random number in the distribution
(public member function) [edit] Characteristics returns the distribution parameters
(public member function) [edit] gets or sets the distribution parameter object
(public member function) [edit] returns the minimum potentially generated value
(public member function) [edit] returns the maximum potentially generated value
(public member function) [edit] [edit] Non-member functions [edit] Example

#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 *

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