/C++

# std::piecewise_linear_distribution

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 $$\small{[b_i, b_{i+1})}$$[b
i
, b
i+1
). The distribution is such that the probability density at each interval boundary is exactly the predefined value $$\small{p_i}$$p
i
. The probability density for any $$\small{ b_i \le x < b_{i+1} }$$b.

i
≤x<b
i+1
is $$\small{p_i\frac{b_{i+1}-x}{b_{i+1}-b_i} + p_{i+1}\frac{x-b_i}{b_{i+1}-b_i} }$$bi+1-x/bi+1-bi + x-bi/bi+1-bi , where probability densities at interval boundaries $$\small{p_k}$$p
k
are calculated as $$\small{w_k/S}$$w
k
/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(w
k
+w
k+1
)(b
k+1
−b
k
).

The set of interval boundaries $$\small{b_i}$$b
i
and the set of weights at boundaries $$\small{w_i}$$w
i
are the parameters of this distribution.

std::piecewise_linear_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

 operator==operator!= (C++11)(C++11)(removed in C++20) compares two distribution objects (function) operator<> (C++11) performs stream input and output on pseudo-random number distribution (function template)

### Example

#include <iostream>
#include <iomanip>
#include <string>
#include <map>
#include <random>

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=0; n<10000; ++n) {
++hist[d(gen)];
}
for(auto p : hist) {
std::cout << std::setw(2) << std::setfill('0') << p.first << ' '
<< std::string(p.second/100,'*') << '\n';
}
}

Possible output:

00 *
01 ***
02 ****
03 ******
04 *********
05 *********
06 *********
07 **********
08 *********
09 **********
10 *********
11 *******
12 ****
13 ***
14 *