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# std::piecewise_linear_distribution

From cppreference.com
< cpp‎ | numeric‎ | random

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 [b
i, b
i+1). The distribution is such that the probability density at each interval boundary is exactly the predefined value p
i.

The probability density for any b
i≤x<b
i+1 is p
i

b i+1-x
b i+1-b i

+ p
i+1

x-b i
b i+1-b i

, where probability densities at interval boundaries p
k are calculated as w
k/S where S is the sum of all

1
2

(w
k+w
k+1)(b
k+1−b
k).

The set of interval boundaries b
i and the set of weights at boundaries w
i are the parameters of this distribution.

### [edit] Member types

Member type | Definition
`result_type` | RealType
`param_type` | the type of the parameter set, unspecified

### [edit] Member functions

(constructor) | constructs new distribution (public member function) [edit]
reset | resets the internal state of the distribution (public member function) [edit]
##### Generation
operator() | generates the next random number in the distribution (public member function) [edit]
##### Characteristics
intervals densities | returns the distribution parameters (public member function) [edit]
param | gets or sets the distribution parameter object (public member function) [edit]
min | returns the minimum potentially generated value (public member function) [edit]
max | returns the maximum potentially generated value (public member function) [edit]

### [edit] Non-member functions

operator==operator!= | compares two distribution objects (function) [edit]
operator<<operator>> | performs stream input and output on pseudo-random number distribution (function) [edit]

### [edit] Example

Run this code

    #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 *

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