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Difference between revisions of "cpp/numeric/random/piecewise linear distribution"

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< cpp‎ | numeric‎ | random
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{{cpp/title|piecewise_linear_distribution}}
 
{{cpp/title|piecewise_linear_distribution}}
 
{{cpp/numeric/random/piecewise_linear_distribution/navbar}}
 
{{cpp/numeric/random/piecewise_linear_distribution/navbar}}
−
{{ddcl | header=random | since=c++11 | 1=
+
{{ddcl|header=random|since=c++11|1=
 
template< class RealType = double >
 
template< class RealType = double >
 
class piecewise_linear_distribution;
 
class piecewise_linear_distribution;
 
}}
 
}}
  
−
{{tt|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 {{mathjax-or|\(\small{[b_i, b_{i+1})}\)|[b{{su|b=i}}, b{{su|b=i+1}})}}. The distribution is such that the probability density at each interval boundary is exactly the predefined value {{mathjax-or|\(\small{p_i}\)|p{{su|b=i}}}}.  
+
{{tt|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 {{mathjax-or|\(\small{[b_i, b_{i+1})}\)|[b{{su|b=i}}, b{{su|b=i+1}})}}. The distribution is such that the probability density at each interval boundary is exactly the predefined value {{mathjax-or|\(\small{p_i}\)|p{{su|b=i}}}}.
  
−
The probability density for any {{mathjax-or|\(\small{ b_i \le x < b_{i+1} }\)|b{{su|b=i}}≤x<b{{su|b=i+1}}}} is {{mathjax-or|\(\small{p_i\frac{b_{i+1}-x}{b_{i+1}-b_i} + p_{i+1}\frac{x-b_i}{b_{i+1}-b_i} }\)|{{mfrac|p{{su|b=i}}|b{{su|b=i+1}}-x|b{{su|b=i+1}}-b{{su|b=i}} }} + {{mfrac|p{{su|b=i+1}}|x-b{{su|b=i}}|b{{su|b=i+1}}-b{{su|b=i}} }} }}, where probability densities at interval boundaries {{mathjax-or|\(\small{p_k}\)|p{{su|b=k}}}} are calculated as {{mathjax-or|\(\small{w_k/S}\)|w{{su|b=k}}/S}} where {{mathjax-or|\(\small{S}\)|S}} is the sum of all {{mathjax-or|\(\small{\frac{1}{2}(w_k + w_{k+1})(b_{k+1} - b_k)}\)|{{mfrac||1|2}}(w{{su|b=k}}+w{{su|b=k+1}})(b{{su|b=k+1}}−b{{su|b=k}})}}.
+
The probability density for any {{mathjax-or|\(\small{ b_i \le x < b_{i+1} }\)|b{{su|b=i}}≤x<b{{su|b=i+1}}}} is {{mathjax-or|\(\small{p_i\frac{b_{i+1}-x}{b_{i+1}-b_i} + p_{i+1}\frac{x-b_i}{b_{i+1}-b_i} }\)|{{mfrac|p{{su|b=i}}|b{{su|b=i+1}}-x|b{{su|b=i+1}}-b{{su|b=i}}}} + {{mfrac|p{{su|b=i+1}}|x-b{{su|b=i}}|b{{su|b=i+1}}-b{{su|b=i}}}}}}, where probability densities at interval boundaries {{mathjax-or|\(\small{p_k}\)|p{{su|b=k}}}} are calculated as {{mathjax-or|\(\small{w_k/S}\)|w{{su|b=k}}/S}} where {{mathjax-or|\(\small{S}\)|S}} is the sum of all {{mathjax-or|\(\small{\frac{1}{2}(w_k + w_{k+1})(b_{k+1} - b_k)}\)|{{mfrac||1|2}}(w{{su|b=k}}+w{{su|b=k+1}})(b{{su|b=k+1}}−b{{su|b=k}})}}.
  
 
The set of interval boundaries {{mathjax-or|\(\small{b_i}\)|b{{su|b=i}}}} and the set of weights at boundaries {{mathjax-or|\(\small{w_i}\)|w{{su|b=i}}}} are the parameters of this distribution.
 
The set of interval boundaries {{mathjax-or|\(\small{b_i}\)|b{{su|b=i}}}} and the set of weights at boundaries {{mathjax-or|\(\small{w_i}\)|w{{su|b=i}}}} are the parameters of this distribution.
  
−
{{tt|std::piecewise_linear_distribution}} satisfies all requirements of {{named req|RandomNumberDistribution}}
+
{{ttt|std::piecewise_linear_distribution}} satisfies all requirements of {{named req|RandomNumberDistribution}}.
  
 
===Template parameters===
 
===Template parameters===
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===Member types===
 
===Member types===
 
{{dsc begin}}
 
{{dsc begin}}
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{{dsc hitem | Member type | Definition}}
+
{{dsc hitem|Member type|Definition}}
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{{dsc | {{tt|result_type}}{{mark c++11}} | {{c|RealType}}}}
+
{{dsc|{{tt|result_type}} {{mark c++11}}|{{co|RealType}}}}
 
{{cpp/numeric/random/param_type}}
 
{{cpp/numeric/random/param_type}}
 
{{dsc end}}
 
{{dsc end}}
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===Member functions===
 
===Member functions===
 
{{dsc begin}}
 
{{dsc begin}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc constructor | piecewise_linear_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc constructor|piecewise_linear_distribution}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc reset | piecewise_linear_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc reset|piecewise_linear_distribution}}
  
−
{{dsc h2 | Generation}}
+
{{dsc h2|Generation}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc operator() | piecewise_linear_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc operator()|piecewise_linear_distribution}}
  
−
{{dsc h2 | Characteristics}}
+
{{dsc h2|Characteristics}}
−
{{dsc inc | cpp/numeric/random/piecewise_linear_distribution/dsc params}}
+
{{dsc inc|cpp/numeric/random/piecewise_linear_distribution/dsc params}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc param | piecewise_linear_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc param|piecewise_linear_distribution}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc min | piecewise_linear_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc min|piecewise_linear_distribution}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc max | piecewise_linear_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc max|piecewise_linear_distribution}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Non-member functions===
 
===Non-member functions===
 
{{dsc begin}}
 
{{dsc begin}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc operator_cmp | piecewise_linear_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc operator_cmp|piecewise_linear_distribution}}
−
{{dsc inc | cpp/numeric/random/distribution/dsc operator_ltltgtgt | piecewise_linear_distribution}}
+
{{dsc inc|cpp/numeric/random/distribution/dsc operator_ltltgtgt|piecewise_linear_distribution}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Example===
 
===Example===
 
{{example
 
{{example
−
| code=
+
|code=
−
#include <iostream>
+
 
#include <iomanip>
 
#include <iomanip>
−
#include <string>
+
#include <iostream>
 
#include <map>
 
#include <map>
 
#include <random>
 
#include <random>
 +
#include <string>
  
 
int main()
 
int main()
 
{
 
{
 
     std::random_device rd;
 
     std::random_device rd;
−
     std::mt19937 gen(rd());
+
     std::mt19937 gen{rd()};
 
     // increase the probability from 0 to 5
 
     // increase the probability from 0 to 5
 
     // remain flat from 5 to 10
 
     // remain flat from 5 to 10
 
     // decrease from 10 to 15 at the same rate
 
     // decrease from 10 to 15 at the same rate
 
     std::vector<double> i{0, 5, 10, 15};
 
     std::vector<double> i{0, 5, 10, 15};
−
     std::vector<double> w{0, 1,   1, 0};
+
     std::vector<double> w{0, 1, 1, 0};
−
     std::piecewise_linear_distribution<> d(i.begin(), i.end(), w.begin());
+
     std::piecewise_linear_distribution<> d{i.begin(), i.end(), w.begin()};
−
 
+
 
     std::map<int, int> hist;
 
     std::map<int, int> hist;
−
     for(int n=0; n<10000; ++n) {
+
     for (int n{}; n < 1e4; ++n)
 
         ++hist[d(gen)];
 
         ++hist[d(gen)];
−
    }
+
 
−
     for(auto p : hist) {
+
     for (auto [x, y] : hist)
−
         std::cout << std::setw(2) << std::setfill('0') << p.first << ' '
+
         std::cout << std::setw(2) << std::setfill('0') << x
−
            << std::string(p.second/100,'*') << '\n';
+
                  << ' ' << std::string(y / 100, '*') << '\n';
−
    }
+
 
}
 
}
−
| p=true
+
|p=true
−
| output=
+
|output=
 
00 *
 
00 *
 
01 ***
 
01 ***

Latest revision as of 01:17, 23 December 2023

 
C++
 
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
(C++17)
(C++17)
Interpolations
(C++20)
(C++20)
Saturation arithmetic
(C++26)
(C++26)
(C++26)
(C++26)
(C++26)

Generic numeric operations
Bit operations
(C++20)    
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++23)
(C++20)
 
Pseudo-random number generation
 
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 [bi, bi+1). The distribution is such that the probability density at each interval boundary is exactly the predefined value pi.

The probability density for any bi≤x<bi+1 is pi
bi+1-x
bi+1-bi
 + pi+1
x-bi
bi+1-bi
, where probability densities at interval boundaries pk are calculated as wk/S where S is the sum of all
1
2
(wk+wk+1)(bk+1−bk).

The set of interval boundaries bi and the set of weights at boundaries wi are the parameters of this distribution.

std::piecewise_linear_distribution satisfies all requirements of RandomNumberDistribution.

Contents

[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

(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]

[edit] Non-member functions

(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]

[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 *
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