Doxygen Files

template<typename T>
class Distribution

#include <Distribution.h>

Contains a distribution of values that can be operated on to perform Monte Carlo error propagation.

As an alternative to first- or second-order error propagation for a random variable with a given mean and uncertainty, one can generate sample data reflecting those values, operate on it element-wise, and find the resulting statistics.

To implement this, this class contains a valarray object of the sample data along with members with statistical information.

Template Parameters:

T – the data type (double, float, etc.).

Public Functions

inline Distribution(std::valarray<T> __samples)

Parameters:

__samples – valarray of sample data contained within the distribution.

inline std::valarray<T> samples() const

inline std::valarray<T> data() const

inline int num_samples() const

Number of samples.

inline int size() const

inline int length() const

inline int len() const

inline T mean() const

Average of the samples.

inline T average() const

inline T avg() const

inline T variance() const

Variance of the samples.

inline T var() const

inline T standard_deviation() const

Standard deviation of the samples.

inline T std_dev() const

inline const T &operator[](int i) const

Provides read-only access to the (i+1)-th sample in the distribution.

Parameters:

i – the index.

Returns:

_samples[i].

inline Distribution<T> apply(T func(T))

Applies a function to samples element-wise.

Parameters:

func – the function to be applied.

Returns:

The resulting distribution.

inline T covariance(const Distribution<T> Dist2)

Computes the covariance of two Distributions.

Parameters:

Dist2 – the second distribution.

Returns:

The covariance of this and Dist2.

inline Distribution<T> operator+(const Distribution<T> Dist2)

Add Distributions by adding their samples element-wise.

Parameters:

Dist2 – second summand.

Returns:

The resulting distribution.

inline Distribution<T> operator-(const Distribution<T> Dist2)

Subtract Distributions by subtracting their samples element-wise.

Parameters:

Dist2 – the subtrahend.

Returns:

The resulting distribution.

inline Distribution<T> operator*(const Distribution<T> Dist2)

Multiply Distributions by multiplying their samples element-wise.

Parameters:

Dist2 – the multiplier.

Returns:

The resulting distribution.

inline Distribution<T> operator/(const Distribution<T> Dist2)

Divide Distributions by dividing their samples element-wise.

Parameters:

Dist2 – the divisor.

Returns:

The resulting distribution.

inline Distribution<T> operator+(const T scalar)

Sum of a Distribution and a scalar.

Parameters:

scalar – summand of type T.

Returns:

The resulting distribution.

inline Distribution<T> operator-(const T scalar)

Subtract a Distribution by a scalar.

Parameters:

scalar – subtrahend of type T.

Returns:

The resulting distribution.

inline Distribution<T> operator*(const T scalar)

Multiply a Distribution by a scalar.

Parameters:

scalar – multiplier of type T.

Returns:

The resulting distribution.

inline Distribution<T> operator/(const T scalar)

Divide a Distribution by a scalar.

Parameters:

scalar – divisor of type T.

Returns:

The resulting distribution.

inline Distribution<T> operator-()

Unary minus.

Returns:

The negated Distribution.

Private Members

std::valarray<T> _samples

valarray containing the sample data.

int _num_samples

Size of the data.

T _mean

T _variance

T _standard_deviation

Friends

template<typename>
friend std::ostream &operator<<(std::ostream &os, const Distribution<T>)

template<typename>
friend Distribution<T> operator+(T, const Distribution<T>)

template<typename>
friend Distribution<T> operator-(T, const Distribution<T>)

template<typename>
friend Distribution<T> operator*(T, const Distribution<T>)

template<typename>
friend Distribution<T> operator/(T, const Distribution<T>)

module conf

Variables

shell

project = 'Distributions'

copyright = "2024, Sam Glosser"

author = 'Sam Glosser'

extensions = ["breathe", "sphinx.ext.autodoc"]

templates_path = ['_templates']

exclude_patterns = []

html_theme = 'sphinx_rtd_theme'

html_static_path = ['_static']

breathe_projects = { "Distributions": "../doxy_files/xml/" }

breathe_default_project = "Distributions"

file conf.py

file Distribution.h

#include <cmath>

#include <iostream>

#include <functional>

#include <valarray>

Functions

template<typename T>
std::ostream &operator<<(std::ostream &os, const Distribution<T> &Dist)

template<typename T>
Distribution<T> operator+(T scalar, const Distribution<T> &Dist)

Add a Distribution to a scalar.

Template Parameters:

T – the data type of the scalar and Distribution.

Parameters:

• scalar – the scalar of type T to multiply by.

• Dist – The Distribution to multiply by.

Returns:

The resulting Distribution.

template<typename T>
Distribution<T> operator-(T scalar, const Distribution<T> &Dist)

Subtract a scalar by a Distribution.

Template Parameters:

T – the data type of the scalar and Distribution.

Parameters:

• scalar – the minuend of type T.

• Dist – The Distribution to subtract.

Returns:

The resulting Distribution.

template<typename T>
Distribution<T> operator*(T scalar, const Distribution<T> &Dist)

Multiply a scalar by a Distribution.

Template Parameters:

T – the data type of the scalar and the samples inDistribution.

Parameters:

• scalar – the multiplicand of type T.

• Dist – The Distribution to multiply by.

Returns:

The resulting Distribution

template<typename T>
Distribution<T> operator/(T scalar, const Distribution<T> &Dist)

Divide a scalar by a Distribution.

Template Parameters:

T – the data type of the scalar and the samples inDistribution.

Parameters:

• scalar – the dividend of type T.

• Dist – The Distribution to divide by.

Returns:

The resulting Distribution.

file RandomDistribution.h

#include “Distribution.h”

#include <random>

Functions

std::mt19937 default_rng(rd())

template<typename T, typename DT>
Distribution<T> RandomDistribution(DT dis, int _num_samples, std::mt19937 gen = default_rng)

Helper function to generate Distribution objects using sources of random numbers.

Template Parameters:

• T – the data type.

• DT – the type of dis.

Parameters:

• dis – a random number distribution (see <random>).

• _num_samples – the number of samples to generate.

• gen – the random seed (defaults to a random value).

Returns:

A Distribution containing the generated data.

template<typename T>
Distribution<T> Normal(T mu, T sigma, int _num_samples = 1000, std::mt19937 gen = default_rng)

Creates a normal Distribution of real numbers with mean mu and standard deviation sigma.

Template Parameters:

T – the data type. Must be float, double, or long double.

Parameters:

• mu – the mean of the distribution.

• b – the standard deviation of the distribution.

• _num_samples – the number of samples to generate (default 1000).

• gen – the random seed (defaults to a random value).

Returns:

A Distribution containing the generated data.

template<typename T>
Distribution<T> Uniform(T a, T b, int _num_samples = 1000, std::mt19937 gen = default_rng)

Creates a uniform Distribution of real numbers on the interval [a, b).

Template Parameters:

T – the data type. Must be float, double, or long double.

Parameters:

• a – the minimum of the distribution (inclusive).

• b – the maximum of the distribution (exclusive).

• _num_samples – the number of samples to generate (default 1000).

• gen – the random seed (defaults to a random value).

Returns:

A Distribution containing the generated data.

Variables

std::random_device rd

file README.md

file Tests.cpp

#include <cassert>

#include <iostream>

#include <sstream>

#include <string>

#include “../include/Distribution.h”

#include “../include/RandomDistribution.h”

Defines

assertm(exp, msg)

asserteq(a, b, msg)

Functions

std::mt19937 test_rng (0)

int main()

dir /home/runner/work/Distributions/Distributions/include

dir source

dir /home/runner/work/Distributions/Distributions/tests

page index

This is my final project for PHY 504 Spring 2024. This package implements a Distribution class that enables Monte Carlo error propagation by generating sample data from distributions and performing arithmetic or other functions on them element-wise.