randomnumbers.hpp File Reference

Set of functions to draw from (multivariate, correlated) normal distributions. More...

#include <vector>

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Functions
double	randn (double mean, double stdv)
	Draws from Gaussian \( \mathcal{N} (\mu,\sigma) \) (mean, standard deviation) using Box-Müller transform. More...
std::vector< double >	randn (std::vector< double > means, std::vector< double > stdv)
	Draws from uncorrelated Gaussians \( \mathcal{N} (\boldsymbol \mu,\boldsymbol{\sigma}) \) (vectors of mean, standard deviation) using Box-Müller transform. Loops over both vectors and calls randn(double mean, double stdv) every iteration. More...
std::vector< double >	randn (std::vector< double > stdv)
	Draws zero-mean samples from uncorrelated Gaussians \( \mathcal{N} (\boldsymbol 0,\boldsymbol{\sigma}) \) (standard deviation) using Box-Müller transform. Loops over both vectors and calls randn(double mean, double stdv) every iteration. More...
std::vector< double >	randn_Cholesky (std::vector< double > mean, std::vector< std::vector< double >> CholeskyLower_CovarianceMatrix)
	Drawing non-zero mean samples from an \( n \) dimensional correlated Gaussian. Invokes randn_Cholesky(std::vector<std::vector<double>> CholeskyLower_CovarianceMatrix) and adds mean. More...
std::vector< double >	randn_Cholesky (std::vector< std::vector< double >> CholeskyLower_CovarianceMatrix)
	Drawing non-zero mean samples from an \( n \) dimensional correlated Gaussian. This algorithm uses the lower Cholesky matrix of the (positive definite Hermitian) covariance matrix to transform (affine transform) n uncorrelated samples with standard deviation 1 to the right covariances. The mean is assumed zero. More...
std::vector< double >	randn (std::vector< std::vector< double >> DiagonalCovarianceMatrix)
	Drawing n zero mean samples from \( \mathcal{N} (\boldsymbol 0,\boldsymbol{\sigma}) \). No correlation is present between the parameters. More...
double	randf (double min, double max)
	Draw uniformly distributed samples between two numbers. More...

Variables
const double	PI = 3.14159265358979323846264338327

Detailed Description

Set of functions to draw from (multivariate, correlated) normal distributions.

This set of functions allows one to sample from mutliple types of normal distributions. All are based on a uniform number generator which transforms to normally distributed samples using the Box-Müller transform.

Definition in file randomnumbers.hpp.

Function Documentation

randf()

double randf	(	double	min,
		double	max
	)

Draw uniformly distributed samples between two numbers.

Parameters

min	Minimum of the distribution.
max	Maximum of the distribution.

Returns

Sample.

Definition at line 13 of file randomnumbers.cpp.

randn() [1/4]

double randn	(	double	mean,
		double	stdv
	)

Draws from Gaussian \( \mathcal{N} (\mu,\sigma) \) (mean, standard deviation) using Box-Müller transform.

Parameters

mean	double containing \( \mu \)
stdv	double containing \( \sigma \)

Returns

double, sample from the distribution

Definition at line 17 of file randomnumbers.cpp.

randn() [2/4]

std::vector<double> randn	(	std::vector< double >	means,
		std::vector< double >	stdv
	)

Draws from uncorrelated Gaussians \( \mathcal{N} (\boldsymbol \mu,\boldsymbol{\sigma}) \) (vectors of mean, standard deviation) using Box-Müller transform. Loops over both vectors and calls randn(double mean, double stdv) every iteration.

Parameters

mean	vector containing \( \mu_i \)
stdv	vector containing \( \sigma_i \)

Returns

Vector of samples from the distributions.

Definition at line 30 of file randomnumbers.cpp.

randn() [3/4]

std::vector<double> randn

(

std::vector< double >

stdv

)

Draws zero-mean samples from uncorrelated Gaussians \( \mathcal{N} (\boldsymbol 0,\boldsymbol{\sigma}) \) (standard deviation) using Box-Müller transform. Loops over both vectors and calls randn(double mean, double stdv) every iteration.

Parameters

stdv	vector containing \( \sigma_i \)

Returns

Vector of samples from the distributions.

Definition at line 36 of file randomnumbers.cpp.

randn() [4/4]

std::vector<double> randn

(

std::vector< std::vector< double >>

DiagonalCovarianceMatrix

)

Drawing n zero mean samples from \( \mathcal{N} (\boldsymbol 0,\boldsymbol{\sigma}) \). No correlation is present between the parameters.

Parameters

DiagonalCovarianceMatrix

Matrix containing on the diagonal the variance, or standard deviation squared.

Returns

Vector containing n samples.

Definition at line 62 of file randomnumbers.cpp.

randn_Cholesky() [1/2]

std::vector<double> randn_Cholesky	(	std::vector< double >	mean,
		std::vector< std::vector< double >>	CholeskyLower_CovarianceMatrix
	)

Drawing non-zero mean samples from an \( n \) dimensional correlated Gaussian. Invokes randn_Cholesky(std::vector<std::vector<double>> CholeskyLower_CovarianceMatrix) and adds mean.

Parameters

mean	vector containing \( n \) means.
CholeskyLower_CovarianceMatrix	Matrix containing the n x n Lower Cholesky matrix of the n x n covariance matrix \( \boldsymbol \Sigma \), must be square and lower triangular.

Returns

Vector containing the non-zero mean correlated samples.

Definition at line 47 of file randomnumbers.cpp.

randn_Cholesky() [2/2]

std::vector<double> randn_Cholesky

(

std::vector< std::vector< double >>

CholeskyLower_CovarianceMatrix

)

Drawing non-zero mean samples from an \( n \) dimensional correlated Gaussian. This algorithm uses the lower Cholesky matrix of the (positive definite Hermitian) covariance matrix to transform (affine transform) n uncorrelated samples with standard deviation 1 to the right covariances. The mean is assumed zero.

Parameters

CholeskyLower_CovarianceMatrix

Matrix containing the n x n Lower Cholesky matrix of the n x n covariance matrix \( \boldsymbol \Sigma \), must be square and lower triangular.

Returns

Vector containing the zero mean correlated samples.

Definition at line 51 of file randomnumbers.cpp.

Variable Documentation

PI

const double PI = 3.14159265358979323846264338327

Definition at line 18 of file randomnumbers.hpp.