MathTools Namespace Reference

Functions
template<class T >
int	roundToInteger (T x)
	Round a floating point number to an integer. More...
double	computeMoment (const std::vector< double > &v, const int n)
	Determine the n-th moment of a distribution stored in a vector. More...
void	normalize (std::vector< double > &vec)
	Normalize a distribution stored in a vector. More...
double	computeNorm (std::vector< double > &vec)
	Compute the norm of a vector. More...
void	coarseGrainSpectrum (const std::vector< double > &X, std::vector< double > &Y, std::function< double(double y)> f, double exponent=0)
double	computeEntropy (const std::vector< double > &v)
	Compute the Shannon entropy of a normalized probability distribution. More...
double	computeRenyiEntropy (const std::vector< double > &v, const double q)
	Compute the Renyi entropy of a normalized probability distribution. More...
int	findMaximum (const std::vector< double > &X, int i, int j)
	Find the component where the vector has its maximum. More...
int	findMaximum (const std::vector< double > &X)
double	findSmoothedMaximum (const std::vector< double > &x)
	Use a parabola to fit the maximum. More...
double	weightedArithmetricMean (const std::vector< double > &Y, size_t start=0, size_t end=std::numeric_limits< size_t >::max())
	Computes the weighted arithmetric mean index of the given Y data. More...
double	restrictToInterval (double x, double xmin, double xmax)
	Restrict floating point value to an interval. More...
template<typename T >
void	transformVector (const std::vector< T > &v, std::vector< T > &w, std::function< T(T)> f)
	Map a vector to a different one by a unary map. More...
template<typename T >
std::vector< T >	transformVector (const std::vector< T > &v, std::function< T(T)> f)

Variables
const double	PI = 3.14159265358979323846
const double	TWO_PI = 2 * PI
const double	LOG2 = 0.69314718055994530942

Function Documentation

void MathTools::coarseGrainSpectrum	(	const std::vector< double > &	X,
		std::vector< double > &	Y,
		std::function< double(double y)>	f,
		double	exponent = 0
	)

Map a distribution in the vector X[x] to another vector Y[y] by means of a (possibly nonlinear) function x=f(y).

It is assumed that the vector Y[y] has already a given size. If the function f maps the index range of Y to a superset of the index range of X, then the map preserves the sum over all components. Therefore, the map is suitable for mapping probability distributions. If the function f maps indices in the range of Y to a subset of the index range of X, i.e., if it does not read all of X, the corresponding probability is lost.

Parameters

X	: Given vector of floating point values (probabilities)
Y	: Target vector of a given size.
f	: Function used for coarse-graining
exponent	: exponent used for the mapping

Definition at line 120 of file mathtools.cpp.

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double MathTools::computeEntropy

(

const std::vector< double > &

v

)

Compute the Shannon entropy of a normalized probability distribution.

Definition at line 56 of file mathtools.cpp.

double MathTools::computeMoment	(	const std::vector< double > &	v,
		const int	n
	)

Determine the n-th moment of a distribution stored in a vector.

The moments are determined with respect to the relative array index between 0 and 1

Definition at line 38 of file mathtools.cpp.

double MathTools::computeNorm

(

std::vector< double > &

vec

)

Compute the norm of a vector.

Definition at line 82 of file mathtools.cpp.

double MathTools::computeRenyiEntropy	(	const std::vector< double > &	v,
		const double	q
	)

Compute the Renyi entropy of a normalized probability distribution.

Definition at line 69 of file mathtools.cpp.

int MathTools::findMaximum	(	const std::vector< double > &	X,
		int	i,
		int	j
	)

Find the component where the vector has its maximum.

Find the index of the maximum in a real-valued vector in the index range from i...j-1.

Returns

Index where the maximum is located.

Definition at line 151 of file mathtools.cpp.

int MathTools::findMaximum

(

const std::vector< double > &

X

)

Definition at line 159 of file mathtools.cpp.

double MathTools::findSmoothedMaximum

(

const std::vector< double > &

x

)

Use a parabola to fit the maximum.

Definition at line 164 of file mathtools.cpp.

void MathTools::normalize

(

std::vector< double > &

vec

)

Normalize a distribution stored in a vector.

Definition at line 92 of file mathtools.cpp.

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double MathTools::restrictToInterval	(	double	x,
		double	xmin,
		double	xmax
	)

Restrict floating point value to an interval.

Definition at line 196 of file mathtools.cpp.

template<class T >

int MathTools::roundToInteger

(

T

x

)

Round a floating point number to an integer.

Definition at line 43 of file mathtools.h.

template<typename T >

void MathTools::transformVector	(	const std::vector< T > &	v,
		std::vector< T > &	w,
		std::function< T(T)>	f
	)

Map a vector to a different one by a unary map.

Definition at line 82 of file mathtools.h.

template<typename T >

std::vector<T> MathTools::transformVector	(	const std::vector< T > &	v,
		std::function< T(T)>	f
	)

Definition at line 87 of file mathtools.h.

double MathTools::weightedArithmetricMean	(	const std::vector< double > &	Y,
		size_t	start = 0,
		size_t	end = std::numeric_limits<size_t>::max()
	)

Computes the weighted arithmetric mean index of the given Y data.

Definition at line 178 of file mathtools.cpp.

Variable Documentation

const double MathTools::LOG2 = 0.69314718055994530942

Definition at line 39 of file mathtools.h.

const double MathTools::PI = 3.14159265358979323846

Definition at line 37 of file mathtools.h.

const double MathTools::TWO_PI = 2 * PI

Definition at line 38 of file mathtools.h.