#include "open_iA_Core_export.h"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstddef>
#include <limits>
#include <numeric>
#include <vector>

Include dependency graph for iAMathUtility.h:

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Typedefs
typedef std::vector< double >	FuncType

Functions
template<typename T >
T	clamp (T const min, T const max, T const value)
	Make sure the given value is inside the given range. More...

open_iA_Core_API double	covariance (FuncType const &func1, FuncType const &func2, double mean1=std::numeric_limits< double >::infinity(), double mean2=std::numeric_limits< double >::infinity(), bool correctDF=true)
	Compute covariance between two functions. More...

template<typename RealType >
bool	dblApproxEqual (RealType a, RealType b, RealType tolerance=std::numeric_limits< RealType >::epsilon())
	Checks whether two real values are equal, given a certain tolerance. More...

open_iA_Core_API FuncType	derivative (FuncType const &func)
	Calculate first derivative of a given function. More...

open_iA_Core_API double	gaussian (double x, double sigma)
	Compute Gaussian function for the given value x and parameter sigma (mean = 0). More...

open_iA_Core_API FuncType	gaussianKernel (double kernelSigma, size_t kernelSteps)
	Compute a gaussian kernel with the given sigma (mean = 0). More...

open_iA_Core_API FuncType	gaussianSmoothing (FuncType const &data, double kernelSigma, int kernelSteps)
	Convolutes the given function with a Gaussian kernel with the given sigma and steps. More...

open_iA_Core_API FuncType	getNormedRanks (FuncType const &func)
	Compute ranks for a given list of values. More...

template<typename T >
T	invertValue (T const *range, T const value)
	Invert value in a given range. More...

template<typename T >
T	linterp (const T a, const T b, const T t)
	Linear interpolation in a given range. More...

template<typename DstType >
DstType	mapNormTo (DstType minDstVal, DstType maxDstVal, double norm)
	Map value from "norm" range [0..1] to the given range. More...

template<typename T >
T	mapToNorm (const T *range, const T value)
	Map values from a given range to the "normalized" range [0..1]. More...

template<typename SrcType >
double	mapToNorm (SrcType const minSrcVal, SrcType const maxSrcVal, SrcType const value)
	map value from given interval to "norm" interval [0..1] if min is bigger than max, a reverse mapping is applied More...

template<typename SrcType , typename DstType >
DstType	mapValue (SrcType minSrcVal, SrcType maxSrcVal, DstType minDstVal, DstType maxDstVal, SrcType value)
	Map value from one range to another. More...

template<typename T >
T	mapValue (T const rangeSrc, T const rangeDst, T const value)
	Map value from one range to another. More...

open_iA_Core_API double	mean (FuncType const &func)
	Compute the mean of a function. More...

template<typename SrcType >
double	minMaxNormalize (SrcType const minSrcVal, SrcType const maxSrcVal, SrcType const value)
	apply minmax normalization if min is bigger than max, a reverse mapping is applied More...

template<typename SrcType >
double	normalizedToMinMax (SrcType const minSrcVal, SrcType const maxSrcVal, SrcType const value)

open_iA_Core_API double	pearsonsCorrelationCoefficient (FuncType const &func1, FuncType const &func2)
	Calculate the Pearson's correlation coefficient between two functions. More...

template<typename T >
T	round (T const &number)
	Round a number to the nearest integer representation (by "round half away from zero" method). More...

template<typename T >
std::vector< size_t >	sort_indexes (const std::vector< T > &v)

open_iA_Core_API double	spearmansCorrelationCoefficient (FuncType const &func1, FuncType const &func2)
	Calculate the Spearman's correlation coefficient between two functions. More...

open_iA_Core_API double	standardDeviation (FuncType const &func, double meanVal=std::numeric_limits< double >::infinity(), bool correctDF=true)
	Compute the standard deviation of a function. mean can be given (to improve speed). More...

open_iA_Core_API double	variance (FuncType const &func, double meanVal=std::numeric_limits< double >::infinity(), bool correctDF=true)
	Compute the variation of a function. If known, mean can be given (to improve speed). More...

Typedef Documentation

◆ FuncType

typedef std::vector<double> FuncType

Function Documentation

◆ clamp()

template<typename T >

T clamp	(	T const	min,
		T const	max,
		T const	value
	)

Make sure the given value is inside the given range.

Parameters

min	the minimum value which should be returned
max	the maximum value which should be returned
value	the value to check

Returns: min if the given value is smaller or equal to min, max if the given value is bigger or equal to max, or the value itself if it is in between min and max

◆ covariance()

open_iA_Core_API double covariance	(	FuncType const &	func1,
		FuncType const &	func2,
		double	mean1 = `std::numeric_limits< double >::infinity()`,
		double	mean2 = `std::numeric_limits< double >::infinity()`,
		bool	correctDF = `true`
	)

Compute covariance between two functions.

◆ dblApproxEqual()

template<typename RealType >

bool dblApproxEqual	(	RealType	a,
		RealType	b,
		RealType	tolerance = `std::numeric_limits<RealType>::epsilon()`
	)

Checks whether two real values are equal, given a certain tolerance.

inspired by https://stackoverflow.com/a/41405501/671366

◆ derivative()

open_iA_Core_API FuncType derivative ( FuncType const & func )

Calculate first derivative of a given function.

◆ gaussian()

open_iA_Core_API double gaussian	(	double	x,
		double	sigma
	)

Compute Gaussian function for the given value x and parameter sigma (mean = 0).

◆ gaussianKernel()

open_iA_Core_API FuncType gaussianKernel	(	double	kernelSigma,
		size_t	kernelSteps
	)

Compute a gaussian kernel with the given sigma (mean = 0).

◆ gaussianSmoothing()

open_iA_Core_API FuncType gaussianSmoothing	(	FuncType const &	data,
		double	kernelSigma,
		int	kernelSteps
	)

Convolutes the given function with a Gaussian kernel with the given sigma and steps.

TODO: number of steps could be calculated from sigma (cut off kernel when factor gets very small)

◆ getNormedRanks()

open_iA_Core_API FuncType getNormedRanks ( FuncType const & func )

Compute ranks for a given list of values.

◆ invertValue()

template<typename T >

T invertValue	(	T const *	range,
		T const	value
	)

Invert value in a given range.

Example: invertValue(range=[0, 1], value=0.2) = 0.8; invertValue(range=[1,2], value=1.3) = 1.7

Parameters

range	an array of size 2 with minimum and maximum value of the range
value	the value to be inverted.

Returns: the inverted value

◆ linterp()

template<typename T >

T linterp	(	const T	a,
		const T	b,
		const T	t
	)

inline

Linear interpolation in a given range.

Parameters

a	minimum of the interpolation range
b	maximum of the interpolation range
t	a value from the range [0..1] specifying the interpolation position

◆ mapNormTo()

template<typename DstType >

DstType mapNormTo	(	DstType	minDstVal,
		DstType	maxDstVal,
		double	norm
	)

Map value from "norm" range [0..1] to the given range.

Parameters

minDstVal	minimum value of destination range
maxDstVal	maximum value of destination range
norm	a value in range [0..1]

Returns: if norm was in [0..1], the corresponding mapped value in range [minDstVal..maxDstVal]

◆ mapToNorm() [1/2]

template<typename T >

T mapToNorm	(	const T *	range,
		const T	value
	)

inline

Map values from a given range to the "normalized" range [0..1].

if min is bigger than max, a reverse mapping is applied

Parameters

range	an array of size 2 with minimum and maximum value of the source range
value	the value to be mapped from the source range to the destination range

Returns: the mapped value; in case the given value is outside given min/max, the value will still be clamped to the range [0..1]

◆ mapToNorm() [2/2]

template<typename SrcType >

double mapToNorm	(	SrcType const	minSrcVal,
		SrcType const	maxSrcVal,
		SrcType const	value
	)

map value from given interval to "norm" interval [0..1] if min is bigger than max, a reverse mapping is applied

Parameters

minSrcVal	minimum value of source interval
maxSrcVal	maximum value of source interval
value	a value in source interval

Returns: if norm was in interval [minSrcVal..maxSrcVal], the corresponding mapped value in interval [0..1]

◆ mapValue() [1/2]

template<typename SrcType , typename DstType >

DstType mapValue	(	SrcType	minSrcVal,
		SrcType	maxSrcVal,
		DstType	minDstVal,
		DstType	maxDstVal,
		SrcType	value
	)

Map value from one range to another.

Parameters

minSrcVal	minimum value of source range
maxSrcVal	maximum value of source range
minDstVal	minimum value of destination range
maxDstVal	maximum value of destination range
value	the value to be mapped from the source range to the destination range

Returns: if value was in range [minSrcVal..maxSrcVal], the corresponding mapped value in range [minDstVal..maxDstVal]

◆ mapValue() [2/2]

template<typename T >

T mapValue	(	T const *	rangeSrc,
		T const *	rangeDst,
		T const	value
	)

inline

Map value from one range to another.

Parameters

rangeSrc	an array of size 2 with minimum and maximum value of the source range
rangeDst	an array of size 2 with minimum and maximum value of the destination range
value	the value to be mapped from the source range to the destination range

Returns: if value was in range [minSrcVal..maxSrcVal], the corresponding mapped value in range [minDstVal..maxDstVal]

◆ mean()

open_iA_Core_API double mean ( FuncType const & func )

Compute the mean of a function.

◆ minMaxNormalize()

template<typename SrcType >

double minMaxNormalize	(	SrcType const	minSrcVal,
		SrcType const	maxSrcVal,
		SrcType const	value
	)

apply minmax normalization if min is bigger than max, a reverse mapping is applied

Parameters

minSrcVal	minimum value of source interval
maxSrcVal	maximum value of source interval
value	a value in source interval

Returns: the corresponding mapped value = (value - minSrcVal) / (maxSrcVal - minSrcVal)

◆ normalizedToMinMax()

template<typename SrcType >

double normalizedToMinMax	(	SrcType const	minSrcVal,
		SrcType const	maxSrcVal,
		SrcType const	value
	)

◆ pearsonsCorrelationCoefficient()

open_iA_Core_API double pearsonsCorrelationCoefficient	(	FuncType const &	func1,
		FuncType const &	func2
	)

Calculate the Pearson's correlation coefficient between two functions.

◆ round()

template<typename T >

T round ( T const & number )

Round a number to the nearest integer representation (by "round half away from zero" method).

Parameters

number the number to round

Returns: the rounded number

◆ sort_indexes()

template<typename T >

std::vector<size_t> sort_indexes ( const std::vector< T > & v )

◆ spearmansCorrelationCoefficient()

open_iA_Core_API double spearmansCorrelationCoefficient	(	FuncType const &	func1,
		FuncType const &	func2
	)

Calculate the Spearman's correlation coefficient between two functions.

◆ standardDeviation()

open_iA_Core_API double standardDeviation	(	FuncType const &	func,
		double	meanVal = `std::numeric_limits< double >::infinity()`,
		bool	correctDF = `true`
	)

Compute the standard deviation of a function. mean can be given (to improve speed).

◆ variance()

open_iA_Core_API double variance	(	FuncType const &	func,
		double	meanVal = `std::numeric_limits< double >::infinity()`,
		bool	correctDF = `true`
	)

Compute the variation of a function. If known, mean can be given (to improve speed).

Typedefs

Functions

Typedef Documentation

◆ FuncType

Function Documentation

◆ clamp()

◆ covariance()

◆ dblApproxEqual()

◆ derivative()

◆ gaussian()

◆ gaussianKernel()

◆ gaussianSmoothing()

◆ getNormedRanks()

◆ invertValue()

◆ linterp()

◆ mapNormTo()

◆ mapToNorm() [1/2]

◆ mapToNorm() [2/2]

◆ mapValue() [1/2]

◆ mapValue() [2/2]

◆ mean()

◆ minMaxNormalize()

◆ normalizedToMinMax()

◆ pearsonsCorrelationCoefficient()

◆ round()

◆ sort_indexes()

◆ spearmansCorrelationCoefficient()

◆ standardDeviation()

◆ variance()