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

Typedefs
typedef std::vector< double >	FuncType

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

template<typename T >
void	computeMinMax (T minVal, T maxVal, T const val1, T const val2, T const *size, int numVal)
	for numVal entries in two arrays, compute component-wise minimum and maximum

iAbase_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.

template<typename OutContainerT = QVector<double>, typename ValueT = double, typename InContainerT >
OutContainerT	createHistogram (const InContainerT &inData, typename OutContainerT::size_type binCount, ValueT &minValue, ValueT &maxValue, bool discrete=false)
	compute histogram from given values

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.

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

template<typename T >
T	frac (T val)
	Compute the fractional part of a floating-point type.

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

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

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

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

template<typename T >
bool	inRange (T const *range, T const value)
	Check whether a value is in a given range.

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

template<typename T1 , typename T2 >
bool	isApproxEqual (T1 a, T2 b, T1 tolerance=std::numeric_limits< T1 >::epsilon())
	comparison of two real type values - merge with above!

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

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

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

template<typename SrcType >
double	mapToNorm (SrcType const minSrcVal, SrcType const maxSrcVal, SrcType const value)
	Map value from given interval to "norm" interval [0..1].

template<typename SrcType >
double	mapToNormNoClamp (SrcType const minSrcVal, SrcType const maxSrcVal, SrcType const value)
	Map value from given interval to "norm" interval [0..1].

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

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

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

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

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

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

iAbase_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).

iAbase_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).

Typedef Documentation

◆ FuncType

typedef std::vector<double> FuncType

Function Documentation

◆ clamp()

template<typename T >

T clamp	(	T const	minVal,
		T const	maxVal,
		T const	value
	)

Make sure the given value is inside the given range.

Parameters

minVal	the minimum value which should be returned
maxVal	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

◆ computeMinMax()

template<typename T >

void computeMinMax	(	T *	minVal,
		T *	maxVal,
		T const *	val1,
		T const *	val2,
		T const *	size,
		int	numVal
	)

for numVal entries in two arrays, compute component-wise minimum and maximum

Parameters

minVal	array with numVal entries, will hold the minimum value for each component in given val1/val2 array
maxVal	array with numVal entries, will hold the maximum value for each component in given val1/val2 array
val1	array with numVal entries
val2	array with numVal entries
size
numVal	number of values in minVal, maxVal, val1, val2, and size

◆ covariance()

iAbase_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.

◆ createHistogram()

template<typename OutContainerT = QVector<double>, typename ValueT = double, typename InContainerT >

OutContainerT createHistogram	(	const InContainerT &	inData,
		typename OutContainerT::size_type	binCount,
		ValueT &	minValue,
		ValueT &	maxValue,
		bool	discrete = `false`
	)

compute histogram from given values

◆ 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 great points about floating point equals at https://stackoverflow.com/a/41405501

◆ derivative()

iAbase_API FuncType derivative ( FuncType const & func )

Calculate first derivative of a given function.

◆ frac()

template<typename T >

T frac ( T val )

Compute the fractional part of a floating-point type.

◆ gaussian()

iAbase_API double gaussian	(	double	x,
		double	sigma
	)

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

◆ gaussianKernel()

iAbase_API FuncType gaussianKernel	(	double	kernelSigma,
		size_t	kernelSteps
	)

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

◆ gaussianSmoothing()

iAbase_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()

iAbase_API FuncType getNormedRanks ( FuncType const & func )

Compute ranks for a given list of values.

◆ inRange()

template<typename T >

bool inRange	(	T const *	range,
		T const	value
	)

Check whether a value is in a given range.

Parameters

range	the range given as minimum (stored at index 0) and maximum (stored at index 1)
value	the value to be checked. return true if value in range (bounds included, i.e. returns true if equal to minimum or maximum), false otherwise

◆ 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

◆ isApproxEqual()

template<typename T1 , typename T2 >

bool isApproxEqual	(	T1	a,
		T2	b,
		T1	tolerance = `std::numeric_limits<T1>::epsilon()`
	)

comparison of two real type values - merge with above!

◆ linterp()

template<typename T >

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

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: the corresponding mapped value in interval [0..1] (0 if input value < minSrcVal, 1 if input value > maxSrcVal)

◆ mapToNormNoClamp()

template<typename SrcType >

double mapToNormNoClamp	(	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: the corresponding mapped value = (value - minSrcVal) / (maxSrcVal - minSrcVal) Note that if the input value is not between minSrcVal and maxSrcVal, the return value is NOT guaranteed to be in the interval 0..1. If you require the return value to be in that interval, use mapToNorm instead!

◆ mapValue() [1/2]

template<typename SrcType , typename DstType >

DstType mapValue	(	SrcType const *	rangeSrc,
		DstType const *	rangeDst,
		SrcType 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]

◆ mapValue() [2/2]

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]

◆ mean()

iAbase_API double mean ( FuncType const & func )

Compute the mean of a function.

◆ pearsonsCorrelationCoefficient()

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

Calculate the Pearson's correlation coefficient between two functions.

◆ sort_indexes()

template<typename T >

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

◆ spearmansCorrelationCoefficient()

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

Calculate the Spearman's correlation coefficient between two functions.

◆ standardDeviation()

iAbase_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()

iAbase_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()

◆ computeMinMax()

◆ covariance()

◆ createHistogram()

◆ dblApproxEqual()

◆ derivative()

◆ frac()

◆ gaussian()

◆ gaussianKernel()

◆ gaussianSmoothing()

◆ getNormedRanks()

◆ inRange()

◆ invertValue()

◆ isApproxEqual()

◆ linterp()

◆ mapNormTo()

◆ mapToNorm() [1/2]

◆ mapToNorm() [2/2]

◆ mapToNormNoClamp()

◆ mapValue() [1/2]

◆ mapValue() [2/2]

◆ mean()

◆ pearsonsCorrelationCoefficient()

◆ sort_indexes()

◆ spearmansCorrelationCoefficient()

◆ standardDeviation()

◆ variance()