Basic mathematics functions. More...

#include <cmath>
#include <list>
#include <vector>

Include dependency graph for UMath.h:

Enumerations
enum	UXMatchMethod { UXCorrRaw, UXCorrBiased, UXCorrUnbiased, UXCorrCoeff, UXCovRaw, UXCovBiased, UXCovUnbiased, UXCovCoeff }

Functions
std::vector< float >	uHamming (unsigned int L)

template<class T >
bool	uIsFinite (const T &value)

template<typename T >
bool	uIsInBounds (const T &value, const T &low, const T &high)

template<class T >
bool	uIsNan (const T &value)

template<class T >
std::list< unsigned int >	uLocalMaxima (const std::vector< T > &v)

template<class T >
std::list< unsigned int >	uLocalMaxima (const T *v, unsigned int size)

template<class T >
T	uMax (const std::vector< T > &v)

template<class T >
T	uMax (const std::vector< T > &v, unsigned int &index)

template<class T >
T	uMax (const T *v, unsigned int size)

template<class T >
T	uMax (const T *v, unsigned int size, unsigned int &index)

template<class T >
T	uMax3 (const T &a, const T &b, const T &c)

template<class T >
T	uMean (const std::list< T > &list)

template<class T >
T	uMean (const std::vector< T > &v)

template<class T >
T	uMean (const T *v, unsigned int size)

template<class T >
T	uMeanSquaredError (const std::vector< T > &x, const std::vector< T > &y)

template<class T >
T	uMeanSquaredError (const T x, unsigned int sizeX, const T y, unsigned int sizeY)

template<class T >
T	uMin (const std::vector< T > &v)

template<class T >
T	uMin (const std::vector< T > &v, unsigned int &index)

template<class T >
T	uMin (const T *v, unsigned int size)

template<class T >
T	uMin (const T *v, unsigned int size, unsigned int &index)

template<class T >
T	uMin3 (const T &a, const T &b, const T &c)

template<class T >
void	uMinMax (const std::vector< T > &v, T &min, T &max)

template<class T >
void	uMinMax (const std::vector< T > &v, T &min, T &max, unsigned int &indexMin, unsigned int &indexMax)

template<class T >
void	uMinMax (const T *v, unsigned int size, T &min, T &max)

template<class T >
void	uMinMax (const T *v, unsigned int size, T &min, T &max, unsigned int &indexMin, unsigned int &indexMax)

template<class T >
T	uNorm (const std::vector< T > &v)

template<class T >
T	uNorm (const T &x1, const T &x2)

template<class T >
T	uNorm (const T &x1, const T &x2, const T &x3)

template<class T >
std::vector< T >	uNormalize (const std::vector< T > &v)

template<class T >
T	uNormSquared (const std::vector< T > &v)

template<class T >
T	uNormSquared (const T &x1, const T &x2)

template<class T >
T	uNormSquared (const T &x1, const T &x2, const T &x3)

template<class T >
int	uSign (const T &v)

template<class T >
T	uSum (const std::list< T > &list)

template<class T >
T	uSum (const std::vector< T > &v)

template<class T >
T	uSum (const T *v, unsigned int size)

template<class T >
T	uSumSquared (const std::vector< T > &v, T subtract=T())

template<class T >
T	uSumSquared (const T *v, unsigned int size, T subtract=T())

template<class T >
T	uVariance (const std::list< T > &list, const T &m)

template<class T >
T	uVariance (const std::vector< T > &v, const T &m)

template<class T >
T	uVariance (const T *v, unsigned int size)

template<class T >
T	uVariance (const T *v, unsigned int size, T meanV)

template<class T >
T	uXMatch (const std::vector< T > &vA, const std::vector< T > &vB, unsigned int index, UXMatchMethod method)

template<class T >
std::vector< T >	uXMatch (const std::vector< T > &vA, const std::vector< T > &vB, UXMatchMethod method)

template<class T >
T	uXMatch (const T vA, const T vB, unsigned int sizeA, unsigned int sizeB, unsigned int index, UXMatchMethod method)

template<class T >
std::vector< T >	uXMatch (const T vA, const T vB, unsigned int sizeA, unsigned int sizeB, UXMatchMethod method)

Detailed Description

Basic mathematics functions.

Definition in file UMath.h.

Enumeration Type Documentation

◆ UXMatchMethod

enum UXMatchMethod

Enum of cross matching methods (cross-correlation, cross-covariance) : UXCorrRaw, UXCorrBiased, UXCorrUnbiased, UXCorrCoeff, UXCovRaw, UXCovBiased, UXCovUnbiased, UXCovCoeff.

Enumerator
UXCorrRaw
UXCorrBiased
UXCorrUnbiased
UXCorrCoeff
UXCovRaw
UXCovBiased
UXCovUnbiased
UXCovCoeff

Definition at line 696 of file UMath.h.

Function Documentation

◆ uHamming()

std::vector<float> uHamming ( unsigned int L )

inline

Return Hamming window of length L.

Parameters

L	the window length

Returns: the Hamming window (values are between 0 and 1)

Definition at line 919 of file UMath.h.

◆ uIsFinite()

template<class T >

bool uIsFinite ( const T & value )

inline

Return true if the number is finite.

Definition at line 53 of file UMath.h.

◆ uIsInBounds()

template<typename T >

bool uIsInBounds	(	const T &	value,
		const T &	low,
		const T &	high
	)

Definition at line 932 of file UMath.h.

◆ uIsNan()

template<class T >

bool uIsNan ( const T & value )

inline

Return true if the number is NAN.

Definition at line 40 of file UMath.h.

◆ uLocalMaxima() [1/2]

template<class T >

std::list<unsigned int> uLocalMaxima ( const std::vector< T > & v )

inline

Find all local maxima.

Definition at line 687 of file UMath.h.

◆ uLocalMaxima() [2/2]

template<class T >

std::list<unsigned int> uLocalMaxima	(	const T *	v,
		unsigned int	size
	)

inline

Find all local maxima.

Definition at line 645 of file UMath.h.

◆ uMax() [1/4]

template<class T >

T uMax ( const std::vector< T > & v )

inline

Get the maximum of a vector.

Parameters

v the array

Returns: the maximum value of the array

Definition at line 144 of file UMath.h.

◆ uMax() [2/4]

template<class T >

T uMax	(	const std::vector< T > &	v,
		unsigned int &	index
	)

inline

Get the maximum of a vector.

Parameters

v	the array
index	the index of the maximum value in the vector.

Returns: the maximum value of the array

Definition at line 120 of file UMath.h.

◆ uMax() [3/4]

template<class T >

T uMax	(	const T *	v,
		unsigned int	size
	)

inline

Get the maximum of a vector.

Parameters

v	the array
size	the size of the array

Returns: the maximum value of the array

Definition at line 132 of file UMath.h.

◆ uMax() [4/4]

template<class T >

T uMax	(	const T *	v,
		unsigned int	size,
		unsigned int &	index
	)

inline

Get the maximum of a vector.

Parameters

v	the array
size	the size of the array
index	the index of the maximum value in the vector.

Returns: the maximum value of the array

Definition at line 92 of file UMath.h.

◆ uMax3()

template<class T >

T uMax3	(	const T &	a,
		const T &	b,
		const T &	c
	)

inline

Get the maximum of the 3 values.

Returns: the maximum value

Definition at line 78 of file UMath.h.

◆ uMean() [1/3]

template<class T >

T uMean ( const std::list< T > & list )

inline

Get the mean of a list. Provided for convenience.

Parameters

list the list

Returns: the mean

Definition at line 419 of file UMath.h.

◆ uMean() [2/3]

template<class T >

T uMean ( const std::vector< T > & v )

inline

Get the mean of a vector. Provided for convenience.

Parameters

v	the vector

Returns: the mean

Definition at line 439 of file UMath.h.

◆ uMean() [3/3]

template<class T >

T uMean	(	const T *	v,
		unsigned int	size
	)

inline

Compute the mean of an array.

Parameters

v	the array
size	the size of the array

Returns: the mean

Definition at line 399 of file UMath.h.

◆ uMeanSquaredError() [1/2]

template<class T >

T uMeanSquaredError	(	const std::vector< T > &	x,
		const std::vector< T > &	y
	)

inline

Compute mean squared error between two arrays: mean((x-y).^2).

Parameters

x	the first array
y	the second array (must be same size as x)

Returns: the mean squared error (return -1 if error cannot be computed)

Definition at line 475 of file UMath.h.

◆ uMeanSquaredError() [2/2]

template<class T >

T uMeanSquaredError	(	const T *	x,
		unsigned int	sizeX,
		const T *	y,
		unsigned int	sizeY
	)

inline

Compute mean squared error between two arrays: mean((x-y).^2).

Parameters

x	the first array
sizeX	the size of the array x
y	the second array
sizeY	the size of the array y (must be same size as x)

Returns: the mean squared error (return -1 if error cannot be computed)

Definition at line 453 of file UMath.h.

◆ uMin() [1/4]

template<class T >

T uMin ( const std::vector< T > & v )

inline

Get the minimum of a vector.

Parameters

v the array

Returns: the minimum value of the array

Definition at line 209 of file UMath.h.

◆ uMin() [2/4]

template<class T >

T uMin	(	const std::vector< T > &	v,
		unsigned int &	index
	)

inline

Get the minimum of a vector.

Parameters

v	the array
index	the index of the minimum value in the vector.

Returns: the minimum value of the array

Definition at line 185 of file UMath.h.

◆ uMin() [3/4]

template<class T >

T uMin	(	const T *	v,
		unsigned int	size
	)

inline

Get the minimum of a vector.

Parameters

v	the array
size	the size of the array

Returns: the minimum value of the array

Definition at line 197 of file UMath.h.

◆ uMin() [4/4]

template<class T >

T uMin	(	const T *	v,
		unsigned int	size,
		unsigned int &	index
	)

inline

Get the minimum of a vector.

Parameters

v	the array
size	the size of the array
index	the index of the minimum value in the vector.

Returns: the minimum value of the array

Definition at line 157 of file UMath.h.

◆ uMin3()

template<class T >

T uMin3	(	const T &	a,
		const T &	b,
		const T &	c
	)

inline

Get the minimum of the 3 values.

Returns: the minimum value

Definition at line 67 of file UMath.h.

◆ uMinMax() [1/4]

template<class T >

void uMinMax	(	const std::vector< T > &	v,
		T &	min,
		T &	max
	)

inline

Get the minimum and maximum of a vector.

Parameters

v	the array
min	reference to output minimum
max	reference to output maximum

Definition at line 289 of file UMath.h.

◆ uMinMax() [2/4]

template<class T >

void uMinMax	(	const std::vector< T > &	v,
		T &	min,
		T &	max,
		unsigned int &	indexMin,
		unsigned int &	indexMax
	)

inline

Get the minimum and maximum of a vector.

Parameters

v	the array
min	reference to output minimum
max	reference to output maximum
min	reference to output minimum index
max	reference to output maximum index

Definition at line 262 of file UMath.h.

◆ uMinMax() [3/4]

template<class T >

void uMinMax	(	const T *	v,
		unsigned int	size,
		T &	min,
		T &	max
	)

inline

Get the minimum and maximum of a vector.

Parameters

v	the array
size	the size of the array
min	reference to output minimum
max	reference to output maximum

Definition at line 275 of file UMath.h.

◆ uMinMax() [4/4]

template<class T >

void uMinMax	(	const T *	v,
		unsigned int	size,
		T &	min,
		T &	max,
		unsigned int &	indexMin,
		unsigned int &	indexMax
	)

inline

Get the minimum and maximum of a vector.

Parameters

v	the array
size	the size of the array
min	reference to output minimum
max	reference to output maximum
min	reference to output minimum index
max	reference to output maximum index

Definition at line 224 of file UMath.h.

◆ uNorm() [1/3]

template<class T >

T uNorm ( const std::vector< T > & v )

inline

Get the norm of the vector : return sqrt(x1*x1 + x2*x2 + x3*x3 + ...)

Returns: the norm of the vector

Definition at line 573 of file UMath.h.

◆ uNorm() [2/3]

template<class T >

T uNorm	(	const T &	x1,
		const T &	x2
	)

inline

Get the norm of the vector : return sqrt(x1*x1 + x2*x2 + x3*x3)

Returns: the norm of the vector

Definition at line 593 of file UMath.h.

◆ uNorm() [3/3]

template<class T >

T uNorm	(	const T &	x1,
		const T &	x2,
		const T &	x3
	)

inline

Get the norm of the vector : return sqrt(x1*x1 + x2*x2 + x3*x3)

Returns: the norm of the vector

Definition at line 613 of file UMath.h.

◆ uNormalize()

template<class T >

std::vector<T> uNormalize ( const std::vector< T > & v )

inline

Normalize the vector : [x1 x2 x3 ...] ./ uNorm([x1 x2 x3 ...])

Returns: the vector normalized

Definition at line 623 of file UMath.h.

◆ uNormSquared() [1/3]

template<class T >

T uNormSquared ( const std::vector< T > & v )

inline

Get the squared norm of the vector : return x1*x1 + x2*x2 + x3*x3 + ...

Returns: the squared norm of the vector

Definition at line 558 of file UMath.h.

◆ uNormSquared() [2/3]

template<class T >

T uNormSquared	(	const T &	x1,
		const T &	x2
	)

inline

Get the squared norm of the vector : return x1*x1 + x2*x2

Returns: the squared norm of the vector

Definition at line 583 of file UMath.h.

◆ uNormSquared() [3/3]

template<class T >

T uNormSquared	(	const T &	x1,
		const T &	x2,
		const T &	x3
	)

inline

Get the squared norm of the vector : return x1*x1 + x2*x2 + x3*x3

Returns: the squared norm of the vector

Definition at line 603 of file UMath.h.

◆ uSign()

template<class T >

int uSign ( const T & v )

inline

Get the sign of value.

Parameters

v the value

Returns: -1 if v<0, otherwise 1

Definition at line 300 of file UMath.h.

◆ uSum() [1/3]

template<class T >

T uSum ( const std::list< T > & list )

inline

Get the sum of all values contained in a list. Provided for convenience.

Parameters

list the list

Returns: the sum of values of the list

Definition at line 318 of file UMath.h.

◆ uSum() [2/3]

template<class T >

T uSum ( const std::vector< T > & v )

inline

Get the sum of all values contained in a vector. Provided for convenience.

Parameters

v	the vector

Returns: the sum of values of the vector

Definition at line 354 of file UMath.h.

◆ uSum() [3/3]

template<class T >

T uSum	(	const T *	v,
		unsigned int	size
	)

inline

Get the sum of all values contained in an array: sum(x).

Parameters

v	the array
size	the size of the array

Returns: the sum of values of the array

Definition at line 335 of file UMath.h.

◆ uSumSquared() [1/2]

template<class T >

T uSumSquared	(	const std::vector< T > &	v,
		T	subtract = `T()`
	)

inline

Get the sum of all squared values contained in an array: sum(x.^2).

Parameters

v	the array
subtract	an optional value to remove to v before squaring v: sum((x-sub).^2)

Returns: the sum of values of the array

Definition at line 387 of file UMath.h.

◆ uSumSquared() [2/2]

template<class T >

T uSumSquared	(	const T *	v,
		unsigned int	size,
		T	subtract = `T()`
	)

inline

Get the sum of all squared values contained in an array: sum(x.^2).

Parameters

v	the array
size	the size of the array
subtract	an optional value to remove to v before squaring v: sum((x-sub).^2)

Returns: the sum of values of the array

Definition at line 367 of file UMath.h.

◆ uVariance() [1/4]

template<class T >

T uVariance	(	const std::list< T > &	list,
		const T &	m
	)

inline

Get the variance of a list. Provided for convenience.

Parameters

list	the list
m	the mean of the list

Returns: the variance

See also: mean()

Definition at line 512 of file UMath.h.

◆ uVariance() [2/4]

template<class T >

T uVariance	(	const std::vector< T > &	v,
		const T &	m
	)

inline

Get the variance of a vector. Provided for convenience.

Parameters

v	the vector
m	the mean of the vector

Returns: the variance

See also: mean()

Definition at line 548 of file UMath.h.

◆ uVariance() [3/4]

template<class T >

T uVariance	(	const T *	v,
		unsigned int	size
	)

inline

Compute the variance of an array.

Parameters

v	the array
size	the size of the array

Returns: the variance

Definition at line 534 of file UMath.h.

◆ uVariance() [4/4]

template<class T >

T uVariance	(	const T *	v,
		unsigned int	size,
		T	meanV
	)

inline

Compute the variance of an array.

Parameters

v	the array
size	the size of the array
meanV	the mean of the array

Returns: the variance

See also: mean()

Definition at line 489 of file UMath.h.

◆ uXMatch() [1/4]

template<class T >

T uXMatch	(	const std::vector< T > &	vA,
		const std::vector< T > &	vB,
		unsigned int	index,
		UXMatchMethod	method
	)

inline

Do a cross correlation between 2 arrays at a specified index.

Parameters

vA	the first array
vB	the second array
sizeA	the size of the first array
sizeB	the size of the second array
index	the index to correlate
method	see UXMatchMethod

Returns: the resulting correlation value

Definition at line 909 of file UMath.h.

◆ uXMatch() [2/4]

template<class T >

std::vector<T> uXMatch	(	const std::vector< T > &	vA,
		const std::vector< T > &	vB,
		UXMatchMethod	method
	)

inline

Do a full cross-correlation or cross-covariance between 2 arrays.

Parameters

vA	the first array
vB	the second array
method	see UXMatchMethod

Returns: the resulting correlation/covariance vector of size = sizeA + sizeB - 1

Definition at line 820 of file UMath.h.

◆ uXMatch() [3/4]

template<class T >

T uXMatch	(	const T *	vA,
		const T *	vB,
		unsigned int	sizeA,
		unsigned int	sizeB,
		unsigned int	index,
		UXMatchMethod	method
	)

inline

Do a cross correlation between 2 arrays at a specified index.

Parameters

vA	the first array
vB	the second array
sizeA	the size of the first array
sizeB	the size of the second array
index	the index to correlate
method	see UXMatchMethod

Returns: the resulting correlation value

Definition at line 836 of file UMath.h.

◆ uXMatch() [4/4]

template<class T >

std::vector<T> uXMatch	(	const T *	vA,
		const T *	vB,
		unsigned int	sizeA,
		unsigned int	sizeB,
		UXMatchMethod	method
	)

inline

Do a full cross-correlation or cross-covariance between 2 arrays.

Parameters

vA	the first array
vB	the second array
sizeA	the size of the first array
sizeB	the size of the second array
method	see UXMatchMethod

Returns: the resulting correlation/covariance vector of size = sizeA + sizeB - 1

Definition at line 708 of file UMath.h.

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ UXMatchMethod

Function Documentation

◆ uHamming()

◆ uIsFinite()

◆ uIsInBounds()

◆ uIsNan()

◆ uLocalMaxima() [1/2]

◆ uLocalMaxima() [2/2]

◆ uMax() [1/4]

◆ uMax() [2/4]

◆ uMax() [3/4]

◆ uMax() [4/4]

◆ uMax3()

◆ uMean() [1/3]

◆ uMean() [2/3]

◆ uMean() [3/3]

◆ uMeanSquaredError() [1/2]

◆ uMeanSquaredError() [2/2]

◆ uMin() [1/4]

◆ uMin() [2/4]

◆ uMin() [3/4]

◆ uMin() [4/4]

◆ uMin3()

◆ uMinMax() [1/4]

◆ uMinMax() [2/4]

◆ uMinMax() [3/4]

◆ uMinMax() [4/4]

◆ uNorm() [1/3]

◆ uNorm() [2/3]

◆ uNorm() [3/3]

◆ uNormalize()

◆ uNormSquared() [1/3]

◆ uNormSquared() [2/3]

◆ uNormSquared() [3/3]

◆ uSign()

◆ uSum() [1/3]

◆ uSum() [2/3]

◆ uSum() [3/3]

◆ uSumSquared() [1/2]

◆ uSumSquared() [2/2]

◆ uVariance() [1/4]

◆ uVariance() [2/4]

◆ uVariance() [3/4]

◆ uVariance() [4/4]

◆ uXMatch() [1/4]

◆ uXMatch() [2/4]

◆ uXMatch() [3/4]

◆ uXMatch() [4/4]