UMath.h File Reference

Basic mathematics functions. More...

#include "rtabmap/utilite/UtiLiteExp.h"
#include <cmath>
#include <list>
#include <vector>

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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 T *v, unsigned int size)
template<class T >
std::list< unsigned int >	uLocalMaxima (const std::vector< T > &v)
template<class T >
T	uMax (const T *v, unsigned int size, unsigned int &index)
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 std::vector< T > &v)
template<class T >
T	uMax3 (const T &a, const T &b, const T &c)
template<class T >
T	uMean (const T *v, unsigned int size)
template<class T >
T	uMean (const std::list< T > &list)
template<class T >
T	uMean (const std::vector< T > &v)
template<class T >
T	uMeanSquaredError (const T *x, unsigned int sizeX, const T *y, unsigned int sizeY)
template<class T >
T	uMeanSquaredError (const std::vector< T > &x, const std::vector< T > &y)
template<class T >
T	uMin (const T *v, unsigned int size, unsigned int &index)
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 std::vector< T > &v)
template<class T >
T	uMin3 (const T &a, const T &b, const T &c)
template<class T >
void	uMinMax (const T *v, unsigned int size, T &min, T &max, unsigned int &indexMin, unsigned int &indexMax)
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 std::vector< T > &v, T &min, T &max)
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 T *v, unsigned int size)
template<class T >
T	uSum (const std::vector< T > &v)
template<class T >
T	uSumSquared (const T *v, unsigned int size, T subtract=T())
template<class T >
T	uSumSquared (const std::vector< T > &v, T subtract=T())
template<class T >
T	uVariance (const T *v, unsigned int size, T meanV)
template<class T >
T	uVariance (const std::list< T > &list, const T &m)
template<class T >
T	uVariance (const T *v, unsigned int size)
template<class T >
T	uVariance (const std::vector< T > &v, const T &m)
template<class T >
std::vector< T >	uXMatch (const T *vA, const T *vB, unsigned int sizeA, unsigned int sizeB, 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 >
T	uXMatch (const std::vector< T > &vA, const std::vector< T > &vB, unsigned int index, UXMatchMethod method)

---

Detailed Description

Basic mathematics functions.

Definition in file UMath.h.

---

Enumeration Type Documentation

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 698 of file UMath.h.

---

Function Documentation

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 921 of file UMath.h.

template<class T >

bool uIsFinite

(

const T &

value

)

[inline]

Return true if the number is finite.

Definition at line 55 of file UMath.h.

template<typename T >

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

Definition at line 934 of file UMath.h.

template<class T >

bool uIsNan

(

const T &

value

)

[inline]

Return true if the number is NAN.

Definition at line 42 of file UMath.h.

template<class T >

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

Find all local maxima.

Definition at line 647 of file UMath.h.

template<class T >

std::list<unsigned int> uLocalMaxima

(

const std::vector< T > &

v

)

[inline]

Find all local maxima.

Definition at line 689 of file UMath.h.

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 94 of file UMath.h.

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 122 of file UMath.h.

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 134 of file UMath.h.

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 146 of file UMath.h.

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 80 of file UMath.h.

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 401 of file UMath.h.

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 421 of file UMath.h.

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 441 of file UMath.h.

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 455 of file UMath.h.

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 477 of file UMath.h.

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 159 of file UMath.h.

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 187 of file UMath.h.

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 199 of file UMath.h.

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 211 of file UMath.h.

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 69 of file UMath.h.

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 226 of file UMath.h.

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 264 of file UMath.h.

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 277 of file UMath.h.

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 291 of file UMath.h.

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 575 of file UMath.h.

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 595 of file UMath.h.

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 615 of file UMath.h.

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 625 of file UMath.h.

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 560 of file UMath.h.

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 585 of file UMath.h.

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 605 of file UMath.h.

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 302 of file UMath.h.

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 320 of file UMath.h.

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 337 of file UMath.h.

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 356 of file UMath.h.

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 369 of file UMath.h.

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 389 of file UMath.h.

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 491 of file UMath.h.

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 514 of file UMath.h.

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 536 of file UMath.h.

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 550 of file UMath.h.

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 710 of file UMath.h.

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 822 of file UMath.h.

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 838 of file UMath.h.

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 911 of file UMath.h.