Collaboration diagram for Maths:

Modules
	Geometry

	Statistics

Namespaces
	crn::Combinatorics
	Combinatorics toolbox.

	crn::LinearSystem
	Solvers for systems of linear equations.

	crn::QuadraticEquation
	Solvers for quadratic equations.

	crn::FuzzyLogic
	Fuzzy logic toolbox.

	crn::literals

	crn::UnivariateRandomTools
	Univariate random toolbox class.

Classes
class	crn::DiscreteHMM
	Discrete HMM class. More...

class	crn::GaussianSCHMM
	Semi-continuous gaussian HMM class. More...

class	crn::Cartesian2DFunction
	Base class for 2D functions. More...

class	crn::CubicSpline
	Cubic spline interpolation. More...

class	crn::LinearInterpolation
	Linear interpolation. More...

class	crn::Matrix< T >
	Base matrix class. More...

class	crn::MatrixComplex
	Complex matrix class. More...

class	crn::MatrixDouble
	double matrix class More...

class	crn::MatrixInt
	Integer matrix class. More...

class	crn::MultivariateGaussianMixture
	Multivariate gaussian mixture. More...

class	crn::MultivariateGaussianPDF
	Multivariate Gaussian distribution. More...

class	crn::MultivariateRandomTools
	Multivariate random toolbox class. More...

class	crn::PolynomialRegression
	Polynomial regression. More...

class	crn::Prop3
	A ternary proposition. More...

class	crn::RealToRealFunction
	Numerical integration toolbox class. More...

class	crn::SquareMatrixDouble
	Square double matrix class. More...

struct	crn::Radian
	Radian angle unit. More...

struct	crn::Degree
	Degree angle unit. More...

struct	crn::ByteAngle
	BYTE angle unit. More...

struct	crn::Angle< Unit >
	A convenience class for angles units. More...

class	crn::UnivariateGaussianMixture
	Univariate Gaussian mixture. More...

class	crn::UnivariateGaussianPDF
	Univariate Gaussian distribution. More...

Typedefs
template<class ANGLE >
using	crn::Unit = typename ANGLE::unit

Enumerations
enum	crn::Direction { crn::Direction::INVALID = 0, crn::Direction::LEFT = 1, crn::Direction::RIGHT = 2, crn::Direction::TOP = 4, crn::Direction::BOTTOM = 8 }
	An enumeration of directions. More...

enum	crn::Orientation { crn::Orientation::INVALID = 0, crn::Orientation::HORIZONTAL, crn::Orientation::VERTICAL }
	An enumeration of orientations. More...

enum	crn::DistanceType { crn::DistanceType::INVALID = 0, crn::DistanceType::D4, crn::DistanceType::D8, crn::DistanceType::EUCLIDEAN }
	An enumeration of distances. More...

Functions
template<typename T >
const T &	crn::Max (const T &a, const T &b)
	Returns the max of two values. More...

template<typename T >
const T &	crn::Min (const T &a, const T &b)
	Returns the min of two values. More...

template<typename T >
const T &	crn::Max (const T &a, const T &b, const T &c)
	Returns the max of three values. More...

template<typename T >
const T &	crn::Min (const T &a, const T &b, const T &c)
	Returns the min of three values. More...

template<typename T >
constexpr TypeInfo< T >::SumType	crn::Twice (const T &v) noexcept(noexcept(v+v))
	Returns the double of a value. More...

template<typename T >
constexpr TypeInfo< T >::SumType	crn::Thrice (const T &v) noexcept(noexcept(v+v))
	Returns three times a value. More...

template<typename T >
constexpr int	crn::SignOf (const T &x) noexcept(noexcept(x< 0))
	Returns the sign (-1 or 1) of a value. More...

template<typename T >
constexpr SumType< T >	crn::Sqr (const T &v) noexcept(noexcept(v *v))
	Returns the square of a value. More...

template<typename T >
constexpr T	crn::Abs (const T &v) noexcept(noexcept(v< 0)&&noexcept(-v))
	Returns the absolute value of a value. More...

template<typename T >
T	crn::Abs (const std::complex< T > &v) noexcept(noexcept(std::abs(std::complex< T >(0))))
	Returns the absolute value of a value. More...

template<typename T >
T	crn::AbsMax (const T &a, const T &b) noexcept(noexcept(Abs(a)))
	Returns the value that has the maximal absolute value. More...

template<typename T >
T	crn::AbsMin (const T &a, const T &b) noexcept(noexcept(Abs(a)))
	Returns the value that has the minimal absolute value. More...

template<typename T >
T	crn::AbsMaxSameSign (const T &a, const T &b) noexcept(noexcept(Abs(a))&&noexcept(SignOf(a)))
	Returns the value that has the maximal absolute value if the values have the same sign. More...

template<typename T >
T	crn::AbsMinSameSign (const T &a, const T &b) noexcept(noexcept(Abs(a))&&noexcept(SignOf(a)))
	Returns the value that has the minimal absolute value if the values have the same sign. More...

template<typename T >
const T &	crn::Cap (const T &v, const T &min, const T &max)
	Bounds a value to an interval. More...

double	crn::Gauss (double x, double sigma)
	Computes Gauss function at x for a given standard deviation (centered in 0) More...

double	crn::MeanGauss (double x, double sigma)
	Computes Gauss function at x for a given standard deviation (centered in 0) – to use with matrices. More...

double	crn::Pythagoras (double a, double b) noexcept
	Computes sqrt(a²+b²) without destructive underflow or overflow. More...

double	crn::Pythagoras (int a, int b) noexcept
	Computes sqrt(a²+b²) without destructive underflow or overflow. More...

double	crn::Pythagoras (double a, double b, double c) noexcept
	Computes sqrt(a²+b²+c²) More...

template<class ITER >
double	crn::Pythagoras (ITER it_begin, ITER it_end)
	Computes euclidean norm. More...

template<class ITER >
void	crn::Scale (ITER it_begin, ITER it_end, const double s)
	Scale a collection of numbers. More...

template<typename Unit >
Direction	crn::ToDirection (const Angle< Unit > &ang) noexcept

Orientation	crn::ToOrientation (Direction d) noexcept

template<typename T , typename std::enable_if< std::is_arithmetic< T >::value, int >::type = 0>
double	crn::Distance (T o1, T o2)
	Distance between two numbers. More...

template<typename Unit >
double	crn::Cosine (typename Unit::type angle) noexcept
	Cosine of an angle. More...

template<typename Unit >
double	crn::Sine (typename Unit::type angle) noexcept
	Sine of an angle. More...

template<typename Unit >
double	crn::Tangent (typename Unit::type angle) noexcept
	Tangent of an angle. More...

template<>
double	crn::Cosine< ByteAngle > (uint8_t angle) noexcept
	Cosine of a byte angle using a lookup table. More...

template<>
double	crn::Sine< ByteAngle > (uint8_t angle) noexcept
	Sine of a byte angle using a lookup table. More...

template<>
double	crn::Tangent< ByteAngle > (uint8_t angle) noexcept
	Tangent of a byte angle using a lookup table. More...

template<typename Unit >
Angle< Unit >	crn::operator+ (const Angle< Unit > &a1, const Angle< Unit > &a2) noexcept(std::is_nothrow_constructible< typename Unit::type >::value &&std::is_nothrow_copy_assignable< typename Unit::type >::value)
	Adds two angles. More...

template<typename Unit >
Angle< Unit >	crn::operator- (const Angle< Unit > &a1, const Angle< Unit > &a2) noexcept(std::is_nothrow_constructible< typename Unit::type >::value &&std::is_nothrow_copy_assignable< typename Unit::type >::value)
	Subtracts two angles. More...

template<typename Unit >
Angle< Unit >	crn::operator* (double f, const Angle< Unit > &a) noexcept(std::is_nothrow_constructible< typename Unit::type >::value &&std::is_nothrow_copy_assignable< typename Unit::type >::value)
	Multiplies an scalar with an angle. More...

template<class A >
double	crn::Cos (const A &a) noexcept

double	crn::Cos (double a) noexcept

double	crn::Cos (uint8_t a) noexcept

template<class A >
double	crn::Sin (const A &a) noexcept

double	crn::Sin (double a) noexcept

double	crn::Sin (uint8_t a) noexcept

template<class A >
double	crn::Tan (const A &a) noexcept

double	crn::Tan (double a) noexcept

double	crn::Tan (uint8_t a) noexcept

template<class A >
A	crn::Atan (double s, double c) noexcept

template<>
double	crn::Atan< double > (double s, double c) noexcept

template<typename Unit >
Unit::type	crn::AngularDistance (const Angle< Unit > &a1, const Angle< Unit > &a2) noexcept(std::is_nothrow_constructible< typename TypeInfo< typename Unit::type >::DiffType >::value &&std::is_nothrow_copy_assignable< typename TypeInfo< typename Unit::type >::DiffType >::value &&std::is_nothrow_constructible< typename Unit::type >::value)
	Distance between two angles. More...

double	crn::AngularDistance (double a1, double a2) noexcept
	Distance between two angles. More...

template<typename ITER >
std::iterator_traits< ITER > ::value_type	crn::AngularMean (ITER beg, ITER en)
	Mean of a set of angles. More...

template<typename ITER >
ITER	crn::AngularMedian (ITER beg, ITER en)
	Mean of a set of angles. More...

template<typename ITER >
double	crn::AngularVariance (ITER beg, ITER en)
	Variance of a set of angles. More...

template<typename ITER >
double	crn::AngularVariance (ITER beg, ITER en, typename std::iterator_traits< ITER >::value_type mean)
	Variance of a set of angles. More...

template<typename ITER >
double	crn::CircularVariance (ITER beg, ITER en)
	Circular (pseudo) variance of a set of angles. More...

template<typename ITER >
double	crn::CircularStdDev (ITER beg, ITER en)
	Circular (pseudo) standard deviation of a set of angles. More...

template<typename ITER >
std::complex< double >	crn::TrigonometricMoment (ITER beg, ITER en, typename std::iterator_traits< ITER >::value_type refer, size_t p)
	Trigonometric moment. More...

template<typename ITER >
double	crn::AngularSkewness (ITER beg, ITER en)
	Skewness of a set of angles. More...

template<typename ITER >
double	crn::AngularKurtosis (ITER beg, ITER en)
	Kurtosis of a set of angles. More...

void	crn::FFT (std::vector< std::complex< double > > &sig, bool direct)
	Fast Fourier transform. More...

Detailed Description

Typedef Documentation

template<class ANGLE >

using crn::Unit = typedef typename ANGLE::unit

Definition at line 259 of file CRNTrigonometry.h.

Enumeration Type Documentation

enum crn::Direction

strong

An enumeration of directions.

An enumeration of directions

Enumerator
INVALID
LEFT
RIGHT
TOP
BOTTOM

Definition at line 122 of file CRNMath.h.

enum crn::DistanceType

strong

An enumeration of distances.

An enumeration of distances

Enumerator
INVALID
D4
D8
EUCLIDEAN

Definition at line 159 of file CRNMath.h.

enum crn::Orientation

strong

An enumeration of orientations.

An enumeration of orientations

Enumerator
INVALID
HORIZONTAL
VERTICAL

Definition at line 152 of file CRNMath.h.

Function Documentation

template<typename T >

constexpr T crn::Abs ( const T & v )

noexcept

Returns the absolute value of a value.

Definition at line 63 of file CRNMath.h.

template<typename T >

T crn::Abs ( const std::complex< T > & v )

inlinenoexcept

Returns the absolute value of a value.

Definition at line 65 of file CRNMath.h.

template<typename T >

T crn::AbsMax	(	const T &	a,
		const T &	b
	)

inlinenoexcept

Returns the value that has the maximal absolute value.

Definition at line 67 of file CRNMath.h.

template<typename T >

T crn::AbsMaxSameSign	(	const T &	a,
		const T &	b
	)

inlinenoexcept

Returns the value that has the maximal absolute value if the values have the same sign.

Definition at line 71 of file CRNMath.h.

template<typename T >

T crn::AbsMin	(	const T &	a,
		const T &	b
	)

inlinenoexcept

Returns the value that has the minimal absolute value.

Definition at line 69 of file CRNMath.h.

template<typename T >

T crn::AbsMinSameSign	(	const T &	a,
		const T &	b
	)

inlinenoexcept

Returns the value that has the minimal absolute value if the values have the same sign.

Definition at line 73 of file CRNMath.h.

template<typename Unit >

Unit::type crn::AngularDistance	(	const Angle< Unit > &	a1,
		const Angle< Unit > &	a2
	)

inlinenoexcept

Distance between two angles.

Distance between two angles

Usage example: AngularDistance<ByteAngle>(35, Angle<ByteAngle>::TOP())

Parameters

[in]	a1	first angle
[in]	a2	second angle

Definition at line 341 of file CRNTrigonometry.h.

double crn::AngularDistance	(	double	a1,
		double	a2
	)

inlinenoexcept

Distance between two angles.

Distance between two angles

Parameters

[in]	a1	first angle
[in]	a2	second angle

Definition at line 359 of file CRNTrigonometry.h.

template<typename ITER >

double crn::AngularKurtosis	(	ITER	beg,
		ITER	en
	)

Kurtosis of a set of angles.

Exceptions

ExceptionDomain empty set of angles

Parameters

[in]	beg	iterator on the first angle
[in]	en	iterator after the last angle

Returns: the kurtosis of the set

Definition at line 530 of file CRNTrigonometry.h.

template<typename ITER >

std::iterator_traits<ITER>::value_type crn::AngularMean	(	ITER	beg,
		ITER	en
	)

Mean of a set of angles.

Exceptions

ExceptionDomain empty set of angles

Parameters

[in]	beg	iterator on the first angle
[in]	en	iterator after the last angle

Returns: the mean angle

Definition at line 371 of file CRNTrigonometry.h.

template<typename ITER >

ITER crn::AngularMedian	(	ITER	beg,
		ITER	en
	)

Mean of a set of angles.

Exceptions

ExceptionDomain empty set of angles

Parameters

[in]	beg	iterator on the first angle
[in]	en	iterator after the last angle

Returns: an iterator to the median angle

Definition at line 391 of file CRNTrigonometry.h.

template<typename ITER >

double crn::AngularSkewness	(	ITER	beg,
		ITER	en
	)

Skewness of a set of angles.

Exceptions

ExceptionDomain empty set of angles

Parameters

[in]	beg	iterator on the first angle
[in]	en	iterator after the last angle

Returns: the skewness of the set

Definition at line 514 of file CRNTrigonometry.h.

template<typename ITER >

double crn::AngularVariance	(	ITER	beg,
		ITER	en
	)

Variance of a set of angles.

Exceptions

ExceptionDomain empty set of angles

Parameters

[in]	beg	iterator on the first angle
[in]	en	iterator after the last angle

Returns: the biased variance

Definition at line 416 of file CRNTrigonometry.h.

template<typename ITER >

double crn::AngularVariance	(	ITER	beg,
		ITER	en,
		typename std::iterator_traits< ITER >::value_type	mean
	)

Variance of a set of angles.

Exceptions

ExceptionDomain empty set of angles

Parameters

[in]	beg	iterator on the first angle
[in]	en	iterator after the last angle
[in]	mean	the mean of the set of angles

Returns: the biased variance

Definition at line 437 of file CRNTrigonometry.h.

template<class A >

A crn::Atan	(	double	s,
		double	c
	)

inlinenoexcept

Returns: the arctangent of a pair or sine/cosine

Definition at line 328 of file CRNTrigonometry.h.

template<>

double crn::Atan< double >	(	double	s,
		double	c
	)

inlinenoexcept

Returns: the arctangent of a pair or sine/cosine

Definition at line 330 of file CRNTrigonometry.h.

template<typename T >

const T& crn::Cap	(	const T &	v,
		const T &	min,
		const T &	max
	)

inline

Bounds a value to an interval.

Definition at line 75 of file CRNMath.h.

template<typename ITER >

double crn::CircularStdDev	(	ITER	beg,
		ITER	en
	)

Circular (pseudo) standard deviation of a set of angles.

Exceptions

ExceptionDomain empty set of angles

Parameters

[in]	beg	iterator on the first angle
[in]	en	iterator after the last angle

Returns: the "circular standard deviation"

Definition at line 476 of file CRNTrigonometry.h.

template<typename ITER >

double crn::CircularVariance	(	ITER	beg,
		ITER	en
	)

Circular (pseudo) variance of a set of angles.

Exceptions

ExceptionDomain empty set of angles

Parameters

[in]	beg	iterator on the first angle
[in]	en	iterator after the last angle

Returns: the "circular variance"

Definition at line 456 of file CRNTrigonometry.h.

template<class A >

double crn::Cos ( const A & a )

inlinenoexcept

Returns: the cosine of the angle

Definition at line 310 of file CRNTrigonometry.h.

double crn::Cos ( double a )

inlinenoexcept

Returns: the cosine of the angle

Definition at line 312 of file CRNTrigonometry.h.

double crn::Cos ( uint8_t a )

inlinenoexcept

Returns: the cosine of the angle

Definition at line 314 of file CRNTrigonometry.h.

template<typename Unit >

double crn::Cosine ( typename Unit::type angle )

inlinenoexcept

Cosine of an angle.

Parameters

[in] angle the angle in the unit given in template

Returns: the cosine of the angle

Definition at line 61 of file CRNTrigonometry.h.

template<>

double crn::Cosine< ByteAngle > ( uint8_t angle )

inlinenoexcept

Cosine of a byte angle using a lookup table.

Parameters

[in] angle the angle in [0..255]

Returns: the cosine of the angle

Definition at line 88 of file CRNTrigonometry.h.

template<typename T , typename std::enable_if< std::is_arithmetic< T >::value, int >::type = 0>

double crn::Distance	(	T	o1,
		T	o2
	)

Distance between two numbers.

Definition at line 166 of file CRNMath.h.

void crn::FFT	(	std::vector< std::complex< double > > &	sig,
		bool	direct
	)

Fast Fourier transform.

Fast Fourier transform

Date: April 2013

Version: 0.1

Exceptions

ExceptionDimension signal does not have a power of 2 size

Parameters

[in]	sig	the signal to process
[in]	direct	direct=true, inverse=false

Definition at line 98 of file CRNMatrixComplex.cpp.

double crn::Gauss	(	double	x,
		double	sigma
	)

inline

Computes Gauss function at x for a given standard deviation (centered in 0)

Definition at line 78 of file CRNMath.h.

template<typename T >

const T& crn::Max	(	const T &	a,
		const T &	b
	)

inline

Returns the max of two values.

Definition at line 47 of file CRNMath.h.

template<typename T >

const T& crn::Max	(	const T &	a,
		const T &	b,
		const T &	c
	)

inline

Returns the max of three values.

Definition at line 51 of file CRNMath.h.

double crn::MeanGauss	(	double	x,
		double	sigma
	)

inline

Computes Gauss function at x for a given standard deviation (centered in 0) – to use with matrices.

Definition at line 81 of file CRNMath.h.

template<typename T >

const T& crn::Min	(	const T &	a,
		const T &	b
	)

inline

Returns the min of two values.

Definition at line 49 of file CRNMath.h.

template<typename T >

const T& crn::Min	(	const T &	a,
		const T &	b,
		const T &	c
	)

inline

Returns the min of three values.

Definition at line 53 of file CRNMath.h.

template<typename Unit >

Angle<Unit> crn::operator*	(	double	f,
		const Angle< Unit > &	a
	)

inlinenoexcept

Multiplies an scalar with an angle.

Definition at line 284 of file CRNTrigonometry.h.

template<typename Unit >

Angle<Unit> crn::operator+	(	const Angle< Unit > &	a1,
		const Angle< Unit > &	a2
	)

inlinenoexcept

Adds two angles.

Definition at line 262 of file CRNTrigonometry.h.

template<typename Unit >

Angle<Unit> crn::operator-	(	const Angle< Unit > &	a1,
		const Angle< Unit > &	a2
	)

inlinenoexcept

Subtracts two angles.

Definition at line 273 of file CRNTrigonometry.h.

double crn::Pythagoras	(	double	a,
		double	b
	)

inlinenoexcept

Computes sqrt(a²+b²) without destructive underflow or overflow.

Definition at line 84 of file CRNMath.h.

double crn::Pythagoras	(	int	a,
		int	b
	)

inlinenoexcept

Computes sqrt(a²+b²) without destructive underflow or overflow.

Definition at line 86 of file CRNMath.h.

double crn::Pythagoras	(	double	a,
		double	b,
		double	c
	)

inlinenoexcept

Computes sqrt(a²+b²+c²)

Definition at line 89 of file CRNMath.h.

template<class ITER >

double crn::Pythagoras	(	ITER	it_begin,
		ITER	it_end
	)

inline

Computes euclidean norm.

Definition at line 92 of file CRNMath.h.

template<class ITER >

void crn::Scale	(	ITER	it_begin,
		ITER	it_end,
		const double	s
	)

inline

Scale a collection of numbers.

Definition at line 103 of file CRNMath.h.

template<typename T >

constexpr int crn::SignOf ( const T & x )

noexcept

Returns the sign (-1 or 1) of a value.

Definition at line 59 of file CRNMath.h.

template<class A >

double crn::Sin ( const A & a )

inlinenoexcept

Returns: the sine of the angle

Definition at line 316 of file CRNTrigonometry.h.

double crn::Sin ( double a )

inlinenoexcept

Returns: the sine of the angle

Definition at line 318 of file CRNTrigonometry.h.

double crn::Sin ( uint8_t a )

inlinenoexcept

Returns: the sine of the angle

Definition at line 320 of file CRNTrigonometry.h.

template<typename Unit >

double crn::Sine ( typename Unit::type angle )

inlinenoexcept

Sine of an angle.

Parameters

[in] angle the angle in the unit given in template

Returns: the sine of the angle

Definition at line 70 of file CRNTrigonometry.h.

template<>

double crn::Sine< ByteAngle > ( uint8_t angle )

inlinenoexcept

Sine of a byte angle using a lookup table.

Parameters

[in] angle the angle in [0..255]

Returns: the sine of the angle

Definition at line 105 of file CRNTrigonometry.h.

template<typename T >

constexpr SumType<T> crn::Sqr ( const T & v )

noexcept

Returns the square of a value.

Definition at line 61 of file CRNMath.h.

template<class A >

double crn::Tan ( const A & a )

inlinenoexcept

Returns: the tangent of the angle

Definition at line 322 of file CRNTrigonometry.h.

double crn::Tan ( double a )

inlinenoexcept

Returns: the tangent of the angle

Definition at line 324 of file CRNTrigonometry.h.

double crn::Tan ( uint8_t a )

inlinenoexcept

Returns: the tangent of the angle

Definition at line 326 of file CRNTrigonometry.h.

template<typename Unit >

double crn::Tangent ( typename Unit::type angle )

inlinenoexcept

Tangent of an angle.

Parameters

[in] angle the angle in the unit given in template

Returns: the tangent of the angle

Definition at line 79 of file CRNTrigonometry.h.

template<>

double crn::Tangent< ByteAngle > ( uint8_t angle )

inlinenoexcept

Tangent of a byte angle using a lookup table.

Parameters

[in] angle the angle in [0..255]

Returns: the tangent of the angle

Definition at line 122 of file CRNTrigonometry.h.

template<typename T >

constexpr TypeInfo<T>::SumType crn::Thrice ( const T & v )

noexcept

Returns three times a value.

Definition at line 57 of file CRNMath.h.

template<typename Unit >

Direction crn::ToDirection ( const Angle< Unit > & ang )

noexcept

Definition at line 123 of file CRNMath.h.

Orientation crn::ToOrientation ( Direction d )

noexcept

Constructor from direction

Parameters

[in] d the direction to import. LEFT and RIGHT map to HORIZONTAL. TOP and BOTTOM map to VERTICAL. Others map to INVALID.

Definition at line 31 of file CRNMath.cpp.

template<typename ITER >

std::complex<double> crn::TrigonometricMoment	(	ITER	beg,
		ITER	en,
		typename std::iterator_traits< ITER >::value_type	refer,
		size_t	p
	)

Trigonometric moment.

Exceptions

ExceptionDomain	empty set of angles
ExceptionInvalidArgument	null order

Parameters

[in]	beg	iterator on the first angle
[in]	en	iterator after the last angle
[in]	refer	the reference angle (typically, the mean angle)
[in]	p	the order of the moment (>= 1)

Returns: the pth trigonometric moment

Definition at line 490 of file CRNTrigonometry.h.

template<typename T >

constexpr TypeInfo<T>::SumType crn::Twice ( const T & v )

noexcept

Returns the double of a value.

Definition at line 55 of file CRNMath.h.

Modules

Namespaces

Classes

Typedefs

Enumerations

Functions

Detailed Description

Typedef Documentation

Enumeration Type Documentation

Function Documentation