Namespaces
	internal

Classes
class	Ackley
	Many local minima with a stingy enveloppe. More...

class	Beale
	Convex function with a very flat minimum. More...

class	Booth

class	Bukin6
	Strong valley. D1 but not C1. More...

class	CrossInTray
	Barriers and local minima Not C1. More...

class	Easom
	Picky hole. More...

class	Eggholder
	Not C1. More...

class	GoldsteinPrice
	Convex function with a very flat minimum and valleys. More...

class	HolderTable
	Not C1. More...

class	incompatible_matrix_exception
	This exception is thrown when an attempt is made at multiplying two matrices with incompatible dimensions. More...

class	Levi13
	Many local minima. More...

class	MatrixBase
	Matrix class implementing matrix operations. More...

class	Matyas
	Smooth valley. More...

class	McCormick

class	Rastrigin
	Many local minima with a smooth enveloppe. More...

class	Rosenbrock
	Convex function with a valley. More...

class	Schaffer2

class	Schaffer4

class	SphereF
	Convex function with a simple minimum. More...

class	StyblinskiTang

class	ThreeHumpCamel
	Very flat valley. More...

Typedefs
typedef MatrixBase< float >	Matrix

typedef MatrixBase< double >	MatrixD

typedef MatrixBase< float >	Vector

typedef MatrixBase< double >	VectorD

Functions
template<typename T >
MatrixBase< T >	asMatrix (carto::VolumeRef< T > &volume)
	Interprets the volume as a matrix. More...

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::multiplies< T, U >::result_type >	operator* (const MatrixBase< T > &a, const MatrixBase< U > &b)
	Matrix product. More...

template<typename T >
MatrixBase< T >	transpose (const MatrixBase< T > &)
	Matrix transposition. More...

template<typename T >
MatrixBase< T >	invert (const MatrixBase< T > &)
	Matrix inversion. More...

template<typename T , typename U >
bool	operator== (const MatrixBase< T > &vol, const MatrixBase< U > &other)
	Returns true if the dimensions are the same and if all elements are equal. More...

template<typename T , typename U >
bool	operator!= (const MatrixBase< T > &vol, const MatrixBase< U > &other)
	Returns false if dimensions are not the same or if any couple of elements is not equal. More...

template<typename T >
MatrixBase< T >	operator- (const MatrixBase< T > &vol)
	Returns a Matrix filled with opposite elements. More...

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::plus< T, U >::result_type >	operator+ (const MatrixBase< T > &vol, const U &value)
	Matrix + Scalar. More...

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::minus< T, U >::result_type >	operator- (const MatrixBase< T > &vol, const U &value)
	Matrix - Scalar. More...

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::multiplies< T, U >::result_type >	operator* (const MatrixBase< T > &vol, const U &value)
	Matrix * Scalar. More...

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::divides< T, U >::result_type >	operator/ (const MatrixBase< T > &vol, const U &value)
	Matrix / Scalar. More...

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::plus< U, T >::result_type >	operator+ (const U &value, const MatrixBase< T > &vol)

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::minus< U, T >::result_type >	operator- (const U &value, const MatrixBase< T > &vol)

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::multiplies< U, T >::result_type >	operator* (const U &value, const MatrixBase< T > &vol)

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::divides< U, T >::result_type >	operator/ (const U &value, const MatrixBase< T > &vol)

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::plus< T, U >::result_type >	operator+ (const MatrixBase< T > &vol, const MatrixBase< U > &other)

template<typename T , typename U >
MatrixBase< typename carto::volumeutil::minus< T, U >::result_type >	operator- (const MatrixBase< T > &vol, const MatrixBase< U > &other)

template<typename T >
std::ostream &	operator<< (std::ostream &out, const MatrixBase< T > &matrix)
	Print the matrix content on the standard output. More...

template<typename T >
void	write (const MatrixBase< T > &matrix, const std::string &file)
	Write the matrix content in an image file. More...

Variables
const double	PI = 3.14159265358979323846

const double	TWO_PI = 6.28318530717958647693

const double	PI_D_TWO = 1.57079632679489661923

const double	ONE_D_PI = 0.318309886183790671538

const double	TWO_D_PI = 0.636619772367581343076

const double	ONE_D_TWO_PI = 0.707106781186547524400

const double	FOUR_M_PI = 0.858407346410206761537

const double	PI_M_THREE = 0.141592653589793238463

const double	RT_PI = 1.77245385090551602720

const double	RT_PI_D_RT_TWO = 1.25331413731550025121

const double	RT_TWO_PI = 2.50662827463100050242

const double	TWO_D_RT_PI = 1.12837916709551257390

const double	ONE_D_RT_TWO_PI = 0.398942280401432677939

const double	POW23_FOUR_M_PI = 0.795316767371597544348

const double	ONE_D_RT_PI = TWO_D_RT_PI / 2.0

const double	RT_TWO = 1.41421356237309504880

const double	ONE_D_RT_TWO = 0.707106781186547524401

const double	ONE_D_THREE = 0.333333333333333333333

const double	TWO_D_THREE = 0.666666666666666666667

Typedef Documentation

◆ Matrix

typedef MatrixBase<float> aims::math::Matrix

Definition at line 26 of file matrix.h.

◆ MatrixD

typedef MatrixBase<double> aims::math::MatrixD

Definition at line 28 of file matrix.h.

◆ Vector

typedef MatrixBase<float> aims::math::Vector

Definition at line 29 of file matrix.h.

◆ VectorD

typedef MatrixBase<double> aims::math::VectorD

Definition at line 30 of file matrix.h.

Function Documentation

◆ asMatrix()

template<typename T >

MatrixBase< T > aims::math::asMatrix ( carto::VolumeRef< T > & volume )

Interprets the volume as a matrix.

Warning: Data will be shared between the two objects.

Definition at line 341 of file matrix_d.h.

◆ invert()

template<typename T >

MatrixBase< T > aims::math::invert ( const MatrixBase< T > & matrix )

Matrix inversion.

Note: The matrix product of the original and the resulting matrices yields the identity matrix.

Definition at line 182 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

Referenced by aims::Newton< O, L >::execute(), and aims::math::MatrixBase< T >::invert().

◆ operator!=()

template<typename T , typename U >

bool aims::math::operator!=	(	const MatrixBase< T > &	vol,
		const MatrixBase< U > &	other
	)

Returns false if dimensions are not the same or if any couple of elements is not equal.

Definition at line 208 of file matrix_d.h.

◆ operator*() [1/3]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::multiplies< T, U >::result_type > aims::math::operator*	(	const MatrixBase< T > &	a,
		const MatrixBase< U > &	b
	)

Matrix product.

Note: ths number of columns in the left hand matrix should be the same as the number of rows in the right hand matrix.

Definition at line 137 of file matrix_d.h.

References aims::math::MatrixBase< T >::ncol(), and aims::math::MatrixBase< T >::nrow().

◆ operator*() [2/3]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::multiplies< T, U >::result_type > aims::math::operator*	(	const MatrixBase< T > &	vol,
		const U &	value
	)

Matrix * Scalar.

Definition at line 238 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator*() [3/3]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::multiplies< U, T >::result_type > aims::math::operator*	(	const U &	value,
		const MatrixBase< T > &	vol
	)

Definition at line 270 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator+() [1/3]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::plus< T, U >::result_type > aims::math::operator+	(	const MatrixBase< T > &	vol,
		const U &	value
	)

Matrix + Scalar.

Definition at line 222 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator+() [2/3]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::plus< U, T >::result_type > aims::math::operator+	(	const U &	value,
		const MatrixBase< T > &	vol
	)

Definition at line 254 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator+() [3/3]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::plus< T, U >::result_type > aims::math::operator+	(	const MatrixBase< T > &	vol,
		const MatrixBase< U > &	other
	)

Definition at line 286 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator-() [1/4]

template<typename T >

MatrixBase< T > aims::math::operator- ( const MatrixBase< T > & vol )

Returns a Matrix filled with opposite elements.

Definition at line 214 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator-() [2/4]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::minus< T, U >::result_type > aims::math::operator-	(	const MatrixBase< T > &	vol,
		const U &	value
	)

Matrix - Scalar.

Definition at line 230 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator-() [3/4]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::minus< U, T >::result_type > aims::math::operator-	(	const U &	value,
		const MatrixBase< T > &	vol
	)

Definition at line 262 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator-() [4/4]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::minus< T, U >::result_type > aims::math::operator-	(	const MatrixBase< T > &	vol,
		const MatrixBase< U > &	other
	)

Definition at line 294 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator/() [1/2]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::divides< T, U >::result_type > aims::math::operator/	(	const MatrixBase< T > &	vol,
		const U &	value
	)

Matrix / Scalar.

Definition at line 246 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator/() [2/2]

template<typename T , typename U >

MatrixBase< typename carto::volumeutil::divides< U, T >::result_type > aims::math::operator/	(	const U &	value,
		const MatrixBase< T > &	vol
	)

Definition at line 278 of file matrix_d.h.

References aims::math::MatrixBase< T >::asMatrix.

◆ operator<<()

template<typename T >

std::ostream & aims::math::operator<<	(	std::ostream &	out,
		const MatrixBase< T > &	matrix
	)

Print the matrix content on the standard output.

Definition at line 327 of file matrix_d.h.

◆ operator==()

template<typename T , typename U >

bool aims::math::operator==	(	const MatrixBase< T > &	vol,
		const MatrixBase< U > &	other
	)

Returns true if the dimensions are the same and if all elements are equal.

Definition at line 196 of file matrix_d.h.

References aims::math::MatrixBase< T >::ncol(), and aims::math::MatrixBase< T >::nrow().

◆ transpose()

template<typename T >

MatrixBase< T > aims::math::transpose ( const MatrixBase< T > & m )

Matrix transposition.

Note: Rows and columns will be inverted.

Definition at line 165 of file matrix_d.h.

References aims::math::MatrixBase< T >::ncol(), and aims::math::MatrixBase< T >::nrow().

Referenced by aims::WolfeLineSearch< O >::checkDirection(), aims::math::MatrixBase< T >::transpose(), aims::WolfeLineSearch< O >::wolfe2s(), and aims::WolfeLineSearch< O >::wolfe2w().

◆ write()

template<typename T >

void aims::math::write	(	const MatrixBase< T > &	matrix,
		const std::string &	file
	)

Write the matrix content in an image file.

Variable Documentation

◆ FOUR_M_PI

const double aims::math::FOUR_M_PI = 0.858407346410206761537

Definition at line 24 of file constants.h.

◆ ONE_D_PI

const double aims::math::ONE_D_PI = 0.318309886183790671538

Definition at line 21 of file constants.h.

◆ ONE_D_RT_PI

const double aims::math::ONE_D_RT_PI = TWO_D_RT_PI / 2.0

Definition at line 33 of file constants.h.

◆ ONE_D_RT_TWO

const double aims::math::ONE_D_RT_TWO = 0.707106781186547524401

Definition at line 36 of file constants.h.

◆ ONE_D_RT_TWO_PI

const double aims::math::ONE_D_RT_TWO_PI = 0.398942280401432677939

Definition at line 31 of file constants.h.

◆ ONE_D_THREE

const double aims::math::ONE_D_THREE = 0.333333333333333333333

Definition at line 38 of file constants.h.

◆ ONE_D_TWO_PI

const double aims::math::ONE_D_TWO_PI = 0.707106781186547524400

Definition at line 23 of file constants.h.

◆ PI

const double aims::math::PI = 3.14159265358979323846

Definition at line 18 of file constants.h.

◆ PI_D_TWO

const double aims::math::PI_D_TWO = 1.57079632679489661923

Definition at line 20 of file constants.h.

◆ PI_M_THREE

const double aims::math::PI_M_THREE = 0.141592653589793238463

Definition at line 25 of file constants.h.

◆ POW23_FOUR_M_PI

const double aims::math::POW23_FOUR_M_PI = 0.795316767371597544348

Definition at line 32 of file constants.h.

◆ RT_PI

const double aims::math::RT_PI = 1.77245385090551602720

Definition at line 27 of file constants.h.

◆ RT_PI_D_RT_TWO

const double aims::math::RT_PI_D_RT_TWO = 1.25331413731550025121

Definition at line 28 of file constants.h.

◆ RT_TWO

const double aims::math::RT_TWO = 1.41421356237309504880

Definition at line 35 of file constants.h.

◆ RT_TWO_PI

const double aims::math::RT_TWO_PI = 2.50662827463100050242

Definition at line 29 of file constants.h.

◆ TWO_D_PI

const double aims::math::TWO_D_PI = 0.636619772367581343076

Definition at line 22 of file constants.h.

◆ TWO_D_RT_PI

const double aims::math::TWO_D_RT_PI = 1.12837916709551257390

Definition at line 30 of file constants.h.

◆ TWO_D_THREE

const double aims::math::TWO_D_THREE = 0.666666666666666666667

Definition at line 39 of file constants.h.

◆ TWO_PI

const double aims::math::TWO_PI = 6.28318530717958647693

Definition at line 19 of file constants.h.

Namespaces

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ Matrix

◆ MatrixD

◆ Vector

◆ VectorD

Function Documentation

◆ asMatrix()

◆ invert()

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator-() [1/4]

◆ operator-() [2/4]

◆ operator-() [3/4]

◆ operator-() [4/4]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator<<()

◆ operator==()

◆ transpose()

◆ write()

Variable Documentation

◆ FOUR_M_PI

◆ ONE_D_PI

◆ ONE_D_RT_PI

◆ ONE_D_RT_TWO

◆ ONE_D_RT_TWO_PI

◆ ONE_D_THREE

◆ ONE_D_TWO_PI

◆ PI

◆ PI_D_TWO

◆ PI_M_THREE

◆ POW23_FOUR_M_PI

◆ RT_PI

◆ RT_PI_D_RT_TWO

◆ RT_TWO

◆ RT_TWO_PI

◆ TWO_D_PI

◆ TWO_D_RT_PI

◆ TWO_D_THREE

◆ TWO_PI