Files
file	matrixAlgorithmsLib.h

file	Z2.h

file	Zp.h

file	algebraicOperations.h

file	algebraicOperations.hpp

file	ColumnVector.h

file	ColumnVector.hpp

file	Container.h

file	Container.hpp

file	Dimension.h

file	iobject.hpp

file	Matrix.h

file	Matrix.hpp

file	Matrix_inline.h

file	Matrix_Interval.hpp

file	MatrixContainer.h

file	MatrixIterator.h

file	MatrixSlice.h

file	Multiindex.h

file	Norm.h

file	Norm.hpp

file	RowVector.h

file	RowVector.hpp

file	SubVector.h

file	SubVector.hpp

file	InvariantManifold.h

Namespaces
	capd

Classes
class	Z2

class	Zp

class	EmptyIntersectionException

class	MatrixIterator< Matrix >

class	const_MatrixIterator< Matrix >

class	MatrixSlice< matrix >
	This class represents a matrix without own container and data it is used for operations on submatrices. More...

class	capd::vectalg::Vector< Scalar, dim >

Macros
#define	CAPD_DEFAULT_DIMENSION 0

Functions
double	nonnegativePart (double x)

double	nonnegativePart (long double x)

double	nonnegativePart (int x)

template<typename SourceIterator , typename Iterator1 , typename Iterator2 >
void	capd::vectalg::split (SourceIterator sourceBegin, SourceIterator sourceEnd, Iterator1 center, Iterator2 diameter)
	splits source object given by [sourceBegin, sourceEnd] into form center + diameter where diameter = [-radius,radius] on each coordinatedimension More...

template<typename IntervalObject1 , typename IntervalObject2 >
void	capd::vectalg::split (IntervalObject1 &v, IntervalObject2 &rv)
	splits IntervalObject v into form center + [-radius, radius] form More...

template<typename IntervalObject , typename CenterType >
void	capd::vectalg::split (const IntervalObject &v, CenterType &center, IntervalObject &diameter)
	splits IntervalObject v into form center + diameter where diameter = [-radius,radius] on each coordinate More...

template<typename IObject >
IObject::ScalarType	capd::vectalg::maxDiam (const IObject &v)
	returns the upper bound for the biggest diameter of IntervalObject (vector or matrix) coordinates More...

template<typename IObject >
capd::TypeTraits< typename IObject::ScalarType >::Real	capd::vectalg::maxWidth (const IObject &v)
	returns the biggest diameter of the interval object (vector or matrix) coordinates (non-rigorous) More...

template<typename IntervalObject >
bool	capd::vectalg::containsZero (const IntervalObject &v)
	checks if IntervalObject v contains zero on all coordinates More...

template<typename IntervalObject >
bool	capd::vectalg::subset (const IntervalObject &v1, const IntervalObject &v2)
	checks if IntervalObject v1 is contained in IntervalObject v2 More...

template<typename IntervalObject >
bool	capd::vectalg::subsetInterior (const IntervalObject &v1, const IntervalObject &v2)
	checks if IntervalObject v1 is contained in interior of IntervalObject v2 More...

template<typename Iterator1 , typename Iterator2 , typename ResultIterator >
bool	capd::vectalg::intersection (Iterator1 b1, Iterator2 b2, ResultIterator b, ResultIterator e)
	intersection of two interval objects (vectors, matrices) More...

template<typename IntervalObject1 , typename IntervalObject2 , typename IntervalObject3 >
bool	capd::vectalg::intersection (const IntervalObject1 &v1, const IntervalObject2 &v2, IntervalObject3 &result)
	intersection of two interval objects (vectors, matrices) More...

template<typename Iterator1 , typename Iterator2 >
bool	capd::vectalg::intersectionIsEmpty (Iterator1 b, Iterator1 e, Iterator2 b1)
	checks if intersection of two interval vectors is empty More...

template<typename IntervalObject1 , typename IntervalObject2 >
bool	capd::vectalg::intersectionIsEmpty (const IntervalObject1 &v, const IntervalObject2 &w)
	checks if intersection of two interval vectors is empty More...

template<typename IntervalObject >
void	capd::vectalg::intervalHull (const IntervalObject &v1, const IntervalObject &v2, IntervalObject &result)

template<typename IntervalObject , typename ResultContainer >
void	capd::vectalg::diameter (const IntervalObject &v, ResultContainer &result)

template<typename IntervalObject , typename ResultType >
void	capd::vectalg::mid (const IntervalObject &v, ResultType &result)

template<typename ResultType , typename IntervalObject >
ResultType	capd::vectalg::midObject (const IntervalObject &v)

template<typename ResultType , typename IntervalObject >
void	capd::vectalg::leftObject (const IntervalObject &v, ResultType &result)

template<typename ResultType , typename IntervalObject >
ResultType	capd::vectalg::leftObject (const IntervalObject &v)

template<typename ResultType , typename IntervalObject >
void	capd::vectalg::rightObject (const IntervalObject &v, ResultType &result)

template<typename ResultType , typename IntervalObject >
ResultType	capd::vectalg::rightObject (const IntervalObject &v)

template<typename ResultType , typename ScalarType >
ResultType	capd::vectalg::convertScalar (const ScalarType &v)

template<typename ResultType , typename ContainerType >
ResultType	capd::vectalg::convertObject (const ContainerType &v)

template<typename VectorType >
VectorType	capd::vectalg::conjVector (const VectorType &v)

template<typename VectorType >
VectorType::ScalarType	power (const VectorType &v, const capd::vectalg::Multiindex &m)
	It computes v^m where v is a vector and m is a multiindex. More...

template<typename VectorType >
VectorType::ScalarType	power (const VectorType &v, const capd::vectalg::Multipointer &m)

template<typename Scalar , __size_type dim>
std::ostream &	capd::vectalg::operator<< (std::ostream &out, const Vector< Scalar, dim > &v)

template<typename Scalar , __size_type dim>
std::istream &	capd::vectalg::operator>> (std::istream &inp, Vector< Scalar, dim > &v)

template<typename Vector >
std::string	capd::vectalg::vectorToString (const Vector &v, int firstIndex=0, int lastIndex=-1, int precision=-1)

template<typename Vector >
std::ostream &	capd::vectalg::printVector (std::ostream &str, const Vector &v, int firstIndex=0, int lastIndex=-1)

template<typename Scalar , __size_type dim>
std::ostream &	capd::vectalg::print (std::ostream &str, const Vector< Scalar, dim > &v, int firstIndex=0, int lastIndex=-1)

template<typename Scalar , __size_type dim>
std::string	capd::vectalg::cppReprezentation (const Vector< Scalar, dim > &A, const std::string &varName, const std::string &typeName)
	It serializes a matrix - gives text reprezentation which can be compiled. More...

	MatrixSlice< matrix >::MatrixSlice (matrix &m, int A_mFirstRow, int A_nLastRow, int A_nFirstCol, int A_nLastCol)

ScalarType *	MatrixSlice< matrix >::at (size_type i, size_type j)

const ScalarType *	MatrixSlice< matrix >::at (size_type i, size_type j) const

size_type	MatrixSlice< matrix >::numberOfRows () const

size_type	MatrixSlice< matrix >::numberOfColumns () const

size_type	MatrixSlice< matrix >::rowStride () const

size_type	MatrixSlice< matrix >::columnStride () const

MatrixIterator< MatrixSlice< matrix > >	MatrixSlice< matrix >::beginMatrix ()

MatrixIterator< MatrixSlice< matrix > >	MatrixSlice< matrix >::endMatrix ()

MatrixIterator< MatrixSlice< matrix > >	MatrixSlice< matrix >::beginOfRow (size_type i)

MatrixIterator< MatrixSlice< matrix > >	MatrixSlice< matrix >::beginOfColumn (size_type j)

MatrixIterator< MatrixSlice< matrix > >	MatrixSlice< matrix >::endOfRow (size_type i)

MatrixIterator< MatrixSlice< matrix > >	MatrixSlice< matrix >::endOfColumn (size_type j)

const_MatrixIterator< MatrixSlice< matrix > >	MatrixSlice< matrix >::beginOfRow (size_type i) const

const_MatrixIterator< MatrixSlice< matrix > >	MatrixSlice< matrix >::beginOfColumn (size_type j) const

const_MatrixIterator< MatrixSlice< matrix > >	MatrixSlice< matrix >::endOfRow (size_type i) const

const_MatrixIterator< MatrixSlice< matrix > >	MatrixSlice< matrix >::endOfColumn (size_type j) const

Detailed Description

Macro Definition Documentation

◆ CAPD_DEFAULT_DIMENSION

#define CAPD_DEFAULT_DIMENSION 0

Function Documentation

◆ at() [1/2]

template<typename matrix >

matrix::ScalarType * MatrixSlice< matrix >::at	(	size_type	i,
		size_type	j
	)

inline

◆ at() [2/2]

template<typename matrix >

const matrix::ScalarType * MatrixSlice< matrix >::at	(	size_type	i,
		size_type	j
	)		const

inline

◆ beginMatrix()

template<typename matrix >

const_MatrixIterator< MatrixSlice< matrix > > MatrixSlice< matrix >::beginMatrix

inline

◆ beginOfColumn() [1/2]

template<typename matrix >

MatrixIterator< MatrixSlice< matrix > > MatrixSlice< matrix >::beginOfColumn ( size_type j )

inline

◆ beginOfColumn() [2/2]

template<typename matrix >

const_MatrixIterator< MatrixSlice< matrix > > MatrixSlice< matrix >::beginOfColumn ( size_type j ) const

inline

◆ beginOfRow() [1/2]

template<typename matrix >

MatrixIterator< MatrixSlice< matrix > > MatrixSlice< matrix >::beginOfRow ( size_type i )

inline

◆ beginOfRow() [2/2]

template<typename matrix >

const_MatrixIterator< MatrixSlice< matrix > > MatrixSlice< matrix >::beginOfRow ( size_type i ) const

inline

◆ columnStride()

template<typename matrix >

MatrixSlice< matrix >::size_type MatrixSlice< matrix >::columnStride

inline

◆ conjVector()

template<typename VectorType >

VectorType capd::vectalg::conjVector ( const VectorType & v )

◆ containsZero()

template<typename IntervalObject >

bool capd::vectalg::containsZero ( const IntervalObject & v )

checks if IntervalObject v contains zero on all coordinates

◆ convertObject()

template<typename ResultType , typename ContainerType >

ResultType capd::vectalg::convertObject ( const ContainerType & v )

◆ convertScalar()

template<typename ResultType , typename ScalarType >

ResultType capd::vectalg::convertScalar ( const ScalarType & v )

◆ cppReprezentation()

template<typename Scalar , __size_type dim>

std::string capd::vectalg::cppReprezentation	(	const Vector< Scalar, dim > &	A,
		const std::string &	varName,
		const std::string &	typeName
	)

It serializes a matrix - gives text reprezentation which can be compiled.

◆ diameter()

template<typename IntervalObject , typename ResultContainer >

void capd::vectalg::diameter	(	const IntervalObject &	v,
		ResultContainer &	result
	)

◆ endMatrix()

template<typename matrix >

const_MatrixIterator< MatrixSlice< matrix > > MatrixSlice< matrix >::endMatrix

inline

◆ endOfColumn() [1/2]

template<typename matrix >

MatrixIterator< MatrixSlice< matrix > > MatrixSlice< matrix >::endOfColumn ( size_type j )

inline

◆ endOfColumn() [2/2]

template<typename matrix >

const_MatrixIterator< MatrixSlice< matrix > > MatrixSlice< matrix >::endOfColumn ( size_type j ) const

inline

◆ endOfRow() [1/2]

template<typename matrix >

MatrixIterator< MatrixSlice< matrix > > MatrixSlice< matrix >::endOfRow ( size_type i )

inline

◆ endOfRow() [2/2]

template<typename matrix >

const_MatrixIterator< MatrixSlice< matrix > > MatrixSlice< matrix >::endOfRow ( size_type i ) const

inline

◆ intersection() [1/2]

template<typename IntervalObject1 , typename IntervalObject2 , typename IntervalObject3 >

bool capd::vectalg::intersection	(	const IntervalObject1 &	v1,
		const IntervalObject2 &	v2,
		IntervalObject3 &	result
	)

inline

intersection of two interval objects (vectors, matrices)

Returns: true and intersection in result if intersection is not empty false if intersection is empty (value of result is meaningless)

◆ intersection() [2/2]

template<typename Iterator1 , typename Iterator2 , typename ResultIterator >

bool capd::vectalg::intersection	(	Iterator1	b1,
		Iterator2	b2,
		ResultIterator	b,
		ResultIterator	e
	)

intersection of two interval objects (vectors, matrices)

Returns: true and intersection in result if intersection is not empty false if intersection is empty (value of result is meaningless)

◆ intersectionIsEmpty() [1/2]

template<typename IntervalObject1 , typename IntervalObject2 >

bool capd::vectalg::intersectionIsEmpty	(	const IntervalObject1 &	v,
		const IntervalObject2 &	w
	)

inline

checks if intersection of two interval vectors is empty

Returns: true if intersection is empty false if intersection is not empty

◆ intersectionIsEmpty() [2/2]

template<typename Iterator1 , typename Iterator2 >

bool capd::vectalg::intersectionIsEmpty	(	Iterator1	b,
		Iterator1	e,
		Iterator2	b1
	)

checks if intersection of two interval vectors is empty

Returns: true if intersection is empty false if intersection is not empty

◆ intervalHull()

template<typename IntervalObject >

void capd::vectalg::intervalHull	(	const IntervalObject &	v1,
		const IntervalObject &	v2,
		IntervalObject &	result
	)

◆ leftObject() [1/2]

template<typename ResultType , typename IntervalObject >

ResultType capd::vectalg::leftObject ( const IntervalObject & v )

inline

◆ leftObject() [2/2]

template<typename ResultType , typename IntervalObject >

void capd::vectalg::leftObject	(	const IntervalObject &	v,
		ResultType &	result
	)

◆ MatrixSlice()

template<typename matrix >

MatrixSlice< matrix >::MatrixSlice	(	matrix &	m,
		int	A_mFirstRow,
		int	A_nLastRow,
		int	A_nFirstCol,
		int	A_nLastCol
	)

◆ maxDiam()

template<typename IObject >

IObject::ScalarType capd::vectalg::maxDiam ( const IObject & v )

returns the upper bound for the biggest diameter of IntervalObject (vector or matrix) coordinates

◆ maxWidth()

template<typename IObject >

capd::TypeTraits< typename IObject::ScalarType >::Real capd::vectalg::maxWidth ( const IObject & v )

returns the biggest diameter of the interval object (vector or matrix) coordinates (non-rigorous)

◆ mid()

template<typename IntervalObject , typename ResultType >

void capd::vectalg::mid	(	const IntervalObject &	v,
		ResultType &	result
	)

◆ midObject()

template<typename ResultType , typename IntervalObject >

ResultType capd::vectalg::midObject ( const IntervalObject & v )

◆ nonnegativePart() [1/3]

double nonnegativePart ( double x )

inline

◆ nonnegativePart() [2/3]

double nonnegativePart ( int x )

inline

◆ nonnegativePart() [3/3]

double nonnegativePart ( long double x )

inline

◆ numberOfColumns()

template<typename matrix >

MatrixSlice< matrix >::size_type MatrixSlice< matrix >::numberOfColumns

inline

◆ numberOfRows()

template<typename matrix >

MatrixSlice< matrix >::size_type MatrixSlice< matrix >::numberOfRows

inline

◆ operator<<()

template<typename Scalar , __size_type dim>

std::ostream & capd::vectalg::operator<<	(	std::ostream &	out,
		const Vector< Scalar, dim > &	v
	)

◆ operator>>()

template<typename Scalar , __size_type dim>

std::istream & capd::vectalg::operator>>	(	std::istream &	inp,
		Vector< Scalar, dim > &	v
	)

◆ power() [1/2]

template<typename VectorType >

VectorType::ScalarType power	(	const VectorType &	v,
		const capd::vectalg::Multiindex &	m
	)

It computes v^m where v is a vector and m is a multiindex.

◆ power() [2/2]

template<typename VectorType >

VectorType::ScalarType power	(	const VectorType &	v,
		const capd::vectalg::Multipointer &	m
	)

◆ print()

template<typename Scalar , __size_type dim>

std::ostream& capd::vectalg::print	(	std::ostream &	str,
		const Vector< Scalar, dim > &	v,
		int	firstIndex = `0`,
		int	lastIndex = `-1`
	)

inline

◆ printVector()

template<typename Vector >

std::ostream & capd::vectalg::printVector	(	std::ostream &	str,
		const Vector &	v,
		int	firstIndex = `0`,
		int	lastIndex = `-1`
	)

◆ rightObject() [1/2]

template<typename ResultType , typename IntervalObject >

ResultType capd::vectalg::rightObject ( const IntervalObject & v )

inline

◆ rightObject() [2/2]

template<typename ResultType , typename IntervalObject >

void capd::vectalg::rightObject	(	const IntervalObject &	v,
		ResultType &	result
	)

◆ rowStride()

template<typename matrix >

MatrixSlice< matrix >::size_type MatrixSlice< matrix >::rowStride

inline

◆ split() [1/3]

template<typename IntervalObject , typename CenterType >

void capd::vectalg::split	(	const IntervalObject &	v,
		CenterType &	center,
		IntervalObject &	diameter
	)

inline

splits IntervalObject v into form center + diameter where diameter = [-radius,radius] on each coordinate

Parameters

[in]	v	object to be splitted,
[out]	center	returns center of the object.
[out]	diameter	returns zero centered set [-radius,radius].

◆ split() [2/3]

template<typename IntervalObject1 , typename IntervalObject2 >

void capd::vectalg::split	(	IntervalObject1 &	v,
		IntervalObject2 &	rv
	)

inline

splits IntervalObject v into form center + [-radius, radius] form

Parameters

[in,out]	v	object to be splitted, returns center of the object.
[out]	rv	returns zero centered set [-radius, radius].

◆ split() [3/3]

template<typename SourceIterator , typename Iterator1 , typename Iterator2 >

void capd::vectalg::split	(	SourceIterator	sourceBegin,
		SourceIterator	sourceEnd,
		Iterator1	center,
		Iterator2	diameter
	)

splits source object given by [sourceBegin, sourceEnd] into form center + diameter where diameter = [-radius,radius] on each coordinatedimension

Parameters

[in]	sourceBegin,sourceEnd	object to be splitted,
[out]	center	returns center of the object (it should be iterator on first element)
[out]	diameter	returns zero centered set [-radius,radius] (it should be iterator on first element)

◆ subset()

template<typename IntervalObject >

bool capd::vectalg::subset	(	const IntervalObject &	v1,
		const IntervalObject &	v2
	)

checks if IntervalObject v1 is contained in IntervalObject v2

◆ subsetInterior()

template<typename IntervalObject >

bool capd::vectalg::subsetInterior	(	const IntervalObject &	v1,
		const IntervalObject &	v2
	)

checks if IntervalObject v1 is contained in interior of IntervalObject v2

◆ vectorToString()

template<typename Vector >

std::string capd::vectalg::vectorToString	(	const Vector &	v,
		int	firstIndex = `0`,
		int	lastIndex = `-1`,
		int	precision = `-1`
	)

Files

Namespaces

Classes

Macros

Functions

Detailed Description

Macro Definition Documentation

◆ CAPD_DEFAULT_DIMENSION

Function Documentation

◆ at() [1/2]

◆ at() [2/2]

◆ beginMatrix()

◆ beginOfColumn() [1/2]

◆ beginOfColumn() [2/2]

◆ beginOfRow() [1/2]

◆ beginOfRow() [2/2]

◆ columnStride()

◆ conjVector()

◆ containsZero()

◆ convertObject()

◆ convertScalar()

◆ cppReprezentation()

◆ diameter()

◆ endMatrix()

◆ endOfColumn() [1/2]

◆ endOfColumn() [2/2]

◆ endOfRow() [1/2]

◆ endOfRow() [2/2]

◆ intersection() [1/2]

◆ intersection() [2/2]

◆ intersectionIsEmpty() [1/2]

◆ intersectionIsEmpty() [2/2]

◆ intervalHull()

◆ leftObject() [1/2]

◆ leftObject() [2/2]

◆ MatrixSlice()

◆ maxDiam()

◆ maxWidth()

◆ mid()

◆ midObject()

◆ nonnegativePart() [1/3]

◆ nonnegativePart() [2/3]

◆ nonnegativePart() [3/3]

◆ numberOfColumns()

◆ numberOfRows()

◆ operator<<()

◆ operator>>()

◆ power() [1/2]

◆ power() [2/2]

◆ print()

◆ printVector()

◆ rightObject() [1/2]

◆ rightObject() [2/2]

◆ rowStride()

◆ split() [1/3]

◆ split() [2/3]

◆ split() [3/3]

◆ subset()

◆ subsetInterior()

◆ vectorToString()