Classes in this module represent geometry of the set. They are basis for 'dynset' classes. Read detailed description of GeomSet for more details. More...

Classes
class	capd::geomset::AffineSet< MatrixT >
	Affine set representanion of the form x0 + B*r . More...

class	capd::geomset::CenteredAffineSet< MatrixT >
	Affine set representation of the form x + B * r which assures that r contains zero. More...

class	capd::geomset::CenteredDoubletonSet< MatrixT >
	Doubleton representation of the form x0 + Cr0 + Br which checks if r0 and r contain 0. More...

class	capd::geomset::CenteredTripletonSet< MatrixT >
	Class CenteredTripletonSet represents a subset of R^n in the following form. More...

class	capd::geomset::DoubletonSet< MatrixT >
	Doubleton representation of the form x0 + Cr0 + Br . More...

class	capd::geomset::MatrixAffineSet< MatrixT >
	Set of matrices represented as D + Bjac * R. More...

class	capd::geomset::MatrixDoubletonSet< MatrixT >
	Set of matrices represented as D + Cjac * R0 + Bjac * R. More...

Functions
	capd::geomset::AffineSet< MatrixT >::AffineSet (size_type)
	sets x:=0, r:=0, B:=Id More...

	capd::geomset::AffineSet< MatrixT >::AffineSet (const VectorType &v)
	sets x:=mid(v), B:=Id, r:=[-radius(v), radius(v)] More...

	capd::geomset::AffineSet< MatrixT >::AffineSet (const VectorType &x, bool)
	sets x:=x, B:=Id, r:=0 More...

	capd::geomset::AffineSet< MatrixT >::AffineSet (const VectorType &x, const VectorType &r)
	sets x:=x r:=r B:=Id More...

	capd::geomset::AffineSet< MatrixT >::AffineSet (const VectorType &x, const MatrixType &B, const VectorType &r)
	sets x:=x r:=r B:=B More...

virtual std::string	capd::geomset::AffineSet< MatrixT >::toString () const
	returns set detailed information More...

virtual VectorType	capd::geomset::AffineSet< MatrixT >::affineTransformation (const MatrixType &, const VectorType &) const
	returns set image after affine transformation More...

virtual ScalarType	capd::geomset::AffineSet< MatrixT >::evalAffineFunctional (const VectorType &gradient, const VectorType &x0) const
	This method computes value of an affine functional f at the vector represented by this set. This set is represented as doubleton X=x+Br. Then f(X) = grad(X-x0) can be computed as grad(x-x0) + (gradB)*r. More...

	capd::geomset::CenteredDoubletonSet< MatrixT >::CenteredDoubletonSet (const VectorType &x)

	capd::geomset::CenteredDoubletonSet< MatrixT >::CenteredDoubletonSet (const VectorType &x, const VectorType &r0)

	capd::geomset::CenteredDoubletonSet< MatrixT >::CenteredDoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0)

	capd::geomset::CenteredDoubletonSet< MatrixT >::CenteredDoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const VectorType &r)

	capd::geomset::CenteredDoubletonSet< MatrixT >::CenteredDoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const MatrixType &B, const VectorType &r)

void	capd::geomset::CenteredTripletonSet< MatrixT >::copyQ ()

	capd::geomset::CenteredTripletonSet< MatrixT >::CenteredTripletonSet (const VectorType &x)

	capd::geomset::CenteredTripletonSet< MatrixT >::CenteredTripletonSet (const VectorType &x, const VectorType &r0)

	capd::geomset::CenteredTripletonSet< MatrixT >::CenteredTripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0)

	capd::geomset::CenteredTripletonSet< MatrixT >::CenteredTripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const VectorType &r)

	capd::geomset::CenteredTripletonSet< MatrixT >::CenteredTripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const MatrixType &B, const VectorType &r)

	capd::geomset::CenteredTripletonSet< MatrixT >::CenteredTripletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const MatrixType &B, const VectorType &r, const MatrixType &Q, const VectorType &q)

virtual VectorType	capd::geomset::CenteredTripletonSet< MatrixT >::affineTransformation (const MatrixType &M, const VectorType &x0) const
	This method computes value of an affine map f at interval vector represented by this set. This set is represented as tripleton X=x+Cr0+intersection(Br,Qq). Then f(X) = M(X-x0) can be computed as M(x-x0) + (MC)r0 + intersection( MB)r, (MQ)*q ) More...

virtual ScalarType	capd::geomset::CenteredTripletonSet< MatrixT >::evalAffineFunctional (const VectorType &gradient, const VectorType &x0) const
	This method computes value of an affine functional f at interval vector represented by this set. This set is represented as tripleton X=x+Cr0+intersection(Br,Qq). Then f(X) = grad(X-x0) can be computed as grad(x-x0) + (gradC)r0 + intersection( gradB)r, (gradQ)*q ) More...

	capd::geomset::DoubletonSet< MatrixT >::DoubletonSet (size_type)
	x:=0, r0:=0, C:=Id, r:=0, r:=Id More...

	capd::geomset::DoubletonSet< MatrixT >::DoubletonSet (const VectorType &x)
	x:=mid(v), r0:=[-radius(v),radius(v)], C:=Id, r:=0, r:=Id More...

	capd::geomset::DoubletonSet< MatrixT >::DoubletonSet (const VectorType &r0, bool)
	x:=0, r0:=r0, C:=Id, r:=0, r:=Id More...

	capd::geomset::DoubletonSet< MatrixT >::DoubletonSet (const VectorType &x, const VectorType &r0)
	x:=x, r0:=r0, C:=Id, r:=0, r:=Id More...

	capd::geomset::DoubletonSet< MatrixT >::DoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0)

	capd::geomset::DoubletonSet< MatrixT >::DoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const VectorType &r)

	capd::geomset::DoubletonSet< MatrixT >::DoubletonSet (const VectorType &x, const MatrixType &C, const VectorType &r0, const MatrixType &B, const VectorType &r)

DoubletonSet &	capd::geomset::DoubletonSet< MatrixT >::operator= (const VectorType &v)

std::string	capd::geomset::DoubletonSet< MatrixT >::toString () const
	returns set detailed information More...

virtual VectorType	capd::geomset::DoubletonSet< MatrixT >::affineTransformation (const MatrixType &M, const VectorType &x0) const
	This method computes value of an affine map f at interval vector represented by this set. This set is represented as tripleton X=x+Cr0+intersection(Br,Qq). Then f(X) = M(X-x0) can be computed as M(x-x0) + (MC)r0 + intersection( MB)r, (MQ)*q ) More...

virtual ScalarType	capd::geomset::DoubletonSet< MatrixT >::evalAffineFunctional (const VectorType &gradient, const VectorType &x0) const
	This method computes value of an affine functional f at the vector represented by this set. This set is represented as doubleton X=x+Cr0+Br. Then f(X) = grad(X-x0) can be computed as grad(x-x0) + (gradC)r0 + (gradB)r. More...

	capd::geomset::MatrixAffineSet< MatrixT >::MatrixAffineSet (size_type dim)
	A:=ID, R:=0, B:=Id. More...

	capd::geomset::MatrixAffineSet< MatrixT >::MatrixAffineSet (const MatrixType &A)
	A:=mid(v), B:=Id, R:=[-radius(v), radius(v)]. More...

	capd::geomset::MatrixAffineSet< MatrixT >::MatrixAffineSet (const MatrixType &D, bool)
	A:=A, B:=Id, R:=0. More...

	capd::geomset::MatrixAffineSet< MatrixT >::MatrixAffineSet (const MatrixType &D, const MatrixType &R)
	A:=A R:=R B:=Id. More...

	capd::geomset::MatrixAffineSet< MatrixT >::MatrixAffineSet (const MatrixType &D, const MatrixType &Bjac, const MatrixType &R)
	A:=A R:=R B:=B. More...

void	capd::geomset::MatrixAffineSet< MatrixT >::setToIdentity ()
	sets the set to identity More...

virtual std::string	capd::geomset::MatrixAffineSet< MatrixT >::toString () const
	returns set detailed information More...

virtual MatrixType	capd::geomset::MatrixAffineSet< MatrixT >::affineMatrixTransformation (const MatrixType &A_M) const
	returns image of the set after affine transformation More...

	capd::geomset::MatrixDoubletonSet< MatrixT >::MatrixDoubletonSet (size_type)
	D:=Id, R0:=0, C:=Id, R:=0, B:=Id. More...

	capd::geomset::MatrixDoubletonSet< MatrixT >::MatrixDoubletonSet (const MatrixType &V)
	D:=mid(V), R0:=[-radius(V),radius(V)], C:=Id, R:=0, B:=Id. More...

	capd::geomset::MatrixDoubletonSet< MatrixT >::MatrixDoubletonSet (const MatrixType &D, bool)
	D:=D, R0:=0, C:=Id, R:=0, B:=Id. More...

	capd::geomset::MatrixDoubletonSet< MatrixT >::MatrixDoubletonSet (const MatrixType &D, const MatrixType &R0)
	D:=D, R0:=R0, C:=Id, R:=0, B:=Id. More...

	capd::geomset::MatrixDoubletonSet< MatrixT >::MatrixDoubletonSet (const MatrixType &D, const MatrixType &Cjac, const MatrixType &R0)

	capd::geomset::MatrixDoubletonSet< MatrixT >::MatrixDoubletonSet (const MatrixType &D, const MatrixType &Cjac, const MatrixType &R0, const MatrixType &R)

	capd::geomset::MatrixDoubletonSet< MatrixT >::MatrixDoubletonSet (const MatrixType &D, const MatrixType &Cjac, const MatrixType &R0, const MatrixType &Bjac, const MatrixType &R)

void	capd::geomset::MatrixDoubletonSet< MatrixT >::setToIdentity (size_type dim)

std::string	capd::geomset::MatrixDoubletonSet< MatrixT >::toString () const
	returns set detailed information More...

virtual MatrixType	capd::geomset::MatrixDoubletonSet< MatrixT >::affineMatrixTransformation (const MatrixType &) const
	returns image of the set after affine transformation More...

Detailed Description

Classes in this module represent geometry of the set. They are basis for 'dynset' classes. Read detailed description of GeomSet for more details.

Function Documentation

◆ affineMatrixTransformation() [1/2]

template<typename MatrixType >

MatrixDoubletonSet< MatrixType >::MatrixType capd::geomset::MatrixDoubletonSet< MatrixType >::affineMatrixTransformation ( const MatrixType & A_M ) const

virtual

returns image of the set after affine transformation

makes affine transformation of set, transformation is given by matrix M result = M * set

Reimplemented from capd::geomset::MatrixAffineSet< MatrixT >.

◆ affineMatrixTransformation() [2/2]

template<typename MatrixType >

MatrixAffineSet< MatrixType >::MatrixType capd::geomset::MatrixAffineSet< MatrixType >::affineMatrixTransformation ( const MatrixType & A_M ) const

virtual

returns image of the set after affine transformation

makes affine transformation of set, transformation is given by matrix M result = M * set

Reimplemented in capd::geomset::MatrixDoubletonSet< MatrixT >, and capd::geomset::MatrixDoubletonSet< GeometricBound::MatrixType >.

◆ AffineSet() [1/5]

template<typename MatrixType >

capd::geomset::AffineSet< MatrixType >::AffineSet ( const VectorType & v )

explicit

sets x:=mid(v), B:=Id, r:=[-radius(v), radius(v)]

◆ AffineSet() [2/5]

template<typename MatrixType >

capd::geomset::AffineSet< MatrixType >::AffineSet	(	const VectorType &	x,
		bool
	)

sets x:=x, B:=Id, r:=0

◆ AffineSet() [3/5]

template<typename MatrixType >

capd::geomset::AffineSet< MatrixType >::AffineSet	(	const VectorType &	x,
		const MatrixType &	B,
		const VectorType &	r
	)

sets x:=x r:=r B:=B

◆ AffineSet() [4/5]

template<typename MatrixType >

capd::geomset::AffineSet< MatrixType >::AffineSet	(	const VectorType &	x,
		const VectorType &	r
	)

sets x:=x r:=r B:=Id

◆ AffineSet() [5/5]

template<typename MatrixType >

capd::geomset::AffineSet< MatrixType >::AffineSet ( size_type dim )

explicit

sets x:=0, r:=0, B:=Id

◆ affineTransformation() [1/3]

template<typename MatrixType >

AffineSet< MatrixType >::VectorType capd::geomset::AffineSet< MatrixType >::affineTransformation	(	const MatrixType &	A_M,
		const VectorType &	A_C
	)		const

virtual

returns set image after affine transformation

makes affine transformation of the set with matrix M and center c

M * (set - c)

Reimplemented in capd::geomset::DoubletonSet< MatrixT >, capd::geomset::DoubletonSet< GeometricBound::MatrixType >, capd::geomset::CenteredTripletonSet< MatrixT >, and capd::dynset::C0HODoubletonSet< MatrixT, Policies >.

◆ affineTransformation() [2/3]

template<typename MatrixType >

CenteredTripletonSet< MatrixType >::VectorType capd::geomset::CenteredTripletonSet< MatrixType >::affineTransformation	(	const MatrixType &	M,
		const VectorType &	x0
	)		const

virtual

This method computes value of an affine map f at interval vector represented by this set. This set is represented as tripleton X=x+C*r0+intersection(B*r,Q*q). Then f(X) = M*(X-x0) can be computed as M*(x-x0) + (M*C)*r0 + intersection( M*B)*r, (M*Q)*q )

Reimplemented from capd::geomset::DoubletonSet< MatrixT >.

◆ affineTransformation() [3/3]

template<typename MatrixType >

DoubletonSet< MatrixType >::VectorType capd::geomset::DoubletonSet< MatrixType >::affineTransformation	(	const MatrixType &	M,
		const VectorType &	x0
	)		const

virtual

This method computes value of an affine map f at interval vector represented by this set. This set is represented as tripleton X=x+C*r0+intersection(B*r,Q*q). Then f(X) = M*(X-x0) can be computed as M*(x-x0) + (M*C)*r0 + intersection( M*B)*r, (M*Q)*q )

Reimplemented from capd::geomset::AffineSet< MatrixT >.

Reimplemented in capd::geomset::CenteredTripletonSet< MatrixT >, and capd::dynset::C0HODoubletonSet< MatrixT, Policies >.

◆ CenteredDoubletonSet() [1/5]

template<typename MatrixType >

capd::geomset::CenteredDoubletonSet< MatrixType >::CenteredDoubletonSet ( const VectorType & x )

explicit

◆ CenteredDoubletonSet() [2/5]

template<typename MatrixType >

capd::geomset::CenteredDoubletonSet< MatrixType >::CenteredDoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0
	)

◆ CenteredDoubletonSet() [3/5]

template<typename MatrixType >

capd::geomset::CenteredDoubletonSet< MatrixType >::CenteredDoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const MatrixType &	B,
		const VectorType &	r
	)

◆ CenteredDoubletonSet() [4/5]

template<typename MatrixType >

capd::geomset::CenteredDoubletonSet< MatrixType >::CenteredDoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const VectorType &	r
	)

◆ CenteredDoubletonSet() [5/5]

template<typename MatrixType >

capd::geomset::CenteredDoubletonSet< MatrixType >::CenteredDoubletonSet	(	const VectorType &	x,
		const VectorType &	r0
	)

◆ CenteredTripletonSet() [1/6]

template<typename MatrixType >

capd::geomset::CenteredTripletonSet< MatrixType >::CenteredTripletonSet ( const VectorType & x )

◆ CenteredTripletonSet() [2/6]

template<typename MatrixType >

capd::geomset::CenteredTripletonSet< MatrixType >::CenteredTripletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0
	)

◆ CenteredTripletonSet() [3/6]

template<typename MatrixType >

capd::geomset::CenteredTripletonSet< MatrixType >::CenteredTripletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const MatrixType &	B,
		const VectorType &	r
	)

◆ CenteredTripletonSet() [4/6]

template<typename MatrixType >

capd::geomset::CenteredTripletonSet< MatrixType >::CenteredTripletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const MatrixType &	B,
		const VectorType &	r,
		const MatrixType &	Q,
		const VectorType &	q
	)

protected

◆ CenteredTripletonSet() [5/6]

template<typename MatrixType >

capd::geomset::CenteredTripletonSet< MatrixType >::CenteredTripletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const VectorType &	r
	)

◆ CenteredTripletonSet() [6/6]

template<typename MatrixType >

capd::geomset::CenteredTripletonSet< MatrixType >::CenteredTripletonSet	(	const VectorType &	x,
		const VectorType &	r0
	)

◆ copyQ()

template<typename MatrixType >

void capd::geomset::CenteredTripletonSet< MatrixType >::copyQ

protected

◆ DoubletonSet() [1/7]

template<typename MatrixType >

capd::geomset::DoubletonSet< MatrixType >::DoubletonSet	(	const VectorType &	r0,
		bool
	)

x:=0, r0:=r0, C:=Id, r:=0, r:=Id

◆ DoubletonSet() [2/7]

template<typename MatrixType >

capd::geomset::DoubletonSet< MatrixType >::DoubletonSet ( const VectorType & x )

explicit

x:=mid(v), r0:=[-radius(v),radius(v)], C:=Id, r:=0, r:=Id

◆ DoubletonSet() [3/7]

template<typename MatrixType >

capd::geomset::DoubletonSet< MatrixType >::DoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0
	)

◆ DoubletonSet() [4/7]

template<typename MatrixType >

capd::geomset::DoubletonSet< MatrixType >::DoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const MatrixType &	B,
		const VectorType &	r
	)

◆ DoubletonSet() [5/7]

template<typename MatrixType >

capd::geomset::DoubletonSet< MatrixType >::DoubletonSet	(	const VectorType &	x,
		const MatrixType &	C,
		const VectorType &	r0,
		const VectorType &	r
	)

◆ DoubletonSet() [6/7]

template<typename MatrixType >

capd::geomset::DoubletonSet< MatrixType >::DoubletonSet	(	const VectorType &	x,
		const VectorType &	r0
	)

x:=x, r0:=r0, C:=Id, r:=0, r:=Id

◆ DoubletonSet() [7/7]

template<typename MatrixType >

capd::geomset::DoubletonSet< MatrixType >::DoubletonSet ( size_type dim )

explicit

x:=0, r0:=0, C:=Id, r:=0, r:=Id

◆ evalAffineFunctional() [1/3]

template<typename MatrixType >

CenteredTripletonSet< MatrixType >::ScalarType capd::geomset::CenteredTripletonSet< MatrixType >::evalAffineFunctional	(	const VectorType &	gradient,
		const VectorType &	x0
	)		const

virtual

This method computes value of an affine functional f at interval vector represented by this set. This set is represented as tripleton X=x+C*r0+intersection(B*r,Q*q). Then f(X) = grad*(X-x0) can be computed as grad*(x-x0) + (grad*C)*r0 + intersection( grad*B)*r, (grad*Q)*q )

Reimplemented from capd::geomset::DoubletonSet< MatrixT >.

◆ evalAffineFunctional() [2/3]

template<typename MatrixType >

AffineSet< MatrixType >::ScalarType capd::geomset::AffineSet< MatrixType >::evalAffineFunctional	(	const VectorType &	gradient,
		const VectorType &	x0
	)		const

virtual

This method computes value of an affine functional f at the vector represented by this set. This set is represented as doubleton X=x+B*r. Then f(X) = grad*(X-x0) can be computed as grad*(x-x0) + (grad*B)*r.

Reimplemented in capd::geomset::DoubletonSet< MatrixT >, capd::geomset::DoubletonSet< GeometricBound::MatrixType >, capd::geomset::CenteredTripletonSet< MatrixT >, and capd::dynset::C0HODoubletonSet< MatrixT, Policies >.

◆ evalAffineFunctional() [3/3]

template<typename MatrixType >

DoubletonSet< MatrixType >::ScalarType capd::geomset::DoubletonSet< MatrixType >::evalAffineFunctional	(	const VectorType &	gradient,
		const VectorType &	x0
	)		const

virtual

This method computes value of an affine functional f at the vector represented by this set. This set is represented as doubleton X=x+C*r0+B*r. Then f(X) = grad*(X-x0) can be computed as grad*(x-x0) + (grad*C)*r0 + (grad*B)*r.

Reimplemented from capd::geomset::AffineSet< MatrixT >.

Reimplemented in capd::geomset::CenteredTripletonSet< MatrixT >, and capd::dynset::C0HODoubletonSet< MatrixT, Policies >.

◆ MatrixAffineSet() [1/5]

template<typename MatrixType >

capd::geomset::MatrixAffineSet< MatrixType >::MatrixAffineSet ( const MatrixType & A )

explicit

A:=mid(v), B:=Id, R:=[-radius(v), radius(v)].

◆ MatrixAffineSet() [2/5]

template<typename MatrixType >

capd::geomset::MatrixAffineSet< MatrixType >::MatrixAffineSet	(	const MatrixType &	D,
		bool
	)

A:=A, B:=Id, R:=0.

◆ MatrixAffineSet() [3/5]

template<typename MatrixType >

capd::geomset::MatrixAffineSet< MatrixType >::MatrixAffineSet	(	const MatrixType &	D,
		const MatrixType &	Bjac,
		const MatrixType &	R
	)

A:=A R:=R B:=B.

◆ MatrixAffineSet() [4/5]

template<typename MatrixType >

capd::geomset::MatrixAffineSet< MatrixType >::MatrixAffineSet	(	const MatrixType &	D,
		const MatrixType &	R
	)

A:=A R:=R B:=Id.

◆ MatrixAffineSet() [5/5]

template<typename MatrixType >

capd::geomset::MatrixAffineSet< MatrixType >::MatrixAffineSet ( size_type dim )

explicit

A:=ID, R:=0, B:=Id.

◆ MatrixDoubletonSet() [1/7]

template<typename MatrixType >

capd::geomset::MatrixDoubletonSet< MatrixType >::MatrixDoubletonSet	(	const MatrixType &	D,
		bool
	)

D:=D, R0:=0, C:=Id, R:=0, B:=Id.

◆ MatrixDoubletonSet() [2/7]

template<typename MatrixType >

capd::geomset::MatrixDoubletonSet< MatrixType >::MatrixDoubletonSet	(	const MatrixType &	D,
		const MatrixType &	Cjac,
		const MatrixType &	R0
	)

◆ MatrixDoubletonSet() [3/7]

template<typename MatrixType >

capd::geomset::MatrixDoubletonSet< MatrixType >::MatrixDoubletonSet	(	const MatrixType &	D,
		const MatrixType &	Cjac,
		const MatrixType &	R0,
		const MatrixType &	Bjac,
		const MatrixType &	R
	)

◆ MatrixDoubletonSet() [4/7]

template<typename MatrixType >

capd::geomset::MatrixDoubletonSet< MatrixType >::MatrixDoubletonSet	(	const MatrixType &	D,
		const MatrixType &	Cjac,
		const MatrixType &	R0,
		const MatrixType &	R
	)

◆ MatrixDoubletonSet() [5/7]

template<typename MatrixType >

capd::geomset::MatrixDoubletonSet< MatrixType >::MatrixDoubletonSet	(	const MatrixType &	D,
		const MatrixType &	R0
	)

D:=D, R0:=R0, C:=Id, R:=0, B:=Id.

◆ MatrixDoubletonSet() [6/7]

template<typename MatrixType >

capd::geomset::MatrixDoubletonSet< MatrixType >::MatrixDoubletonSet ( const MatrixType & V )

explicit

D:=mid(V), R0:=[-radius(V),radius(V)], C:=Id, R:=0, B:=Id.

D:=mid(A), R0:=[-radius(A),radius(A)], C:=Id, R:=0, B:=Id.

◆ MatrixDoubletonSet() [7/7]

template<typename MatrixType >

capd::geomset::MatrixDoubletonSet< MatrixType >::MatrixDoubletonSet ( size_type dim )

explicit

D:=Id, R0:=0, C:=Id, R:=0, B:=Id.

◆ operator=()

template<typename MatrixType >

DoubletonSet< MatrixType > & capd::geomset::DoubletonSet< MatrixType >::operator= ( const VectorType & v )

◆ setToIdentity() [1/2]

template<typename MatrixType >

void capd::geomset::MatrixAffineSet< MatrixType >::setToIdentity

sets the set to identity

◆ setToIdentity() [2/2]

template<typename MatrixType >

void capd::geomset::MatrixDoubletonSet< MatrixType >::setToIdentity ( size_type dim )

◆ toString() [1/4]

template<typename MatrixType >

std::string capd::geomset::MatrixAffineSet< MatrixType >::toString

virtual

returns set detailed information

Reimplemented in capd::geomset::MatrixDoubletonSet< MatrixT >, capd::geomset::MatrixDoubletonSet< GeometricBound::MatrixType >, and capd::dynset::C11Rect2Set< MatrixT >.

◆ toString() [2/4]

template<typename MatrixType >

std::string capd::geomset::AffineSet< MatrixType >::toString

virtual

returns set detailed information

Reimplemented in capd::geomset::DoubletonSet< MatrixT >, capd::geomset::DoubletonSet< GeometricBound::MatrixType >, and capd::dynset::C11Rect2Set< MatrixT >.

◆ toString() [3/4]

template<typename MatrixType >

std::string capd::geomset::MatrixDoubletonSet< MatrixType >::toString

virtual

returns set detailed information

Reimplemented from capd::geomset::MatrixAffineSet< MatrixT >.

◆ toString() [4/4]

template<typename MatrixType >

std::string capd::geomset::DoubletonSet< MatrixType >::toString

virtual

returns set detailed information

Reimplemented from capd::geomset::AffineSet< MatrixT >.

Classes

Functions

Detailed Description

Function Documentation

◆ affineMatrixTransformation() [1/2]

◆ affineMatrixTransformation() [2/2]

◆ AffineSet() [1/5]

◆ AffineSet() [2/5]

◆ AffineSet() [3/5]

◆ AffineSet() [4/5]

◆ AffineSet() [5/5]

◆ affineTransformation() [1/3]

◆ affineTransformation() [2/3]

◆ affineTransformation() [3/3]

◆ CenteredDoubletonSet() [1/5]

◆ CenteredDoubletonSet() [2/5]

◆ CenteredDoubletonSet() [3/5]

◆ CenteredDoubletonSet() [4/5]

◆ CenteredDoubletonSet() [5/5]

◆ CenteredTripletonSet() [1/6]

◆ CenteredTripletonSet() [2/6]

◆ CenteredTripletonSet() [3/6]

◆ CenteredTripletonSet() [4/6]

◆ CenteredTripletonSet() [5/6]

◆ CenteredTripletonSet() [6/6]

◆ copyQ()

◆ DoubletonSet() [1/7]

◆ DoubletonSet() [2/7]

◆ DoubletonSet() [3/7]

◆ DoubletonSet() [4/7]

◆ DoubletonSet() [5/7]

◆ DoubletonSet() [6/7]

◆ DoubletonSet() [7/7]

◆ evalAffineFunctional() [1/3]

◆ evalAffineFunctional() [2/3]

◆ evalAffineFunctional() [3/3]

◆ MatrixAffineSet() [1/5]

◆ MatrixAffineSet() [2/5]

◆ MatrixAffineSet() [3/5]

◆ MatrixAffineSet() [4/5]

◆ MatrixAffineSet() [5/5]

◆ MatrixDoubletonSet() [1/7]

◆ MatrixDoubletonSet() [2/7]

◆ MatrixDoubletonSet() [3/7]

◆ MatrixDoubletonSet() [4/7]

◆ MatrixDoubletonSet() [5/7]

◆ MatrixDoubletonSet() [6/7]

◆ MatrixDoubletonSet() [7/7]

◆ operator=()

◆ setToIdentity() [1/2]

◆ setToIdentity() [2/2]

◆ toString() [1/4]

◆ toString() [2/4]

◆ toString() [3/4]

◆ toString() [4/4]