fcl::TaylorModel< S > Class Template Reference

TaylorModel implements a third order Taylor model, i.e., a cubic approximation of a function over a time interval, with an interval remainder. All the operations on two Taylor models assume their time intervals are the same. More...

#include <taylor_model.h>

Public Member Functions
S &	coeff (std::size_t i)
S	coeff (std::size_t i) const
Interval< S >	getBound () const
Interval< S >	getBound (S l, S r) const
Interval< S >	getBound (S t) const
Interval< S >	getTightBound () const
Interval< S >	getTightBound (S l, S r) const
const std::shared_ptr< TimeInterval< S > > &	getTimeInterval () const
TaylorModel	operator* (const TaylorModel &other) const
	Taylor model multiplication: f(t) = c0+c1*t+c2*t^2+c3*t^3+[a,b] g(t) = c0'+c1'*t+c2'*t^2+c3'*t^2+[c,d] f(t)g(t)= c0c0'+ (c0c1'+c1c0')t+ (c0c2'+c1c1'+c2c0')t^2+ (c0c3'+c1c2'+c2c1'+c3c0')t^3+ [a,b][c,d]+ (c1c3'+c2c2'+c3c1')t^4+ (c2c3'+c3c2')t^5+ (c3c3')t^6+ (c0+c1*t+c2*t^2+c3*t^3)[c,d]+ (c0'+c1'*t+c2'*t^2+c3'*c^3)[a,b]. More...
TaylorModel	operator* (S d) const
TaylorModel &	operator*= (const TaylorModel &other)
TaylorModel &	operator*= (S d)
TaylorModel	operator+ (const TaylorModel &other) const
TaylorModel	operator+ (S d) const
TaylorModel &	operator+= (const TaylorModel &other)
TaylorModel &	operator+= (S d)
TaylorModel	operator- () const
TaylorModel	operator- (const TaylorModel &other) const
TaylorModel	operator- (S d) const
TaylorModel &	operator-= (const TaylorModel &other)
TaylorModel &	operator-= (S d)
void	print () const
Interval< S > &	remainder ()
const Interval< S > &	remainder () const
void	setTimeInterval (const std::shared_ptr< TimeInterval< S >> &time_interval)
void	setTimeInterval (S l, S r)
void	setZero ()
	TaylorModel ()
	TaylorModel (const std::shared_ptr< TimeInterval< S >> &time_interval)
	TaylorModel (S c0, S c1, S c2, S c3, const Interval< S > &r, const std::shared_ptr< TimeInterval< S >> &time_interval)
	TaylorModel (S coeff, const std::shared_ptr< TimeInterval< S >> &time_interval)
	TaylorModel (S coeffs[3], const Interval< S > &r, const std::shared_ptr< TimeInterval< S >> &time_interval)

Private Attributes
S	coeffs_ [4]
	Coefficients of the cubic polynomial approximation. More...
Interval< S >	r_
	interval remainder More...
std::shared_ptr< TimeInterval< S > >	time_interval_
	time interval More...

Detailed Description

template<typename S>
class fcl::TaylorModel< S >

TaylorModel implements a third order Taylor model, i.e., a cubic approximation of a function over a time interval, with an interval remainder. All the operations on two Taylor models assume their time intervals are the same.

Definition at line 58 of file taylor_model.h.

Constructor & Destructor Documentation

TaylorModel() [1/5]

template<typename S >

fcl::TaylorModel< S >::TaylorModel

Definition at line 128 of file taylor_model-inl.h.

TaylorModel() [2/5]

template<typename S >

fcl::TaylorModel< S >::TaylorModel

(

const std::shared_ptr< TimeInterval< S >> &

time_interval

)

Definition at line 135 of file taylor_model-inl.h.

TaylorModel() [3/5]

template<typename S >

fcl::TaylorModel< S >::TaylorModel	(	S	coeff,
		const std::shared_ptr< TimeInterval< S >> &	time_interval
	)

Definition at line 142 of file taylor_model-inl.h.

TaylorModel() [4/5]

template<typename S >

fcl::TaylorModel< S >::TaylorModel	(	S	coeffs[3],
		const Interval< S > &	r,
		const std::shared_ptr< TimeInterval< S >> &	time_interval
	)

Definition at line 150 of file taylor_model-inl.h.

TaylorModel() [5/5]

template<typename S >

fcl::TaylorModel< S >::TaylorModel	(	S	c0,
		S	c1,
		S	c2,
		S	c3,
		const Interval< S > &	r,
		const std::shared_ptr< TimeInterval< S >> &	time_interval
	)

Definition at line 162 of file taylor_model-inl.h.

Member Function Documentation

coeff() [1/2]

template<typename S >

S & fcl::TaylorModel< S >::coeff

(

std::size_t

i

)

Definition at line 107 of file taylor_model-inl.h.

coeff() [2/2]

template<typename S >

S fcl::TaylorModel< S >::coeff

(

std::size_t

i

)

const

Definition at line 100 of file taylor_model-inl.h.

getBound() [1/3]

template<typename S >

Interval< S > fcl::TaylorModel< S >::getBound

Definition at line 357 of file taylor_model-inl.h.

getBound() [2/3]

template<typename S >

Interval< S > fcl::TaylorModel< S >::getBound	(	S	l,
		S	r
	)		const

Definition at line 346 of file taylor_model-inl.h.

getBound() [3/3]

template<typename S >

Interval< S > fcl::TaylorModel< S >::getBound

(

S

t

)

const

Definition at line 339 of file taylor_model-inl.h.

getTightBound() [1/2]

template<typename S >

Interval< S > fcl::TaylorModel< S >::getTightBound

Definition at line 449 of file taylor_model-inl.h.

getTightBound() [2/2]

template<typename S >

Interval< S > fcl::TaylorModel< S >::getTightBound	(	S	l,
		S	r
	)		const

Definition at line 364 of file taylor_model-inl.h.

getTimeInterval()

template<typename S >

const std::shared_ptr< TimeInterval< S > > & fcl::TaylorModel< S >::getTimeInterval

Definition at line 93 of file taylor_model-inl.h.

operator*() [1/2]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator*

(

const TaylorModel< S > &

other

)

const

Taylor model multiplication: f(t) = c0+c1*t+c2*t^2+c3*t^3+[a,b] g(t) = c0'+c1'*t+c2'*t^2+c3'*t^2+[c,d] f(t)g(t)= c0c0'+ (c0c1'+c1c0')t+ (c0c2'+c1c1'+c2c0')t^2+ (c0c3'+c1c2'+c2c1'+c3c0')t^3+ [a,b][c,d]+ (c1c3'+c2c2'+c3c1')t^4+ (c2c3'+c3c2')t^5+ (c3c3')t^6+ (c0+c1*t+c2*t^2+c3*t^3)[c,d]+ (c0'+c1'*t+c2'*t^2+c3'*c^3)[a,b].

Definition at line 259 of file taylor_model-inl.h.

operator*() [2/2]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator*

(

S

d

)

const

Definition at line 268 of file taylor_model-inl.h.

operator*=() [1/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator*=

(

const TaylorModel< S > &

other

)

Definition at line 275 of file taylor_model-inl.h.

operator*=() [2/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator*=

(

S

d

)

Definition at line 313 of file taylor_model-inl.h.

operator+() [1/2]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator+

(

const TaylorModel< S > &

other

)

const

Definition at line 204 of file taylor_model-inl.h.

operator+() [2/2]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator+

(

S

d

)

const

Definition at line 174 of file taylor_model-inl.h.

operator+=() [1/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator+=

(

const TaylorModel< S > &

other

)

Definition at line 220 of file taylor_model-inl.h.

operator+=() [2/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator+=

(

S

d

)

Definition at line 181 of file taylor_model-inl.h.

operator-() [1/3]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator-

Definition at line 325 of file taylor_model-inl.h.

operator-() [2/3]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator-

(

const TaylorModel< S > &

other

)

const

Definition at line 212 of file taylor_model-inl.h.

operator-() [3/3]

template<typename S >

TaylorModel< S > fcl::TaylorModel< S >::operator-

(

S

d

)

const

Definition at line 189 of file taylor_model-inl.h.

operator-=() [1/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator-=

(

const TaylorModel< S > &

other

)

Definition at line 233 of file taylor_model-inl.h.

operator-=() [2/2]

template<typename S >

TaylorModel< S > & fcl::TaylorModel< S >::operator-=

(

S

d

)

Definition at line 196 of file taylor_model-inl.h.

print()

template<typename S >

void fcl::TaylorModel< S >::print

Definition at line 332 of file taylor_model-inl.h.

remainder() [1/2]

template<typename S >

Interval<S>& fcl::TaylorModel< S >::remainder

(

)

remainder() [2/2]

template<typename S >

Interval< S > & fcl::TaylorModel< S >::remainder

Definition at line 114 of file taylor_model-inl.h.

setTimeInterval() [1/2]

template<typename S >

void fcl::TaylorModel< S >::setTimeInterval

(

const std::shared_ptr< TimeInterval< S >> &

time_interval

)

setTimeInterval() [2/2]

template<typename S >

void fcl::TaylorModel< S >::setTimeInterval	(	S	l,
		S	r
	)

Definition at line 79 of file taylor_model-inl.h.

setZero()

template<typename S >

void fcl::TaylorModel< S >::setZero

Definition at line 456 of file taylor_model-inl.h.

Member Data Documentation

coeffs_

template<typename S >

S fcl::TaylorModel< S >::coeffs_[4]

private

Coefficients of the cubic polynomial approximation.

Definition at line 64 of file taylor_model.h.

r_

template<typename S >

Interval<S> fcl::TaylorModel< S >::r_

private

interval remainder

Definition at line 67 of file taylor_model.h.

time_interval_

template<typename S >

std::shared_ptr<TimeInterval<S> > fcl::TaylorModel< S >::time_interval_

private

time interval

Definition at line 61 of file taylor_model.h.

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The documentation for this class was generated from the following files:

• taylor_model.h
• taylor_model-inl.h