codac2_Ellipsoid.h File Reference

#include "codac2_Matrix.h"
#include "codac2_Vector.h"
#include "codac2_IntervalVector.h"
#include "codac2_AnalyticFunction.h"
#include "codac2_BoolInterval.h"

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Classes
class	codac2::Ellipsoid
	Ellipsoid representation. More...

Functions
Ellipsoid	codac2::operator+ (const Ellipsoid &e1, const Ellipsoid &e2)
	Compute the Minkowski sum of two ellipsoids.
Ellipsoid	codac2::linear_mapping (const Ellipsoid &e, const Matrix &A, const Vector &b)
	Guaranteed linear evaluation A*e+b, considering the rounding errors.
Ellipsoid	codac2::unreliable_linear_mapping (const Ellipsoid &e, const Matrix &A, const Vector &b)
	Nonrigorous linear evaluation A*e+b.
Ellipsoid	codac2::nonlinear_mapping (const Ellipsoid &e, const AnalyticFunction< VectorType > &f)
	(Rigorous?) non-linear evaluation f(e)
Ellipsoid	codac2::nonlinear_mapping (const Ellipsoid &e, const AnalyticFunction< VectorType > &f, const Vector &trig, const Vector &q)
	(Rigorous?) non-linear evaluation f(e), with parameters
Matrix	codac2::nonlinear_mapping_base (const Matrix &G, const Matrix &J, const IntervalMatrix &J_box, const Vector &trig, const Vector &q)
	(Rigorous?) non-linear evaluation f(e), from Jacobian information
std::ostream &	codac2::operator<< (std::ostream &os, const Ellipsoid &e)
	Streams out an Ellipsoid.

Detailed Description

Date

2024

Author

Morgan Louédec

Copyright

Copyright 2024 Codac Team

License: GNU Lesser General Public License (LGPL)

Function Documentation

operator+()

Ellipsoid codac2::operator+	(	const Ellipsoid &	e1,
		const Ellipsoid &	e2 )

Compute the Minkowski sum of two ellipsoids.

Parameters

e1	first ellipsoid
e2	second ellipsoid

Returns

the Minkowski sum

linear_mapping()

Ellipsoid codac2::linear_mapping	(	const Ellipsoid &	e,
		const Matrix &	A,
		const Vector &	b )

Guaranteed linear evaluation A*e+b, considering the rounding errors.

Parameters

e	input ellipsoid
A	matrix
b	vector

Returns

a rigorous outer enclosure of the linear mapping

unreliable_linear_mapping()

Ellipsoid codac2::unreliable_linear_mapping	(	const Ellipsoid &	e,
		const Matrix &	A,
		const Vector &	b )

Nonrigorous linear evaluation A*e+b.

Note

This function is used in linear_mapping() and provides a faster output than its guaranteed counterpart.

Parameters

e	input ellipsoid
A	matrix
b	vector

Returns

a nonrigorous approximation of the linear mapping

nonlinear_mapping() [1/2]

Ellipsoid codac2::nonlinear_mapping	(	const Ellipsoid &	e,
		const AnalyticFunction< VectorType > &	f )

(Rigorous?) non-linear evaluation f(e)

Parameters

e	input ellipsoid
f	non-linear analytical function

Returns

a (rigorous?) outer enclosure of the non-linear mapping

nonlinear_mapping() [2/2]

Ellipsoid codac2::nonlinear_mapping	(	const Ellipsoid &	e,
		const AnalyticFunction< VectorType > &	f,
		const Vector &	trig,
		const Vector &	q )

(Rigorous?) non-linear evaluation f(e), with parameters

Parameters

e	input ellipsoid
f	non-linear analytical function
trig	(?)
q	(?)

Returns

a (rigorous?) outer enclosure of the non-linear mapping

nonlinear_mapping_base()

Matrix codac2::nonlinear_mapping_base	(	const Matrix &	G,
		const Matrix &	J,
		const IntervalMatrix &	J_box,
		const Vector &	trig,
		const Vector &	q )

(Rigorous?) non-linear evaluation f(e), from Jacobian information

Parameters

G	(?)
J	approximated Jacobian matrix of f
J_box	reliable enclosure of the Jacobian matrix of f
trig	(?)
q	(?)

Returns

a (rigorous?) outer enclosure of the non-linear mapping

operator<<()

std::ostream & codac2::operator<<	(	std::ostream &	os,
		const Ellipsoid &	e )

Streams out an Ellipsoid.

Parameters

os	the stream to be updated
e	the ellipsoid stream out

Returns

a reference to the updated stream