#include "codac_Interval.h"
#include "codac_IntervalVector.h"
#include "codac_Tube.h"
#include "codac_TubeVector.h"

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Namespaces
namespace	codac
	FixPoint of a separator The fixpoint of a separator is computed by calling the "::"separate function on a given box until the Hausdorff distance between two iterations is less than a given ratio. This operation can be seen as a contractor on the boundary of the solution set.

Functions
Scalar outputs
const Tube	codac::cos (const Tube &x)
	\(\cos([x](\cdot))\)

const Tube	codac::sin (const Tube &x)
	\(\sin([x](\cdot))\)

const Tube	codac::abs (const Tube &x)
	\(\mid[x](\cdot)\mid\)

const Tube	codac::sqr (const Tube &x)
	\([x]^2(\cdot)\)

const Tube	codac::sqrt (const Tube &x)
	\(\sqrt{[x](\cdot)}\)

const Tube	codac::exp (const Tube &x)
	\(\exp([x](\cdot))\)

const Tube	codac::log (const Tube &x)
	\(\log([x](\cdot))\)

const Tube	codac::tan (const Tube &x)
	\(\tan([x](\cdot))\)

const Tube	codac::acos (const Tube &x)
	\(\arccos([x](\cdot))\)

const Tube	codac::asin (const Tube &x)
	\(\arcsin([x](\cdot))\)

const Tube	codac::atan (const Tube &x)
	\(\arctan([x](\cdot))\)

const Tube	codac::cosh (const Tube &x)
	\(\cosh([x](\cdot))\)

const Tube	codac::sinh (const Tube &x)
	\(\sinh([x](\cdot))\)

const Tube	codac::tanh (const Tube &x)
	\(\tanh([x](\cdot))\)

const Tube	codac::acosh (const Tube &x)
	\(\mathrm{arccosh}([x](\cdot))\)

const Tube	codac::asinh (const Tube &x)
	\(\mathrm{arcsinh}([x](\cdot))\)

const Tube	codac::atanh (const Tube &x)
	\(\mathrm{arctanh}([x](\cdot))\)

const Tube	codac::atan2 (const Tube &y, const Tube &x)
	\(\mathrm{arctan2}([y](\cdot),[x](\cdot))\)

const Tube	codac::atan2 (const Tube &y, const Interval &x)
	\(\mathrm{arctan2}([y](\cdot),[x])\)

const Tube	codac::atan2 (const Interval &y, const Tube &x)
	\(\mathrm{arctan2}([y],[x](\cdot))\)

const Tube	codac::pow (const Tube &x, int p)
	\([x]^p(\cdot)\)

const Tube	codac::pow (const Tube &x, double p)
	\([x]^p(\cdot)\)

const Tube	codac::pow (const Tube &x, const Interval &p)
	\([x]^{[p]}(\cdot)\)

const Tube	codac::root (const Tube &x, int p)
	\(\sqrt[p]{[x](\cdot)}\)

const Tube	codac::min (const Tube &y, const Tube &x)
	\(\min([y](\cdot),[x](\cdot))\)

const Tube	codac::min (const Tube &y, const Interval &x)
	\(\min([y](\cdot),[x])\)

const Tube	codac::min (const Interval &y, const Tube &x)
	\(\min([y],[x](\cdot))\)

const Tube	codac::max (const Tube &y, const Tube &x)
	\(\max([y](\cdot),[x](\cdot))\)

const Tube	codac::max (const Tube &y, const Interval &x)
	\(\max([y](\cdot),[x])\)

const Tube	codac::max (const Interval &y, const Tube &x)
	\(\max([y],[x](\cdot))\)

const Tube	codac::operator+ (const Tube &x)
	\([x](\cdot)\)

const Tube	codac::operator+ (const Tube &x, const Tube &y)
	\([x](\cdot)+[y](\cdot)\)

const Tube	codac::operator+ (const Tube &x, const Interval &y)
	\([x](\cdot)+[y]\)

const Tube	codac::operator+ (const Interval &x, const Tube &y)
	\([x]+[y](\cdot)\)

const Tube	codac::operator+ (const Tube &x, const Trajectory &y)
	\([x](\cdot)+y(\cdot)\)

const Tube	codac::operator+ (const Trajectory &x, const Tube &y)
	\(x(\cdot)+[y](\cdot)\)

const Tube	codac::operator- (const Tube &x)
	\(-[x](\cdot)\)

const Tube	codac::operator- (const Tube &x, const Tube &y)
	\([x](\cdot)-[y](\cdot)\)

const Tube	codac::operator- (const Tube &x, const Interval &y)
	\([x](\cdot)-[y]\)

const Tube	codac::operator- (const Interval &x, const Tube &y)
	\([x]-[y](\cdot)\)

const Tube	codac::operator- (const Tube &x, const Trajectory &y)
	\([x](\cdot)-y(\cdot)\)

const Tube	codac::operator- (const Trajectory &x, const Tube &y)
	\(x(\cdot)-[y](\cdot)\)

const Tube	codac::operator* (const Tube &x, const Tube &y)
	\([x](\cdot)\cdot[y](\cdot)\)

const Tube	codac::operator* (const Tube &x, const Interval &y)
	\([x](\cdot)\cdot[y]\)

const Tube	codac::operator* (const Interval &x, const Tube &y)
	\([x]\cdot[y](\cdot)\)

const Tube	codac::operator* (const Tube &x, const Trajectory &y)
	\([x](\cdot)\cdot y(\cdot)\)

const Tube	codac::operator* (const Trajectory &x, const Tube &y)
	\(x(\cdot)\cdot[y](\cdot)\)

const Tube	codac::operator/ (const Tube &x, const Tube &y)
	\([x](\cdot)/[y](\cdot)\)

const Tube	codac::operator/ (const Tube &x, const Interval &y)
	\([x](\cdot)/[y]\)

const Tube	codac::operator/ (const Interval &x, const Tube &y)
	\([x]/[y](\cdot)\)

const Tube	codac::operator/ (const Tube &x, const Trajectory &y)
	\([x](\cdot)/y(\cdot)\)

const Tube	codac::operator/ (const Trajectory &x, const Tube &y)
	\(x(\cdot)/[y](\cdot)\)

const Tube	codac::operator\| (const Tube &x, const Tube &y)
	\([x](\cdot)\sqcup[y](\cdot)\)

const Tube	codac::operator\| (const Tube &x, const Interval &y)
	\([x](\cdot)\sqcup[y]\)

const Tube	codac::operator\| (const Interval &x, const Tube &y)
	\([x]\sqcup[y](\cdot)\)

const Tube	codac::operator\| (const Tube &x, const Trajectory &y)
	\([x](\cdot)\sqcup y(\cdot)\)

const Tube	codac::operator\| (const Trajectory &x, const Tube &y)
	\(x(\cdot)\sqcup [y](\cdot)\)

const Tube	codac::operator& (const Tube &x, const Tube &y)
	\([x](\cdot)\cap[y](\cdot)\)

const Tube	codac::operator& (const Tube &x, const Interval &y)
	\([x](\cdot)\cap[y]\)

const Tube	codac::operator& (const Interval &x, const Tube &y)
	\([x]\cap[y](\cdot)\)

const Tube	codac::operator& (const Tube &x, const Trajectory &y)
	\([x](\cdot)\cap y(\cdot)\)

const Tube	codac::operator& (const Trajectory &x, const Tube &y)
	\(x(\cdot)\cap [y](\cdot)\)

Vector outputs
const TubeVector	codac::operator+ (const TubeVector &x)
	\([\mathbf{x}](\cdot)\)

const TubeVector	codac::operator+ (const TubeVector &x, const TubeVector &y)
	\([\mathbf{x}](\cdot)+[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator+ (const TubeVector &x, const IntervalVector &y)
	\([\mathbf{x}](\cdot)+[\mathbf{y}]\)

const TubeVector	codac::operator+ (const IntervalVector &x, const TubeVector &y)
	\([\mathbf{x}]+[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator+ (const TubeVector &x, const TrajectoryVector &y)
	\([\mathbf{x}](\cdot)+\mathbf{y}(\cdot)\)

const TubeVector	codac::operator+ (const TrajectoryVector &x, const TubeVector &y)
	\(\mathbf{x}(\cdot)+[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator- (const TubeVector &x)
	\(-[\mathbf{x}](\cdot)\)

const TubeVector	codac::operator- (const TubeVector &x, const TubeVector &y)
	\([\mathbf{x}](\cdot)-[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator- (const TubeVector &x, const IntervalVector &y)
	\([\mathbf{x}](\cdot)-[\mathbf{y}]\)

const TubeVector	codac::operator- (const IntervalVector &x, const TubeVector &y)
	\([\mathbf{x}]-[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator- (const TubeVector &x, const TrajectoryVector &y)
	\([\mathbf{x}](\cdot)-\mathbf{y}(\cdot)\)

const TubeVector	codac::operator- (const TrajectoryVector &x, const TubeVector &y)
	\(\mathbf{x}(\cdot)-[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator* (const Tube &x, const TubeVector &y)
	\([x](\cdot)\cdot[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator* (const Interval &x, const TubeVector &y)
	\([x]\cdot[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator* (const Tube &x, const IntervalVector &y)
	\([x](\cdot)\cdot[\mathbf{y}]\)

const TubeVector	codac::operator* (const Trajectory &x, const TubeVector &y)
	\(x(\cdot)\cdot[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator/ (const TubeVector &x, const Tube &y)
	\([\mathbf{x}](\cdot)/[y](\cdot)\)

const TubeVector	codac::operator/ (const TubeVector &x, const Interval &y)
	\([\mathbf{x}](\cdot)/[y]\)

const TubeVector	codac::operator/ (const IntervalVector &x, const Tube &y)
	\([\mathbf{x}]/[y](\cdot)\)

const TubeVector	codac::operator/ (const TubeVector &x, const Trajectory &y)
	\([\mathbf{x}](\cdot)/y(\cdot)\)

const TubeVector	codac::operator\| (const TubeVector &x, const TubeVector &y)
	\([\mathbf{x}](\cdot)\sqcup[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator\| (const TubeVector &x, const IntervalVector &y)
	\([\mathbf{x}](\cdot)\sqcup[\mathbf{y}]\)

const TubeVector	codac::operator\| (const IntervalVector &x, const TubeVector &y)
	\([\mathbf{x}]\sqcup[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator\| (const TubeVector &x, const TrajectoryVector &y)
	\([\mathbf{x}](\cdot)\sqcup\mathbf{y}(\cdot)\)

const TubeVector	codac::operator\| (const TrajectoryVector &x, const TubeVector &y)
	\(\mathbf{x}(\cdot)\sqcup[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator& (const TubeVector &x, const TubeVector &y)
	\([\mathbf{x}](\cdot)\cap[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator& (const TubeVector &x, const IntervalVector &y)
	\([\mathbf{x}](\cdot)\cap[\mathbf{y}]\)

const TubeVector	codac::operator& (const IntervalVector &x, const TubeVector &y)
	\([\mathbf{x}]\cap[\mathbf{y}](\cdot)\)

const TubeVector	codac::operator& (const TubeVector &x, const TrajectoryVector &y)
	\([\mathbf{x}](\cdot)\cap\mathbf{y}(\cdot)\)

const TubeVector	codac::operator& (const TrajectoryVector &x, const TubeVector &y)
	\(\mathbf{x}(\cdot)\cap[\mathbf{y}](\cdot)\)

const TubeVector	codac::abs (const TubeVector &x)
	\(\mid\mathbf{x}(\cdot)\mid\)

Detailed Description

Arithmetic operations on tubes

Date: 2015

Author: Simon Rohou

License: This program is distributed under the terms of: the GNU Lesser General Public License (LGPL).

Namespaces

Functions

Detailed Description

Arithmetic operations on tubes