Creates an ellipsoid (x - c)^T Q^{-1} (x-c) <= 1
=============================================================================
Create an ellipsoid object defined by the equation
E = { x \in R^{n} : (x - c)^{T} Q^{-1} (x - c) <= 1 }
These ellipsoid objects are often used when creating bounded disturbances
for the SReachSet Lagrangian methods when using Gaussian disturbances
Usage:
------
% Create unit ellipsoid
sre = SReachEllipsoid([0;0], eye(2));
=============================================================================
SReachEllipsoid Properties:
---------------------------
center - Center of the ellipsoid (c)
shape_matrix - Shape matrix of the ellipsoid Q
dim - Dimension of the ellipsoid
SReachEllipsoid Methods:
------------------------
SReachEllipsoid/SReachEllipsoid - Constructor
support - Support function of the ellipsoid
contains - Checks if a point (column vector) or a
collection of points (matrix of column
vectors) is within the ellipsoid
Apart from these methods, the following commands work
disp - Displays critical info about the ellipsoid
F * ell | ell * F - Multiplication of ellipsoid by a n x dim -
dimensional matrix or a scalar F
F + ell | ell + F | ell + poly - Add a deterministic vector/scalar to an
ellipsoid | Overapproximate the Minkowski
sum of a polyhedron with ellipsoid
Notes:
------
* The ellipsoid can be full-dimensional (Q non-singular) or be a
lower-dimensional ellipsoid embedded in a high dimensional space (Q
singular)
===========================================================================
This function is part of the Stochastic Reachability Toolbox.
License for the use of this function is given in
https://sreachtools.github.io/license/
Reference page in Doc Center
doc SReachEllipsoid
Creates an ellipsoid (x - c)^T Q^{-1} (x-c) <= 1
=============================================================================
Create an ellipsoid object defined by the equation
E = { x \in R^{n} : (x - c)^{T} Q^{-1} (x - c) <= 1 }
These ellipsoid objects are often used when creating bounded disturbances
for the SReachSet Lagrangian methods when using Gaussian disturbances
Usage:
------
% Create unit ellipsoid
sre = SReachEllipsoid([0;0], eye(2));
=============================================================================
SReachEllipsoid Properties:
---------------------------
center - Center of the ellipsoid (c)
shape_matrix - Shape matrix of the ellipsoid Q
dim - Dimension of the ellipsoid
SReachEllipsoid Methods:
------------------------
SReachEllipsoid/SReachEllipsoid - Constructor
support - Support function of the ellipsoid
contains - Checks if a point (column vector) or a
collection of points (matrix of column
vectors) is within the ellipsoid
Apart from these methods, the following commands work
disp - Displays critical info about the ellipsoid
F * ell | ell * F - Multiplication of ellipsoid by a n x dim -
dimensional matrix or a scalar F
F + ell | ell + F | ell + poly - Add a deterministic vector/scalar to an
ellipsoid | Overapproximate the Minkowski
sum of a polyhedron with ellipsoid
Notes:
------
* The ellipsoid can be full-dimensional (Q non-singular) or be a
lower-dimensional ellipsoid embedded in a high dimensional space (Q
singular)
===========================================================================
This function is part of the Stochastic Reachability Toolbox.
License for the use of this function is given in
https://sreachtools.github.io/license/
Reference page in Doc Center
doc SReachEllipsoid
SReachEllipsoid/center
==================================================================
Column vector indicating the center of the ellipsoid
SReachEllipsoid/shape_matrix
==================================================================
Shape matrix for the ellipsoid
SReachEllipsoid/dim
==================================================================
Dimension of the ellipsoid dimension
Checks if a point (column vector) or a collection of points (matrix of
column vectors) is within the ellipsoid
====================================================================
Inputs:
-------
obj - Ellipsoid object
test_points - Point (column vector) or a N collection of points
(matrix of column vectors) is within the ellipsoid
Outputs:
--------
newobj - Boolean vector Nx1 that describe the containment
Notes:
------
* Requires CVX for vectorized norm.
====================================================================
This function is part of the Stochastic Reachability Toolbox.
License for the use of this function is given in
https://sreachtools.github.io/license/
Override of MATLAB plus command
====================================================================
Inputs:
-------
obj - Ellipsoid object
v - Deterministic vector to be added to the random vector OR
a Polytope object
Outputs:
--------
newobj - Ellipsoid obj (obj + v) for deterministic vector/scalar v
Polyhedron obj (obj \oplus v) for polytopic v (overapprox)
Notes:
------
* For a polytopic v, newobj is an (Polyhedron overapproximation of the
minkowski sum, computed via sampling the support function.
====================================================================
This function is part of the Stochastic Reachability Toolbox.
License for the use of this function is given in
https://sreachtools.github.io/license/
Override of MATLAB multiplication command
====================================================================
Inputs:
-------
obj - SReachEllipsoid object
F - Linear transformation matrix for multiplication
Outputs:
--------
newobj - SReachEllipsoid object (F*obj)
====================================================================
This function is part of the Stochastic Reachability Toolbox.
License for the use of this function is given in
https://sreachtools.github.io/license/
Support function of the ellipsoid object
====================================================================
Inputs:
-------
l - A query column vector or a collection of query vectors stacked
as columns
Outputs:
--------
val - max_{y \in ellipsoid} l'*y
=====================================================================
This function is part of the Stochastic Reachability Toolbox.
License for the use of this function is given in
https://sreachtools.github.io/license/