Get/plot (minimum volume) ellispoids corresponding to a Monte-Carlo simulation
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Computes (and plots) the Lowner-John ellipsoid (Boyd and Vandenberghe, Convex
Optimization, Ch. 8.4.1) that fits the set of samples at each time instant in
the trajectory. This function is typically useful in conjunction with
generateMonteCarloSims to understand the spread of the Monte-Carlo simulated
trajectories.
Usage: See examples/cwhSReachPoint.m
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set_of_ellipsoids = ellipsoidsFromMonteCarloSims(...
concat_state_realization, state_dim, relv_states, plot_options)
Inputs:
-------
concat_state_realization
- Matrix of concatenate state (row) vectors stacked
columnwise. Each row comprises of the state trajectory
as [x_1; x_2; ...; x_N]
state_dim - State dimension
relv_states - A two-element vector with indices of relevant states
among the states indexed from 1 to state_dim
plot_options - Plot options that are directly passed to the plot. Leave
empty if plotting is not desired.
Outputs:
--------
set_of_ellipsoids - Set of ellipsoids that cover these points. A cell array
of cells are provided with each cell containing the
ellipsoid center q and its shape matrix Q. The ellipsoid
is (x-q)^T Q^{-1} (x-q) <= 1.
See also generateMonteCarloSims
Notes:
------
* Requires CVX for solving the convex optimization problem using SDPT3
* Note that the initial state is NOT a part of the
concatenated_state_realization
* Uses code obtained from
http://web.cvxr.com/cvx/examples/cvxbook/Ch08_geometric_probs/min_vol_elp_finite_set.m
============================================================================
This function is part of the Stochastic Reachability Toolbox.
License for the use of this function is given in
https://sreachtools.github.io/license/