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    %% Grid Over Multi-Dimensional Parameter Spaces
% This example illustrates the different options in gridding
% high-dimensional (e.g., |n| greater than 2) parameter spaces. 
%%
% Construct an uncertain matrix, |m|, from four uncertain real parameters,
% |a|, |b|, |c|, and |d|, each making up the individual entries in |m|.

% Copyright 2015 The MathWorks, Inc.

a = ureal('a',1); 
b = ureal('b',2); 
c = ureal('c',3); 
d = ureal('d',4); 
m = [a b;c d]; 
%%
% First, grid the |(a,b)| space at five
% places, and the |(c,d)| space at three places. 
m1 = gridureal(m,{'a';'b'},5,{'c';'d'},3); 
%%
% |gridureal| evaluates the uncertain matrix |m| at these 15
% grid points, resulting in the numerical matrix |m1|.
%%
% Next, grid the |(a,b,c,d)| space 
% at 15 places.
m2 = gridureal(m,{'a';'b';'c';'d'},15); 
%%
% |gridureal| samples the uncertain matrix |m| 
% at these 15 points, resulting in the numerical matrix |m2|.
%%
% The (2,1) entry of |m| is just the uncertain real
% parameter |c|. Plot the histograms 
% of the (2,1) entry of both |m1| and |m2|.
% The (2,1) entry of |m1| only takes on three distinct
% values, while the (2,1) entry of |m2| 
% takes on 15 distinct values uniformly through its range.
subplot(2,1,1) 
hist(squeeze(m1(2,1,:))) 
title('2,1 entry of m1') 
subplot(2,1,2) 
hist(squeeze(m2(2,1,:)))
title('2,1 entry of m2')