%% Combine Categorical Arrays Using Multiplication
% This example shows how to use the times function to combine categorical arrays, including ordinal categorical arrays and arrays with undefined elements. When you call times on two categorical arrays, the output is a categorical array with new categories. The set of new categories is the set of all the ordered pairs created from the categories of the input arrays, or the Cartesian product. times forms each element of the output array as the ordered pair of the corresponding elements of the input arrays. The output array has the same size as the input arrays.
%% Combine Two Categorical Arrays
% Combine two categorical arrays using times. The input arrays must have the same number of elements, but can have different numbers of categories.

A = categorical({'blue','red','green'});
B = categorical({'+','-','+'});
C = A.*B

%
%% Cartesian Product of Categories
% Show the categories of C. The categories are all the ordered pairs that can be created from the categories of A and B, also known as the Cartesian product.

categories(C)

%
% As a consequence, A.*B does not equal B.*A.

D = B.*A

%

categories(D)

%
%% Multiplication with Undefined Elements
% Combine two categorical arrays. If either A or B have an undefined element, the corresponding element of C is undefined.

A = categorical({'blue','red','green','black'});
B = categorical({'+','-','+','-'});
A = removecats(A,{'black'});
C = A.*B

%
%% Cartesian Product of Ordinal Categorical Arrays
% Combine two ordinal categorical arrays. C is an ordinal categorical array only if A and B are both ordinal. The ordering of the categories of C follows from the orderings of the input categorical arrays.

A = categorical({'blue','red','green'},{'green','red','blue'},'Ordinal',true);
B = categorical({'+','-','+'},'Ordinal',true);
C = A.*B;
categories(C)

% Copyright 2015 The MathWorks, Inc.