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

C = 1x3 categorical
     blue +      red -      green + 

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)

ans = 6x1 cell
    {'blue +' }
    {'blue -' }
    {'green +'}
    {'green -'}
    {'red +'  }
    {'red -'  }

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

D = B.*A

D = 1x3 categorical
     + blue      - red      + green 

categories(D)

ans = 6x1 cell
    {'+ blue' }
    {'+ green'}
    {'+ red'  }
    {'- blue' }
    {'- green'}
    {'- red'  }

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

C = 1x4 categorical
     blue +      red -      green +      <undefined> 

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)

ans = 6x1 cell
    {'green +'}
    {'green -'}
    {'red +'  }
    {'red -'  }
    {'blue +' }
    {'blue -' }