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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```
```C = 1x3 categorical array 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 array {'blue +' } {'blue -' } {'green +'} {'green -'} {'red +' } {'red -' } ```

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

`D = B.*A`
```D = 1x3 categorical array + blue - red + green ```
`categories(D)`
```ans = 6x1 cell array {'+ 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 array 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 array {'green +'} {'green -'} {'red +' } {'red -' } {'blue +' } {'blue -' } ```