# Arrays

## Overview

Teaching: 15 min
Exercises: 5 min
Questions
• How can I access subsets of data?

Objectives
• Select individual values and subsections from data.

## Array indexing

Now that we understand what kind of data can be stored in an array, we need to learn the proper syntax for working with arrays in MATLAB. To do this we will begin by discussing array indexing, which is the method by which we can select one or more different elements of an array. A solid understanding of array indexing will greatly assist our ability to organize our data.

Let’s start by creating an 8-by-8 “magic” Matrix:

``````>> M = magic(8)
``````
``````ans =

64    2    3   61   60    6    7   57
9   55   54   12   13   51   50   16
17   47   46   20   21   43   42   24
40   26   27   37   36   30   31   33
32   34   35   29   28   38   39   25
41   23   22   44   45   19   18   48
49   15   14   52   53   11   10   56
8   58   59    5    4   62   63    1
``````

We want to access a single value from the matrix: To do that, we must provide its index in parentheses:

``````>> M(5, 6)
``````
``````ans = 38
``````

Indices are provided as (row, column). So the index `(5, 6)` selects the element on the fifth row and sixth column.

An index like `(5, 6)` selects a single element of an array, but we can also access sections of the matrix, or slices. To access a row of values: we can do:

``````>> M(5, :)
``````
``````ans =

32   34   35   29   28   38   39   25

``````

Providing `:` as the index for a dimension selects all elements along that dimension. So, the index `(5, :)` selects the elements on row `5`, and all columns—effectively, the entire row. We can also select multiple rows, ``````>> M(1:4, :)
``````
``````ans =

64    2    3   61   60    6    7   57
9   55   54   12   13   51   50   16
17   47   46   20   21   43   42   24
40   26   27   37   36   30   31   33
``````

and columns: ``````>> M(:, 6:end)
``````
``````ans =

6    7   57
51   50   16
43   42   24
30   31   33
38   39   25
19   18   48
11   10   56
62   63    1
``````

To select a submatrix, we have to take slices in both dimensions:

``````>> M(4:6, 5:7)
``````
``````ans =

36   30   31
28   38   39
45   19   18

``````

We don’t have to take all the values in the slice—if we provide a stride. Let’s say we want to start with row `2`, and subsequently select every third row: ``````>> M(2:3:end, :)
``````
``````ans =

9   55   54   12   13   51   50   16
32   34   35   29   28   38   39   25
8   58   59    5    4   62   63    1
``````

And we can also select values in a “checkerboard”, by taking appropriate strides in both dimensions:

``````>> M(1:3:end, 2:2:end)
``````
``````ans =

2   61    6   57
26   37   30   33
15   52   11   56
``````

## Slicing

A subsection of an array is called a slice. We can take slices of character strings as well:

``````>> element = 'oxygen';
>> disp(['first three characters: ', element(1:3)])
>> disp(['last three characters: ', element(4:6)])
``````
``````first three characters: oxy
last three characters: gen
``````
1. What is the value of `element(4:end)`? What about `element(1:2:end)`? Or `element(2:end - 1)`?

2. For any size array, MATLAB allows us to index with a single colon operator (`:`). This can have surprising effects. For instance, compare `element` with `element(:)`. What is `size(element)` versus `size(element(:))`? Finally, try using the single colon on the matrix `M` above: `M(:)`. What seems to be happening when we use the single colon operator for slicing?

## Solution

1. Exercises using slicing

`````` element(4:end)   % Select all elements from 4th to last
ans =
'gen'
element(1:2:end) % Select every other element starting at first
ans =
'oye
element(2:end-1) % Select elements starting with 2nd, until last-but-one
ans =
'xyge'
``````
2. The colon operator ‘flattens’ a vector or matrix into a column vector. The order of the elements in the resulting vector comes from appending each column of the original array in turn. Have a look at the order of the values in `M(:)` vs `M`

## Key Points

• `M(row, column)` indices are used to select data points

• `:` is used to take slices of data