Arrays
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Estimated time: 20 minutes
Overview
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 8by8 “magic” Matrix:
OUTPUT
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:
OUTPUT
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:
OUTPUT
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,
OUTPUT
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:
OUTPUT
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:
OUTPUT
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:
OUTPUT
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:
OUTPUT
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:
MATLAB
>> element = 'oxygen';
>> disp(['first three characters: ', element(1:3)])
>> disp(['last three characters: ', element(4:6)])
OUTPUT
first three characters: oxy
last three characters: gen
What is the value of
element(4:end)
? What aboutelement(1:2:end)
? Orelement(2:end  1)
?For any size array, MATLAB allows us to index with a single colon operator (
:
). This can have surprising effects. For instance, compareelement
withelement(:)
. What issize(element)
versussize(element(:))
? Finally, try using the single colon on the matrixM
above:M(:)
. What seems to be happening when we use the single colon operator for slicing?
 Exercises using slicing
MATLAB
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:end1) % Select elements starting with 2nd, until lastbutone
ans =
'xyge'
 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(:)
vsM
Key Points

M(row, column)
indices are used to select data points 
:
is used to take slices of data