Introduction
In this tutorial we learn how to index a vector in MATLAB. Properly indexing vectors is necessary when working with them in MATLAB. If you want to use MATLAB effectively then understanding this topic can help you a lot in learning to properly access modify or use values stored in a vector.
Defining a Vector that will be indexed
Lets start by defining a vector of length 10 and call it “a”. We are going to use this vector throughout this tutorial to understand various ways of indexing a vector. We can write the following command in the command window to define “a”
>> a = [10 20 30 40 50 60 70 80 90 100]
a =
10 20 30 40 50 60 70 80 90 100How to index a vector in MATLAB
There are 4 main methods for indexing vectors in MATLAB. Lets look at each one in detail
Indexing a vector using a single index
First way of indexing a vector is by using a single index or element number. Using this method you can access or modify (depending on how the command is written) a single element of vector “a” at a time. The syntax for this method is
vector_name(index)Indexing in MATLAB starts from 1. index can be any value from 1 to the length of vector. Lets look at an example
>> a(5)
ans =
50a(5) returns the 5th element of vector “a” which is 50 in our case. Lets try another example
>> a(end)
ans =
100a(end) returns the last element of vector “a”. end always equals the length (i.e. last index) of the vector. a(end-1) should return the second last element. We can easily verify this
>> a(end-1)
ans =
90index cannot be 0 or greater than length of the vector. Using a(0) or a(12) result in an error since they are not valid indices.
>> a(0)
Subscript indices must either be real positive integers or logicals.>> a(12)
Index exceeds matrix dimensions.You can change the value of one of the elements of vector “a” by assigning it a new value. Lets look at an example
>> a(1) = 50
a =
50 20 30 40 50 60 70 80 90 100a(1) is now 50.
Indexing a vector using a vector of indices
Lets redefine vector “a” on which we are going to do indexing on.
>> a = [10 20 30 40 50 60 70 80 90 100]
a =
10 20 30 40 50 60 70 80 90 100You can access more than one element of a vector by giving a vector of indices. MATLAB returns a vector of same length as the input vector. Moreover, the order of elements in the returned vector is according to the order of indices in the input vector.
vector_name(vector_of_indices)Lets see an example
>> a([5 1 end-1])
ans =
50 10 90All the indices in the input vector must be valid indices otherwise MATLAB will give an error.
>> a([5 0 10])
Subscript indices must either be real positive integers or logicals.>> a([5 15 10])
Index exceeds matrix dimensions.You can use this indexing method to modify the selected elements of a vector. Lets look at an example where all the indexed elements are replaced with a single value
>> a([4 3 2 1]) = 20
a =
20 20 20 20 50 60 70 80 90 100If you want to assign separate values to each element then you can provide a vector of new values. The vector must be the same length as the vector used for indexing. Each element at the index specified in the indexing vector will be replaced with corresponding entry from the vector of new values.
>> a([3 2 1 4]) = [30 20 10 40]
a =
10 20 30 40 50 60 70 80 90 100MATLAB returns an error if the vector length is not the same as “shape” of left side.
>> a([3 2 1 4]) = [30 20]
In an assignment A(:) = B, the number of elements in A and B must be the same.Indexing a vector using a range
The third method for indexing vector is by using a range of indices that is defined using : (colon). The syntax is
vector_name(range_low:increment:range_high)range_low and range_high are the start and end of the range (of indices). In this case MATLAB generates a vector from range_low to range_high with the given increment and then uses it to index the vector. increment is optional and can be omitted. The syntax for such a case is
vector_name(range_low:range_high)In this case MATLAB assumes increment of 1 and generates a vector of length range_high–range_low–1 consisting of numbers from range_low to range_high. Lets try a few examples
>> a(1:6)
ans =
10 20 30 40 50 60a(1:6) returns a vector of first six elements of vector “a”. The increment is 1 (default) since we didn’t specify it during indexing.
Writing a(0:6) or a(1:15) return an error because our range has invalid indices.
>> a(0:6)
Subscript indices must either be real positive integers or logicals.>> a(1:15)
Index exceeds matrix dimensions.If odd elements of “a” are required we can write.
>> a(1:2:10)
ans =
10 30 50 70 90100 is not included in the output even though we gave 10 as range_high. This is due to starting from 1 and using increment of 2. Index 10 is not included in our range. Increment can also be negative. We can get the elements of “a” in reverse order by using the following command
>> a(end:-1:1)
ans =
100 90 80 70 60 50 40 30 20 10Logical indexing
In logical indexing, instead of using an index, vector or range, we provide a logical expression. As an example, to get all the elements of “a” that are less than 50, we can write
>> a(a<50)
ans =
10 20 30 40To replace all the elements of “a” that are greater or equal to 70, we can write
>> a(a>=70) = 10
a =
10 20 30 40 50 60 10 10 10 10I have done a video version of the same tutorial in Urdu / Hindi on Youtube. Please subscribe to my Youtube channel.
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