Colon Notation

The colon(:) is one of the most useful operator in MATLAB. It is used to create vectors, subscript arrays, and specify for iterations.

If you want to create a row vector, containing integers from 1 to 10, you write −

1:10

MATLAB executes the statement and returns a row vector containing the integers from 1 to 10 −

ans =                                                                           
                                                                                
   1    2    3    4    5    6    7    8    9   10 

If you want to specify an increment value other than one, for example −

100: -5: 50

MATLAB executes the statement and returns the following result −

ans =
   100    95    90    85    80    75    70    65    60    55    50

Let us take another example −

0:pi/8:pi

MATLAB executes the statement and returns the following result −

ans =
   Columns 1 through 7
      0    0.3927    0.7854    1.1781    1.5708    1.9635    2.3562
   Columns 8 through 9
      2.7489    3.1416

You can use the colon operator to create a vector of indices to select rows, columns or elements of arrays.

The following table describes its use for this purpose (let us have a matrix A) −

Format	Purpose
A(:,j)	is the jth column of A.
A(i,:)	is the ith row of A.
A(:,:)	is the equivalent two-dimensional array. For matrices this is the same as A.
A(j:k)	is A(j), A(j+1),…,A(k).
A(:,j:k)	is A(:,j), A(:,j+1),…,A(:,k).
A(:,:,k)	is the kth page of three-dimensional array A.
A(i,j,k,:)	is a vector in four-dimensional array A. The vector includes A(i,j,k,1), A(i,j,k,2), A(i,j,k,3), and so on.
A(:)	is all the elements of A, regarded as a single column. On the left side of an assignment statement, A(:) fills A, preserving its shape from before. In this case, the right side must contain the same number of elements as A.

Example

Create a script file and type the following code in it −

A = [1 2 3 4; 4 5 6 7; 7 8 9 10]
A(:,2)      % second column of A
A(:,2:3)    % second and third column of A
A(2:3,2:3)  % second and third rows and second and third columns

When you run the file, it displays the following result −

A =
      1     2     3     4
      4     5     6     7
      7     8     9    10

ans =
      2
      5
      8

ans =
      2     3
      5     6
      8     9

ans =
      5     6
      8     9