colon, :

Vector creation, array subscripting, and for-loop iteration

Syntax

x = j:k
x = j:i:k
A(:,n)
A(m,:)
A(:)
A(j:k)

Description

The colon is one of the most useful operators in MATLAB^®. It can create vectors, subscript arrays, and specify for iterations.

x = j:k creates a unit-spaced vector x with elements [j,j+1,j+2,...,j+m] where m = fix(k-j). If j and k are both integers, then this is simply [j,j+1,...,k].

x = j:i:k creates a regularly-spaced vector x using i as the increment between elements. The vector elements are roughly equal to [j,j+i,j+2*i,...,j+m*i] where m = fix((k-j)/i). However, if i is not an integer, then floating point arithmetic plays a role in determining whether colon includes the endpoint k in the vector, since k might not be exactly equal to j+m*i. If you specify nonscalar arrays, then MATLAB interprets j:i:k as j(1):i(1):k(1).

x = colon(j,k) and x = colon(j,i,k) are alternate ways to execute the commands j:k and j:i:k, but are rarely used. These syntaxes enable operator overloading for classes.

A(:,n), A(m,:), A(:), and A(j:k) are common indexing expressions for a matrix A that contain a colon. When you use a colon as a subscript in an indexing expression, such as A(:,n), it acts as shorthand to include all subscripts in a particular array dimension. It is also common to create a vector with a colon for the purposes of indexing, such as A(j:k). Some indexing expressions combine both uses of the colon, as in A(:,j:k).

Common indexing expressions that contain a colon are:

• A(:,n) is the nth column of matrix A.

• A(m,:) is the mth row of matrix A.

• A(:,:,p) is the pth page of three-dimensional array A.

• A(:) reshapes all elements of A into a single column vector. This has no effect if A is already a column vector.

• A(:,:) reshapes all elements of A into a two-dimensional matrix. This has no effect if A is already a matrix or vector.

• A(j:k) uses the vector j:k to index into A and is therefore equivalent to the vector [A(j), A(j+1), ..., A(k)].

• A(:,j:k) includes all subscripts in the first dimension but uses the vector j:k to index in the second dimension. This returns a matrix with columns [A(:,j), A(:,j+1), ..., A(:,k)].

Examples

Create Unit-Spaced Vector

Create a unit-spaced vector of numbers between 1 and 10. The colon operator uses a default increment of +1.

x = 1:10

x = 1×10

     1     2     3     4     5     6     7     8     9    10

Create Vector with Specified Increment

Create vectors that increment or decrement by a specified value.

Create a vector whose elements increment by 0.1.

x = 0:0.1:1

x = 1×11

         0    0.1000    0.2000    0.3000    0.4000    0.5000    0.6000    0.7000    0.8000    0.9000    1.0000

Create a vector whose elements decrement by -2.

y = 10:-2:0

y = 1×6

    10     8     6     4     2     0

Index Matrix Rows and Columns

Examine several ways to index a matrix using a colon :.

Create a 3-by-3 matrix. Index the first row.

A = magic(3)

A = 3×3

     8     1     6
     3     5     7
     4     9     2

A(1,:)

ans = 1×3

     8     1     6

Index the second and third column.

A(:,2:3)

ans = 3×2

     1     6
     5     7
     9     2

Reshape the matrix into a column vector.

A(:)

ans = 9×1

     8
     3
     4
     1
     5
     9
     6
     7
     2

Specify for-loop Iterations

In the context of a for-loop, the colon specifies the loop iterations.

Write a for-loop that squares a number for values of n between 1 and 4.

for n = 1:4
    n^2
end

ans = 1

ans = 4

ans = 9

ans = 16

Input Arguments

j — Starting vector value

scalar

Starting vector value, specified as a real numeric scalar. If j < k so that the output vector is not empty, then j is the first element in the vector.

Example: x = 0:5

Example: x = 0:0.5:5

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | char | datetime | duration

k — Ending vector value

scalar

Ending vector value, specified as a real numeric scalar. k is the last value in the vector only when the increment lines up to exactly land on k. For example, the vector 0:5 includes 5 as the last value, but 0:0.3:1 does not include the value 1 as the last value since the increment does not line up with the endpoint.

Example: x = 0:5

Example: x = 0:0.5:5

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | char | datetime | duration

i — Increment between vector elements

1 (default) | scalar

Increment between vector elements, specified as a real numeric scalar.

Example: x = 0:0.5:5

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | char | datetime | duration

Output Arguments

x — Regularly-spaced vector

row vector

Regularly-spaced vector, returned as a row vector. If j > k, then x = j:k is an empty matrix. More generally, the syntax x = j:i:k returns an empty matrix when:

• i, j, or k is an empty input

• i == 0

• i > 0 and j > k

• i < 0 and j < k

Tips

• The for reference page has a description of how to use : in the context of loop statements.

• linspace is similar to the colon operator :, but it gives direct control over the number of points and always includes the endpoints. The sibling function logspace generates logarithmically spaced values.

• When you create a vector to index into a cell array or structure array (such as cellName{:} or structName(:).fieldName), MATLAB returns multiple outputs in a comma-separated list. For more information, see How to Use the Comma-Separated Lists.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function supports tall arrays with some limitations. For more information, see Index and View Tall Array Elements.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Complex inputs are not supported.

• The input i cannot have a logical value.

• Vector inputs are not supported.

• Inputs must be constants.

• Uses single-precision arithmetic to produce single-precision results.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• To run this function on a GPU and obtain a gpuArray output, use any of the following syntaxes:

  x = gpuArray.colon(j,k)
  x = gpuArray.colon(j,i,k)

  Alternatively, you can also pass gpuArray objects directly to the colon operator:

  x = gpuArray(j):gpuArray(k)
  x = gpuArray(j):gpuArray(i):gpuArray(k)

• 64-bit integers are not supported.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).