Vector creation, array subscripting, and for-loop iteration
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Syntax
x = j:kx = j:i:kA(:,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].
example
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.
example
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 thenth column of matrixA.A(m,:)is themth row of matrixA.A(:,:,p)is thepth page of three-dimensional arrayA.A(:)reshapes all elements ofAinto a single column vector. This has no effect ifAis already a column vector.A(:,:)reshapes all elements ofAinto a two-dimensional matrix. This has no effect ifAis already a matrix or vector.A(j:k)uses the vectorj:kto index intoA. If A is a vector, thenA(j:k)has the same orientation asA. IfAis a matrix, thenA(j:k)is a row vector.A(:,j:k)includes all subscripts in the first dimension but uses the vectorj:kto index in the second dimension. This returns a matrix with columns[A(:,j), A(:,j+1), ..., A(:,k)].
example
Examples
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Create Unit-Spaced Vector
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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 10Create Vector with Specified Increment
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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 1.0000Create a vector whose elements decrement by -2.
y = 10:-2:0
y = 1×6 10 8 6 4 2 0Index Matrix Rows and Columns
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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 2A(1,:)
ans = 1×3 8 1 6Index the second and third column.
A(:,2:3)
ans = 3×2 1 6 5 7 9 2Reshape the matrix into a column vector.
A(:)
ans = 9×1 8 3 4 1 5 9 6 7 2Specify for-Loop Iterations
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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^2end
ans = 1
ans = 4
ans = 9
ans = 16
Input Arguments
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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
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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, orkis an empty inputi == 0i > 0andj > ki < 0andj < 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{:}structName(:).fieldName
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
icannot 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™.
The colon function supports GPU array input with these usage notes and limitations:
To run this function on a GPU and obtain a
gpuArrayoutput, use any of the following syntaxes:x = gpuArray.colon(j,k)x = gpuArray.colon(j,i,k)
Alternatively, you can also pass
gpuArrayobjects 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).
Version History
Introduced before R2006a
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R2024a: Vector creation with nonscalar operands warns
colon now issues a warning when creating vectors if one or more operands are not scalar. For example, expressions like [1 2 3]:2:10 now warn. This warning will become an error in a future release, removing support for nonscalar operands. Previously, colon used the first element of any nonscalar operands to evaluate the expression.
See Also
for | linspace | logspace | reshape | varargin
Topics
- Generate Sequence of Dates and Time
- MATLAB Operators and Special Characters
- Array Indexing
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