Moving mean
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Syntax
M = movmean(A,k)
M = movmean(A,[kb kf])
M = movmean(___,dim)
M = movmean(___,nanflag)
M = movmean(___,Name,Value)
Description
example
M = movmean(A,k) returnsan array of local k-point mean values, where each mean is calculated overa sliding window of length k across neighboringelements of A. When k is odd,the window is centered about the element in the current position.When k is even, the window is centered about thecurrent and previous elements. The window size is automatically truncatedat the endpoints when there are not enough elements to fill the window.When the window is truncated, the average is taken over only the elementsthat fill the window. M is the same size as A.
If
Ais a vector, thenmovmeanoperates along the length of the vectorA.If
Ais a multidimensional array, thenmovmeanoperates along the first dimension ofAwhose size does not equal 1.
example
M = movmean(A,[kb kf]) computesthe mean with a window of length kb+kf+1 that includesthe element in the current position, kb elementsbackward, and kf elements forward.
example
M = movmean(___,dim) specifies the dimension of A to operate along for any of the previous syntaxes. For example, if A is a matrix, then movmean(A,k,2) operates along the columns of A, computing the k-element sliding mean for each row.
example
M = movmean(___,nanflag) specifies whether to include or omit NaN values in A. For example, movmean(A,k,"omitnan") ignores NaN values when computing each mean. By default, movmean includes NaN values.
example
M = movmean(___,Name,Value) specifies additional parameters for the moving average using one or more name-value arguments. For example, if x is a vector of time values, then movmean(A,k,"SamplePoints",x) computes the moving average relative to the times in x.
Examples
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Centered Moving Average of Vector
Open Live Script
Compute the three-point centered moving average of a row vector. When there are fewer than three elements in the window at the endpoints, take the average over the elements that are available.
A = [4 8 6 -1 -2 -3 -1 3 4 5];M = movmean(A,3)
M = 1×10 6.0000 6.0000 4.3333 1.0000 -2.0000 -2.0000 -0.3333 2.0000 4.0000 4.5000Trailing Moving Average of Vector
Open Live Script
Compute the three-point trailing moving average of a row vector. When there are fewer than three elements in the window at the endpoints, take the average over the elements that are available.
A = [4 8 6 -1 -2 -3 -1 3 4 5];M = movmean(A,[2 0])
M = 1×10 4.0000 6.0000 6.0000 4.3333 1.0000 -2.0000 -2.0000 -0.3333 2.0000 4.0000Moving Average of Matrix
Open Live Script
Compute the three-point centered moving average for each row of a matrix. The window starts on the first row, slides horizontally to the end of the row, then moves to the second row, and so on. The dimension argument is two, which slides the window across the columns of A.
A = [4 8 6; -1 -2 -3; -1 3 4]
A = 3×3 4 8 6 -1 -2 -3 -1 3 4M = movmean(A,3,2)
M = 3×3 6.0000 6.0000 7.0000 -1.5000 -2.0000 -2.5000 1.0000 2.0000 3.5000Moving Average of Vector with Missing Values
Open Live Script
Compute the three-point centered moving average of a row vector containing two NaN elements.
A = [4 8 NaN -1 -2 -3 NaN 3 4 5];M = movmean(A,3)
M = 1×10 6.0000 NaN NaN NaN -2.0000 NaN NaN NaN 4.0000 4.5000Recalculate the average, but omit the NaN values. When movmean omits NaN elements, it computes the average over the remaining elements in the window.
M = movmean(A,3,"omitnan")M = 1×10 6.0000 6.0000 3.5000 -1.5000 -2.0000 -2.5000 0 3.5000 4.0000 4.5000Sample Points for Moving Average
Open Live Script
Compute a 3-hour centered moving average of the data in A according to the time vector t.
A = [4 8 6 -1 -2 -3];k = hours(3);t = datetime(2016,1,1,0,0,0) + hours(0:5)
t = 1x6 datetime 01-Jan-2016 00:00:00 01-Jan-2016 01:00:00 01-Jan-2016 02:00:00 01-Jan-2016 03:00:00 01-Jan-2016 04:00:00 01-Jan-2016 05:00:00M = movmean(A,k,"SamplePoints",t)M = 1×6 6.0000 6.0000 4.3333 1.0000 -2.0000 -2.5000Return Only Full-Window Averages
Open Live Script
Compute the three-point centered moving average of a row vector, but discard any calculation that uses fewer than three points from the output. In other words, return only the averages computed from a full three-element window, discarding endpoint calculations.
A = [4 8 6 -1 -2 -3 -1 3 4 5];M = movmean(A,3,"Endpoints","discard")
M = 1×8 6.0000 4.3333 1.0000 -2.0000 -2.0000 -0.3333 2.0000 4.0000Input Arguments
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A — Input array
vector | matrix | multidimensional array
Input array, specified as a vector, matrix, or multidimensionalarray.
k — Window length
numeric or duration scalar
Window length, specified as a numeric or duration scalar. When k is a positive integer scalar, the centered average includes the element in the current position plus surrounding neighbors.
For example, movmean(A,3) computes an array of local three-point mean values.
[kb kf] — Directional window length
numeric or duration row vector containing two elements
Directional window length, specified as a numeric or duration row vector containing two elements. When kb and kf are positive integer scalars, the calculation is over kb+kf+1 elements. The calculation includes the element in the current position, kb elements before the current position, and kf elements after the current position.
For example, movmean(A,[2 1]) computes an array of local four-point mean values.
dim — Dimension to operate along
positive integer scalar
Dimension to operate along, specified as a positive integer scalar. If you do not specify the dimension, then the default is the first array dimension of size greater than 1.
Dimension dim indicates the dimension that movmean operatesalong, that is, the direction in which the specified window slides.
Consider an m-by-n input matrix, A:
movmean(A,k,1)computes thek-element sliding mean for each column ofAand returns anm-by-nmatrix.
movmean(A,k,2)computes thek-element sliding mean for each row ofAand returns anm-by-nmatrix.
nanflag — Missing value condition
"includemissing" (default) | "includenan" | "omitmissing" | "omitnan"
Missing value condition, specified as one of these values:
"includemissing"or"includenan"— IncludeNaNvalues inAwhen computing each mean. If any element in the window isNaN, then the corresponding element inMisNaN."includemissing"and"includenan"have the same behavior."omitmissing"or"omitnan"— IgnoreNaNvalues inAand compute each mean over fewer points. If all elements in the window areNaN, then the corresponding element inMisNaN."omitmissing"and"omitnan"have the same behavior.
Name-Value Arguments
Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose Name in quotes.
Example: M = movmean(A,k,"Endpoints","fill")
Endpoints — Method to treat windows near endpoints
"shrink" (default) | "discard" | "fill" | numeric or logical scalar
Method to treat windows near endpoints, specified as one of these options:
| Value | Description |
|---|---|
"shrink" | Shrink the window size near the endpoints of the input to include only existing elements. |
"discard" | Do not output any average values when the window does not completely overlap with existing elements. |
"fill" | Replace nonexisting elements with NaN. |
| numeric or logical scalar | Replace nonexisting elements with the specified numeric or logical value. |
SamplePoints — Sample points for computing averages
vector
Sample points for computing averages, specified as a vector. The sample points represent the locations of the data in A. Sample points do not need to be uniformly sampled. By default, the sample points vector is [1 2 3 ... ].
Moving windows are defined relative to the sample points, which must be sorted and contain unique elements. For example, if t is a vector of times corresponding to the input data, then movmean(rand(1,10),3,"SamplePoints",t) has a window that represents the time interval between t(i)-1.5 and t(i)+1.5.
When the sample points vector has data type datetime or duration, then the moving window length must have type duration.
If the sample points are nonuniformly spaced and Endpoints is specified, then its value must be "shrink".
More About
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Mean
For a finite-length vector A made up of N scalar observations, the mean is defined as
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
This function supports tall arrays with the limitations:
The
SamplePointsname-value argument is not supported.
For more information, see Tall Arrays.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
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:
The
SamplePointsname-value argument is 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 in R2016a
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R2023a: Specify missing value condition
Include or omit missing values in the input array when computing each mean by using the "includemissing" or "omitmissing" options. These options have the same behavior as the "includenan" and "omitnan" options, respectively.
R2023a: Improved performance when computing over matrix with sample points
The movmean function shows improved performance when computing over a matrix when there are sample points.
For example, this code computes the moving mean of a 300-by-300 matrix with corresponding sample points. The code is about 1.9x faster than in the previous release.
function timingMovmeanA = randn(300);t = sort(rand(300,1));ticfor k = 1:2000 movmean(A,0.1,"SamplePoints",t);endtocend
The approximate execution times are:
R2022b: 1.04 s
R2023a: 0.56
The code was timed on a Windows® 10, Intel® Xeon® CPU E5-1650 v4 @ 3.60 GHz test system by calling the timingMovmean function.
See Also
Functions
- movmedian | movvar | movstd | movsum | movmad | mean | smoothdata
Topics
- Data Smoothing and Outlier Detection
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