# movsum

## Description

M = movsum(A,k) returns an array of local k-point sums, where each sum is calculated over a sliding window of length k across neighboring elements 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 the current and previous elements. The window size is automatically truncated at the endpoints when there are not enough elements to fill the window. When the window is truncated, the sum is taken over only the elements that fill the window. M is the same size as A.

• If A is a vector, then movsum operates along the length of the vector A.

• If A is a multidimensional array, then movsum operates along the first dimension of A whose size does not equal 1.

example

M = movsum(A,[kb kf]) computes the sum with a window of length kb+kf+1 that includes the element in the current position, kb elements backward, and kf elements forward.

example

M = movsum(___,dim) specifies the dimension of A to operate along for any of the previous syntaxes. For example, if A is a matrix, then movsum(A,k,2) operates along the columns of A, computing the k-element sliding sum for each row.

example

M = movsum(___,nanflag) specifies whether to include or omit NaN values in A. For example, movsum(A,k,"omitnan") ignores all NaN values when computing each sum. By default, movsum includes NaN values.

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M = movsum(___,Name,Value) specifies additional parameters for the sum using one or more name-value arguments. For example, if x is a time vector, then movsum(A,k,"SamplePoints",x) computes the moving sum of A relative to the times in x.

example

## Examples

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Compute the three-point centered moving sum of a row vector. When there are fewer than three elements in the window at the endpoints, take the sum over the elements that are available.

A = [4 8 6 -1 -2 -3 -1 3 4 5];
M = movsum(A,3)
M = 1×10

12    18    13     3    -6    -6    -1     6    12     9

Compute the three-point trailing moving sum of a row vector. When there are fewer than three elements in the window at the endpoints, movsum takes the sum over the number of elements that are available.

A = [4 8 6 -1 -2 -3 -1 3 4 5];
M = movsum(A,[2 0])
M = 1×10

4    12    18    13     3    -6    -6    -1     6    12

Compute the three-point centered moving sum 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     4

M = movsum(A,3,2)
M = 3×3

12    18    14
-3    -6    -5
2     6     7

Create a row vector containing NaN values.

A = [4 8 NaN -1 -2 -3 NaN 3 4 5];

Compute the three-point centered moving sum of the vector, excluding NaN values. For windows that contain any NaN value, movsum computes with the non-NaN elements.

M = movsum(A,3,"omitnan")
M = 1×10

12    12     7    -3    -6    -5     0     7    12     9

Compute a 3-hour centered moving sum of the data in A according to the time vector t.

A = [4 8 6 -1 -2 -3];
k = hours(3);
t = datetime(16,1,1,0,0,0) + hours(0:5)
t = 1x6 datetime
01-Jan-0016 00:00:00   01-Jan-0016 01:00:00   01-Jan-0016 02:00:00   01-Jan-0016 03:00:00   01-Jan-0016 04:00:00   01-Jan-0016 05:00:00

M = movsum(A,k,"SamplePoints",t)
M = 1×6

12    18    13     3    -6    -5

Compute the three-point centered moving sum of a row vector, but discard any calculation that uses fewer than three points from the output. In other words, return only the sums computed from a full three-element window, discarding endpoint calculations.

A = [4 8 6 -1 -2 -3 -1 3 4 5];
M = 1×8

18    13     3    -6    -6    -1     6    12

## Input Arguments

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Input array, specified as a vector, matrix, or multidimensional array.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Window length, specified as a numeric or duration scalar. When k is a positive integer scalar, the centered sum includes the element in the current position plus surrounding neighbors.

For example, movsum(A,3) computes an array of local three-point sums.

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, movsum(A,[2 1]) computes an array of local four-point sums.

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 whose size does not equal 1.

Dimension dim indicates the dimension that movsum operates along, that is, the direction in which the specified window slides.

Consider an m-by-n input matrix, A:

• movsum(A,k,1) computes the k-element sliding sum for each column of A and returns an m-by-n matrix.

• movsum(A,k,2) computes the k-element sliding sum for each row of A and returns an m-by-n matrix.

Missing value condition, specified as one of these values:

• "includemissing" or "includenan" — Include NaN values in A when computing each sum. If any element in the window is NaN, then the corresponding element in M is NaN. "includemissing" and "includenan" have the same behavior.

• "omitmissing" or "omitnan" — Ignore NaN values in A, and compute each sum over fewer points. If all elements in the window are NaN, then the corresponding element in M is 0. "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 = movsum(A,k,"Endpoints","fill")

Method to treat windows near endpoints, specified as one of these options:

ValueDescription
"shrink"Shrink the window size near the endpoints of the input to include only existing elements.
"discard"Do not output any sums when the window does not completely overlap with existing elements.
"fill"Replace nonexisting elements with NaN.
numeric or logical scalarReplace nonexisting elements with the specified numeric or logical value.

Sample points for computing sums, 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 movsum(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".

## Version History

Introduced in R2016a

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