movprod

Moving product

Syntax

M = movprod(A,k)

M = movprod(A,[kb kf])

M = movprod(___,dim)

M = movprod(___,nanflag)

M = movprod(___,Name,Value)

Description

M = movprod(A,k) returns an array of local k-point products, where each product is calculated over a sliding window of length k across neighboring elements of A. M is the same size as 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 product is taken over only the elements that fill the window.

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

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

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

M = movprod(___,dim) computes the product along dimension dim for any of the previous syntaxes. For example, if A is a matrix, then movprod(A,k,2) operates across the columns of A, computing the k-element sliding product for each row.

M = movprod(___,nanflag) specifies whether to include or omit NaN values from the calculation for any of the previous syntaxes. movprod(A,k,'includenan') includes all NaN values in the calculation, which is the default. movprod(A,k,'omitnan') ignores them and computes the product over fewer points.

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

Examples

Centered Moving Product of Vector

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

A = [1 2 4 -1 -2 -3 -1 3 2 1];
M = movprod(A,3)

M = 1×10

     2     8    -8     8    -6    -6     9    -6     6     2

Trailing Moving Product of Vector

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

A = [1 2 1 -1 -2 -3 -1 3 4 1];
M = movprod(A,[2 0])

M = 1×10

     1     2     2    -2     2    -6    -6     9   -12    12

Moving Product of Matrix

Compute the 3-point centered moving product for each row of a matrix. The dimension argument is 2, which slides the window across the columns of A. The window starts on the first row, slides horizontally to the end of the row, then moves to the second row, and so on.

A = [1 2 1; -1 -2 -3; -1 3 4]

A = 3×3

     1     2     1
    -1    -2    -3
    -1     3     4

M = movprod(A,3,2)

M = 3×3

     2     2     2
     2    -6     6
    -3   -12    12

Moving Product of Vector with NaN Elements

Compute the three-point centered moving product of a row vector containing two NaN elements.

A = [2 1 NaN -1 -2 -3 NaN 3 4 1];
M = movprod(A,3)

M = 1×10

     2   NaN   NaN   NaN    -6   NaN   NaN   NaN    12     4

Recalculate the product, but omit the NaN values. When movprod discards NaN elements, it takes the product over the remaining elements in the window.

M = movprod(A,3,'omitnan')

M = 1×10

     2     2    -1     2    -6     6    -9    12    12     4

Sample Points for Moving Product

Compute a 3-hour centered moving product 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
Columns 1 through 3

   01-Jan-2016 00:00:00   01-Jan-2016 01:00:00   01-Jan-2016 02:00:00

Columns 4 through 6

   01-Jan-2016 03:00:00   01-Jan-2016 04:00:00   01-Jan-2016 05:00:00

M = movprod(A,k,'SamplePoints',t)

M = 1×6

    32   192   -48    12    -6     6

Return Only Full-Window Products

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

A = [1 2 1 -1 -2 -3 -1 3 4 1];
M = movprod(A,3,'Endpoints','discard')

M = 1×8

     2    -2     2    -6    -6     9   -12    12

Input Arguments

A — Input array

vector | matrix | multidimensional array

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

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

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 product includes the element in the current position plus surrounding neighbors. For example, a three-point product defined by a window of length three results in the following calculation for a vector A:

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

[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, a four-point MAD defined by the directional window [2 1] results in the following calculation for a vector A:

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

dim — Dimension to operate along

positive integer scalar

Dimension to operate along, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 1.

Consider a matrix A.

• If dim = 1, then movprod(A,k,1) starts with the first column and slides vertically over each row. The product is computed over k elements at a time. Then it moves to the second column and repeats the computation. This process continues until all columns are exhausted.

  

• If dim = 2, then movprod(A,k,2) starts with the first row and slides horizontally across each column. The product is computed over k elements at a time. Then it moves to the second row and repeats the computation. This process continues until all rows are exhausted.

  

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

nanflag — NaN condition

'includenan' (default) | 'omitnan'

NaN condition, specified as one of these values:

• 'includenan' — Include NaN values from the input when computing the product, resulting in NaN output.

• 'omitnan' — Ignore all NaN values in the input. If a window contains only NaN values, then movprod returns 1.

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: M = movprod(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 the comma-separated pair consisting of 'Endpoints' and one of the following:

'Endpoints' Value	Description
'shrink'	Shrink the window size near the endpoints of the input to include only existing elements.
'discard'	Do not output any products 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.

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

SamplePoints — Sample points for computing products

vector

Sample points for computing products, specified as the comma-separated pair consisting of 'SamplePoints' and 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 movprod(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 the 'Endpoints' name-value pair is specified, then its value must be 'shrink'.

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

Extended Capabilities

Tall Arrays

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

This function supports tall arrays with the limitations:

The 'SamplePoints' name-value pair 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 'SamplePoints' name-value pair is not supported.

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