matlab.tall.movingWindow

Apply moving window function to blocks of data

Syntax

tA = matlab.tall.movingWindow(fcn,window,tX)

[tA,tB,...] = matlab.tall.movingWindow(fcn,window,tX,tY,...)

[___] = matlab.tall.movingWindow(___,Name,Value)

Description

tA = matlab.tall.movingWindow(fcn,window,tX) applies the function fcn once per window as the window moves over the first dimension of tX. The output tA is the vertical concatenation of the results of applying fcn to each window.

[tA,tB,...] = matlab.tall.movingWindow(fcn,window,tX,tY,...), where fcn is a function handle that returns multiple outputs, returns arrays tA,tB,..., each corresponding to one of the output arguments of fcn. The inputs to fcn are windows of data from the arguments tX, tY, .... This syntax has these requirements:

• fcn must return the same number of outputs as were requested from matlab.tall.movingWindow.

• Each output of fcn must be the same type as the first data input tX.

• All outputs tA,tB,... must have the same height.

[___] = matlab.tall.movingWindow(___,Name,Value) specifies additional options with one or more name-value pair arguments using any of the previous syntaxes. For example, to adjust the step size between windows, you can specify 'Stride' and a scalar. Or to change the treatment of endpoints where there are not enough elements to complete a window, you can specify 'EndPoints' and a valid option ('shrink', 'discard', or a numeric padding value).

Examples

Moving Window Calculation with Tall Array

Use matlab.tall.movingWindow to calculate the moving median of airline arrival and departure delays.

Create a datastore for the airlinesmall.csv data set and convert it into a tall array. The data contains information about arrival and departure times of US flights. Extract the ArrDelay and DepDelay variables, which are vectors of flight delays, to create a tall array containing the delays as separate columns.

varnames = {'ArrDelay', 'DepDelay'};
ds = tabularTextDatastore('airlinesmall.csv', 'TreatAsMissing', 'NA', ...
    'SelectedVariableNames', varnames);
tt = tall(ds);
tX = [tt.ArrDelay tt.DepDelay]

tX =

  Mx2 tall double matrix

     8    12
     8     1
    21    20
    13    12
     4    -1
    59    63
     3    -2
    11    -1
    :     :
    :     :

Use matlab.tall.movingWindow to calculate the moving median of the data in the first dimension. Use a window size of 5,000.

fcn = @(x) median(x,1,'omitnan');
tA = matlab.tall.movingWindow(fcn,5000,tX)

tA =

  MxNx... tall double array

    ?    ?    ?    ...
    ?    ?    ?    ...
    ?    ?    ?    ...
    :    :    :
    :    :    :

Gather the unique rows of the result into memory.

tA = gather(unique(tA,'rows'))

Evaluating tall expression using the Local MATLAB Session:
- Pass 1 of 2: Completed in 1.3 sec
- Pass 2 of 2: Completed in 59 sec
Evaluation completed in 1 min 1 sec

tA = 31×2

   -4.0000   -2.0000
   -3.5000   -2.0000
   -3.0000   -2.0000
   -3.0000   -1.5000
   -3.0000   -1.0000
   -3.0000   -0.5000
   -3.0000         0
   -2.5000   -1.0000
   -2.5000         0
   -2.0000   -1.0000
      ⋮

Apply Window Function with Multiple Outputs

Use matlab.tall.movingWindow to apply a function with multiple outputs to windows of data.

Create a tall array from an in-memory random matrix.

X = rand(1000,5);
tX = tall(X)

tX =

  1,000x5 tall double matrix

    0.8147    0.6312    0.7449    0.3796    0.4271
    0.9058    0.3551    0.8923    0.3191    0.9554
    0.1270    0.9970    0.2426    0.9861    0.7242
    0.9134    0.2242    0.1296    0.7182    0.5809
    0.6324    0.6525    0.2251    0.4132    0.5403
    0.0975    0.6050    0.3500    0.0986    0.7054
    0.2785    0.3872    0.2871    0.7346    0.0050
    0.5469    0.1422    0.9275    0.6373    0.7825
      :         :         :         :         :
      :         :         :         :         :

Create a function that finds the sum, mean, median, and mode of each window of data in the first dimension. Each output needs to have the same size in the first dimension, but the other dimensions can have different sizes. For each window of data, the sum calculation produces a scalar, while the other calculations produce 1-by-N vectors.

Save the function in your local workspace.

function [S,mn,mdn,md] = mystats(X)
  S = sum(X,[2 1]);
  mn = mean(X,1);
  mdn = median(X,1);
  md = mode(X,1);
end

Note: This function is included at the end of the example as a local function.

Use matlab.tall.movingWindow to apply the mystats function to the data with a window size of 250. Specify four output arguments to return all of the outputs from mystats. Use the 'EndPoints' name-value pair to discard incomplete windows.

[tS,tmn,tmdn,tmd] = matlab.tall.movingWindow(@mystats, 250, tX, 'EndPoints', 'discard')

tS =

  MxNx... tall double array

    ?    ?    ?    ...
    ?    ?    ?    ...
    ?    ?    ?    ...
    :    :    :
    :    :    :


tmn =

  MxNx... tall double array

    ?    ?    ?    ...
    ?    ?    ?    ...
    ?    ?    ?    ...
    :    :    :
    :    :    :


tmdn =

  MxNx... tall double array

    ?    ?    ?    ...
    ?    ?    ?    ...
    ?    ?    ?    ...
    :    :    :
    :    :    :


tmd =

  MxNx... tall double array

    ?    ?    ?    ...
    ?    ?    ?    ...
    ?    ?    ?    ...
    :    :    :
    :    :    :

function [S,mn,mdn,md] = mystats(X)
  S = sum(X,[2 1]);
  mn = mean(X,1);
  mdn = median(X,1);
  md = mode(X,1);
end

Input Arguments

fcn — Window function to apply

function handle | anonymous function

Window function to apply, specified as a function handle or anonymous function. Each output of fcn must be the same type as the first input tX. You can use the 'OutputsLike' option to return outputs of different data types.

The general functional signature of fcn is

[a, b, c, ...] = fcn(x, y, z, ...)

fcn must satisfy these requirements:

1. Input Arguments — The inputs [x, y, z, ...] are blocks of data that fit in memory. The blocks are produced by extracting data from the respective tall array inputs [tX, tY, tZ, ...]. The inputs [x, y, z, ...] satisfy these properties:

   • All of the inputs [x, y, z, ...] have the same size in the first dimension.

   • The blocks of data in [x, y, z, ...] come from the same index in the tall dimension, assuming the tall array is nonsingleton in the tall dimension. For example, if tX and tY are nonsingleton in the tall dimension, then the first set of blocks might be x = tX(1:20000,:) and y = tY(1:20000,:).

   • When the first dimension of any of [tX, tY, tZ, ...] has a size of 1, the corresponding block [x, y, z, ...] consists of all the data in that tall array.

   • Applying fcn must result in a reduction of the input data to a scalar or a slice of an array of height 1.

     When the input is a matrix, N-D array, table, or timetable, applying fcn must result in a reduction of the input data in each of its columns or variables.

2. Output Arguments — The outputs [a, b, c, ...] are blocks that fit in memory, to be sent to the respective outputs [tA, tB, tC, ...]. The outputs [a, b, c, ...] satisfy these properties:

   • All of the outputs [a, b, c, ...] must have the same size in the first dimension.

   • All of the outputs [a, b, c, ...] are vertically concatenated with the respective results of previous calls to fcn.

   • All of the outputs [a, b, c, ...] are sent to the same index in the first dimension in their respective destination output arrays.

3. Functional Rules — fcn must satisfy the functional rule:

   • F([inputs1; inputs2]) == [F(inputs1); F(inputs2)]: Applying the function to the concatenation of the inputs should be the same as applying the function to the inputs separately and then concatenating the results.

For example, this function calculates the mean and standard deviation of the elements in a window and returns two output arrays:

function [mv,sd] = movstats(tX)
mv = mean(tX,1,'omitnan');
sd = std(tX,1,'omitnan');
end

After you save this function to an accessible folder, you can invoke the function with a window size of 5 using this command:

[tA,tB] = matlab.tall.movingWindow(@movstats,5,tX)

Example: tA = matlab.tall.movingWindow(@(x) std(x,1,'omitnan'), tX) specifies an anonymous function to calculate the standard deviation of each window, ignoring NaNs.

Example: tA = matlab.tall.movingWindow(@mean,3,tX) specifies a function handle @mean to calculate the mean value of each three-element window.

Data Types: function_handle

window — Window size

positive integer scalar | two-element row vector

Window size, specified as a positive integer scalar or a two-element row vector [NB NF].

• If window is a scalar, then:

  • When the window size is odd, each window is centered on the corresponding element in the data.

    

  • When the window size is even, each window is centered about the current and previous elements.

    

• If window is a vector [NB NF], then the window includes the previous NB elements, the current element, and the next NF elements of the inputs.

  

By default, the window size is automatically truncated at the endpoints when not enough elements are available to fill the window. When the window is truncated in this manner, the function operates only on the elements that fill the window. You can change this behavior with the EndPoints name-value pair.

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

tX, tY — Input arrays (as separate arguments)

scalars | vectors | matrices | multidimensional arrays | tables | timetables

Input arrays, specified as separate arguments of scalars, vectors, matrices, multidimensional arrays, tables, or timetables. The input arrays can be tall or in-memory arrays. The input arrays are used as inputs to the transform function fcn. Each input array tX,tY,... must have the same height.

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: tA = matlab.tall.movingWindow(@myFcn, window, tX, 'Stride', 2)

Stride — Step size between windows

1 (default) | positive integer scalar

Step size between windows, specified as the comma-separated pair consisting of 'Stride' and a positive integer scalar. After fcn operates on a window of data, the calculation advances by the 'Stride' value before operating on the next window. Increasing the value of 'Stride' from the default value of 1 is the same as reducing the size of the output by picking out every other element, or every third element, and so on.

By default, the value of 'Stride' is 1, so that each window is centered on each element in the input. For example, here is a moving sum calculation with a window size of 3 operating on the vector [1 2 3 4 5 6]':

If the value of 'Stride' is 2, then the calculation changes so that each window is centered on every second element in the input (1, 3, 5). The moving sum now returns three partial sums rather than six:

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

EndPoints — Method to treat leading and trailing windows

'shrink' (default) | 'discard' | padding value

Method to treat leading and trailing windows, specified as the comma-separated pair consisting of 'EndPoints' and one of the values in the table.

At the beginning and end of a windowed calculation, the window of elements being operated on is incomplete. The 'EndPoints' option specifies how to treat these incomplete windows.

'EndPoints' Value	Description	Example: Moving Sum
'shrink'	Shrink the window size near the endpoints of the input to include only existing elements.
'discard'	Do not output any results where the window does not completely overlap with existing elements.
Numeric or logical padding value	Substitute nonexisting elements with a specified numeric or logical value. The padding value must have the same type as tX. The size of the padding value in the first dimension must be equal to 1, and the size in other dimensions must match tX.

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

OutputsLike — Prototype of output arrays

cell array

Prototype of output arrays, specified as the comma-separated pair consisting of 'OutputsLike' and a cell array containing prototype arrays. When you specify 'OutputsLike', the output arrays tA,tB,... returned by matlab.tall.movingWindow have the same data types and attributes as the specified prototype arrays {PA,PB,...}. You must specify 'OutputsLike' whenever the data type of an output array is different than that of the input array. If you specify 'OutputsLike', then you must specify a prototype array for each output.

Example: tA = matlab.tall.movingWindow(..., tX, 'OutputsLike', {int8(1)});, where tX is a double-precision tall array, returns tA as int8 instead of double.

Data Types: cell

Output Arguments

tA, tB — Output arrays

scalars | vectors | matrices | multidimensional arrays

Output arrays, returned as scalars, vectors, matrices, or multidimensional arrays. If any input to matlab.tall.movingWindow is tall, then all output arguments are also tall. Otherwise, all output arguments are in-memory arrays.

• The size and data type of the output arrays depend on the specified window function fcn.

• The output arrays tA,tB,... all have the same height, which depends on the value of 'Stride' and 'EndPoints'. By default the output arrays are the same size as the input arrays.

• In general, the outputs tA,tB,... must all have the same data type as the first input tX. However, you can specify 'OutputsLike' to return different data types. In cases where the input arrays tX, tY, ... are empty, or when 'EndPoints' is 'discard' and there are not enough elements to fill a full-sized window, matlab.tall.movingWindow returns empty outputs. The sizes of the empty outputs are based on the size of the input array tX, or on the sizes of the prototype arrays provided to 'OutputsLike', if specified.

Tips

• Use matlab.tall.movingWindow for simple sliding-window calculations. matlab.tall.blockMovingWindow is an advanced API designed to provide more flexibility to perform sliding-window calculations on tall arrays. As such, it is more complicated to use since the functions must accurately process blocks of data that contain many complete windows. However, with properly vectorized calculations, you can reduce the necessary number of function calls and improve performance.