Apply moving window function and block reduction to padded blocks of data
applies tA
= matlab.tall.blockMovingWindow(windowfcn
,blockfcn
,window
,tX
)blockfcn
to complete windows of data and
windowfcn
to incomplete windows of data near the edges.
window
specifies the size of the sliding window. The result contains
the vertical concatenation of applying blockfcn
and
windowfcn
to these windows of data.
[
,
where tA
,tB
,...] = matlab.tall.blockMovingWindow(windowfcn
,blockfcn
,window
,tX
,tY
,...)windowfcn
and blockfcn
are function handles that
return multiple outputs, returns arrays tA, tB, ...
, each corresponding
to one of the output arguments of windowfcn
and
blockfcn
. The inputs to windowfcn
and
blockfcn
are pieces of data from the arguments tX, tY,
...
. This syntax has these requirements:
windowfcn
and blockfcn
must return the same
number of outputs as were requested from
matlab.tall.blockMovingWindow
.
Each output of windowfcn
and blockfcn
must
be the same type as the first data input tX
.
All outputs tA,tB,...
must have the same height.
[___] = matlab.tall.blockMovingWindow(___,
specifies additional options with one or more namevalue pair arguments using any of the
previous syntaxes. For example, to adjust the step size between windows, you can specify
Name,Value
)'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).
Use matlab.tall.blockMovingWindow
to calculate the moving mean 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 = datastore('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.blockMovingWindow
to calculate the moving mean of the data in the first dimension with a window size of 10. Since windowfcn
applies only to single windows of data, you can use the mean
function to reduce the windows of data down into a matrix with one row. The blockfcn
applies to whole blocks of data, so use the movmean
function to calculate the mean of each full window of data in the blocks.
windowfcn = @(info,x) mean(x,1,'omitnan'); blockfcn = @(info,x) movmean(x,info.Window,1,'omitnan','EndPoints','discard'); A = matlab.tall.blockMovingWindow(windowfcn, blockfcn, 10, tX)
A = MxNx... tall double array ? ? ? ... ? ? ? ... ? ? ? ... : : : : : :
Gather a portion of the results into memory.
gather(A(1:10,:))
Evaluating tall expression using the Local MATLAB Session:  Pass 1 of 2: Completed in 1.5 sec  Pass 2 of 2: Completed in 11 sec Evaluation completed in 14 sec
ans = 10×2
10.8000 8.8000
18.8333 17.8333
16.5714 15.0000
15.8750 13.0000
14.4444 11.8889
13.2000 10.8000
14.0000 11.1000
13.5000 11.9000
15.3000 11.4000
19.7000 13.4000
Calculate moving statistics on the variables of a table.
Load the outages.csv
data set as a tall table. The data contains information about power outages.
T = tall(readtable('outages.csv'))
T = 1,468×6 tall table Region OutageTime Loss Customers RestorationTime Cause _____________ ________________ ______ __________ ________________ ___________________ {'SouthWest'} 20020201 12:18 458.98 1.8202e+06 20020207 16:50 {'winter storm' } {'SouthEast'} 20030123 00:49 530.14 2.1204e+05 NaT {'winter storm' } {'SouthEast'} 20030207 21:15 289.4 1.4294e+05 20030217 08:14 {'winter storm' } {'West' } 20040406 05:44 434.81 3.4037e+05 20040406 06:10 {'equipment fault'} {'MidWest' } 20020316 06:18 186.44 2.1275e+05 20020318 23:23 {'severe storm' } {'West' } 20030618 02:49 0 0 20030618 10:54 {'attack' } {'West' } 20040620 14:39 231.29 NaN 20040620 19:16 {'equipment fault'} {'West' } 20020606 19:28 311.86 NaN 20020607 00:51 {'equipment fault'} : : : : : : : : : : : :
Use matlab.tall.blockMovingWindow
to apply a movingwindow function to blocks of the tall table. Specify these options:
blkstats
as the block function to operate on complete blocks of data (included at the end of the example as a local function).
A window size of 50 and a stride of 5.
EndPoints
as 'discard'
to ignore incomplete windows of data. With this value, the windowfcn
input can be specified as empty []
since only complete windows of data are operated on.
The input table has six variables, but the two outputs are doubleprecision vectors. Specify scalar doubles as the value for OutputsLike
so that the function permits this change in data type and size.
[A, B] = matlab.tall.blockMovingWindow([], @blkstats, 50, T, 'Stride', 5, ... 'EndPoints', 'discard', 'OutputsLike', {1, 1});
Preview a few rows in the results.
[A,B] = gather(head(A),head(B))
Evaluating tall expression using the Local MATLAB Session:  Pass 1 of 2: Completed in 0.16 sec  Pass 2 of 2: Completed in 0.24 sec Evaluation completed in 0.63 sec
A = 8×1
254.0861
254.0861
340.3499
452.0191
464.8524
471.9737
464.8524
464.8524
B = 8×1
10^{5} ×
1.3447
1.0779
1.4227
1.4509
1.2888
1.2888
1.2308
1.3722
The blkstats
function calculates the moving median value of the Loss
and Customers
table variables in the first dimension using the specified window size. The function applies the Stride
value to reduce the size of the output, and then it returns the results as two vectors.
function [out1, out2] = blkstats(info, t) a = movmedian([t.Loss t.Customers], info.Window, 1, 'omitnan', 'EndPoints', 'discard'); a = a(1:info.Stride:end, :); out1 = a(:,1); out2 = a(:,2); end
windowfcn
— Function to apply to incomplete windows of data[]
Function to apply to incomplete windows of data, specified as a function handle,
anonymous function, or []
. windowfcn
is invoked
once per incomplete window as the calculation moves over data in the tall dimension.
matlab.tall.blockMovingWindow
applies
windowfcn
only when 'EndPoints'
has the default
value of 'shrink'
. If you specify a different value for
'EndPoints'
, then set windowfcn
to
[]
.
Each output of windowfcn
must be the same type as the first data
input tX
. You can use the 'OutputsLike'
option to
return outputs of different data types.
The general functional signature of
windowfcn
is
[a, b, c, ...] = windowfcn(info, x, y, ...)
info
input is a structure provided by
matlab.tall.blockMovingWindow
that includes these fields:
Stride
— Specified step size between windows (default: 1). Set
this value with the 'Stride'
namevalue pair.
Window
— Specified window size. Set this value with the
window
input argument.
windowfcn
must satisfy these requirements:
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 windowfcn
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, ND array, table, or timetable, applying
windowfcn
must result in a reduction of the input
data in each of its columns or variables.
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
windowfcn
.
All of the outputs [a, b, c, ...]
are sent to the same
index in the first dimension in their respective destination output
arrays.
Functional Rules — windowfcn
must satisfy this 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.
Example: A = matlab.tall.blockMovingWindow(@windowfcn, @blockfcn, 10,
tX)
Example: A = matlab.tall.blockMovingWindow([], @blockfcn, 10, tX,
'EndPoints', 'discard')
Data Types: function_handle
blockfcn
— Function to apply to blocks of dataFunction to apply to blocks of data, specified as a function handle or anonymous
function. blockfcn
is applied to blocks of data that contain complete
windows of data. Thus, blockfcn
must operate in a vectorized manner
on entire blocks of data and return output that has the proper size for the specified
window size and stride.
Each output of blockfcn
must be the same type as the first data
input tX
. You can use the 'OutputsLike'
option to
return outputs of different data types.
matlab.tall.blockMovingWindow
applies
blockfcn
to blocks of data whenever the block contains only
complete windows:
For middle blocks when 'EndPoints'
is set to
'shrink'
(default behavior). In this case
windowfcn
operates on the incomplete windows of data on the
ends.
For all blocks when 'EndPoints'
is set to
'discard'
or a padding value.
The general functional signature of blockfcn
is
[a, b, c, ...] = blockfcn(info, bX, bY, bZ, ...)
info
input is a structure provided by
matlab.tall.blockMovingWindow
that includes these fields:
Stride
— Specified step size between windows (default: 1). Set
this value with the 'Stride'
namevalue pair.
Window
— Specified window size. Set this value with the
window
input argument.
The blocks of data bX, bY, bZ, ...
that
matlab.tall.blockMovingWindow
provides to blockfcn
have these properties:
The blocks contain only fullsized windows. blockfcn
does not
have to define a behavior for incomplete windows of data.
The first window of data starts at the first element of the block. The last element of the last window is the last element of the block.
blockfcn
must satisfy these requirements:
Input Arguments — The inputs [bX, bY,
bZ, ...]
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 [bX, bY, bZ, ...]
satisfy
these properties:
All of the inputs [bX, bY, bZ, ...]
have the same size
in the first dimension after any allowed expansion.
The blocks of data in [bX, bY, bZ, ...]
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 bX = tX(1:20000,:)
and
bY = tY(1:20000,:)
.
If the first dimension of any of the data inputs [tX, tY, tZ,
...]
has a size of 1
, then the
corresponding block [bX, bY, bZ, ...]
consists of all the
data in that tall array.
Applying blockfcn
must result in a reduction of the
input data such that the result has height equal to the number of windows in
the block. You can use info.Window
and
info.Stride
to determine the number of windows in a
block.
If the input is a matrix, ND array, table, or timetable, then applying
blockfcn
must result in a reduction of the input data
in each of its columns or variables.
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
blockfcn
.
All of the outputs [a, b, c, ...]
are sent to the same
index in the first dimension in their respective destination output
arrays.
Functional Rules — blockfcn
must satisfy this 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.
Example: A = matlab.tall.blockMovingWindow(@windowfcn, @blockfcn, 10,
tX)
Example: A = matlab.tall.blockMovingWindow([], @blockfcn, 10, tX,
'EndPoints', 'discard')
Data Types: function_handle
window
— Window sizeWindow size, specified as a positive integer scalar or a twoelement 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
namevalue pair.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
tX
, tY
— Input arrays (as separate arguments)Input arrays, specified as separate arguments of scalars, vectors, matrices,
multidimensional arrays, tables, or timetables. The input arrays can be tall or
inmemory arrays. The input arrays are used as inputs to the transform function
fcn
. Each input array tX,tY,...
must have the
same height.
Specify optional
commaseparated 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
.
tA = matlab.tall.blockMovingWindow(@windowfcn, blockfcn, window, tX,
'Stride', 2)
'Stride'
— Step size between windows1
(default)  positive integer scalarStep size between windows, specified as the commaseparated 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 valueMethod to treat leading and trailing windows, specified as the commaseparated 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 the window size near the endpoints of the input to include only existing elements.  
 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.

Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 logical
 char
 string
'OutputsLike'
— Prototype of output arraysPrototype of output arrays, specified as the commaseparated 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.
The prototype arrays {PA,PB,...}
that you specify must have
the same data type and nontall dimension sizes as the corresponding output
arrays.
Example: tA = matlab.tall.blockMovingWindow(..., tX, 'OutputsLike', {int8(1)});
, where
tX
is a doubleprecision tall array, returns tA
as
int8
instead of double
.
Data Types: cell
tA
, tB
— Output arraysOutput arrays, returned as scalars, vectors, matrices, or multidimensional arrays.
If any input to matlab.tall.blockMovingWindow
is tall, then all
output arguments are also tall. Otherwise, all output arguments are inmemory
arrays.
The size and data type of the output arrays depend on the specified window
functions windowfcn
and blockfcn
.
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 data 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 fullsized window,
matlab.tall.blockMovingWindow
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.
Use matlab.tall.movingWindow
for simple slidingwindow calculations.
matlab.tall.blockMovingWindow
is an advanced API designed to
provide more flexibility to perform slidingwindow 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.
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