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ArrayFilter—Wolfram Documentation

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ArrayFilter[f,array,r]

applies f to all range-r blocks in the specified array.

ArrayFilter[f,array,{r1,r2,…}]

applies f to blocks with ranges r1, r2, … in successive dimensions.

ArrayFilter[f,array,template]

applies f over blocks specified by the position of 1s in the array template.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Padding  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

ArrayFilter

ArrayFilter[f,array,r]

applies f to all range-r blocks in the specified array.

ArrayFilter[f,array,{r1,r2,…}]

applies f to blocks with ranges r1, r2, … in successive dimensions.

ArrayFilter[f,array,template]

applies f over blocks specified by the position of 1s in the array template.

Details and Options

  • ArrayFilter[f,array,…] requires that array is full array to a certain depth.
  • ArrayFilter[f,array,r] applies f to all overlapping blocks of elements in array.
  • Both array and template can be SparseArray objects.
  • With ArrayFilter[f,array,template], neighborhood elements corresponding to 0s of template are replaced with Missing[] before being passed to f.
  • ArrayFilter has the option Padding, which specifies how neighborhoods should be formed at the edges of the array. The following settings can be used:
  • Nonereturns a smaller array
    valuse val for padding
    "Fixed"repeat edge elements (default)
    "Periodic"periodic in each dimension

Examples

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Basic Examples  (3)

Apply f to each element of a list and its range-1 neighbors:

Wolfram Language code: ArrayFilter[f, Range[10], 1]

Apply f to each element of a list and its range-2 neighbors:

Wolfram Language code: ArrayFilter[f, Range[10], 2]

Apply f to all 3x3 blocks of range-1 neighbors around each element:

Wolfram Language code: ArrayFilter[f, (| | | | | --- | --- | --- | | 1 | 2 | 3 | | 10 | 20 | 30 | | 100 | 200 | 300 |), {0, 1}]

Show as matrices:

Wolfram Language code: TraditionalForm[%]

Scope  (4)

Specify length-3 blocks using a template:

Wolfram Language code: ArrayFilter[fun, {a, b, c, d, e, f}, {1, 1, 1}]

Specify length-3 blocks using a template where the center element is not considered:

Wolfram Language code: ArrayFilter[fun, {a, b, c, d, e, f}, {1, 0, 1}]

Specify length-3 blocks using a template where only the left element is considered:

Wolfram Language code: ArrayFilter[fun, {a, b, c, d, e, f}, {1, 0, 0}]

Use DeleteMissing to remove elements according to a specified template:

Wolfram Language code: ArrayFilter[fun[DeleteMissing[#]]&, {a, b, c, d, e, f}, {1, 0, 0}]

Options  (6)

Padding  (6)

By default, fixed padding is used for neighborhoods at the border:

Wolfram Language code: ArrayFilter[fun, {a, b, c, d, e, f}, 1]

Pad neighborhoods using a constant value:

Wolfram Language code: ArrayFilter[fun, {a, b, c, d, e, f}, 1, Padding -> 0]

Periodic padding for a list:

Wolfram Language code: ArrayFilter[fun, {a, b, c, d, e, f}, 1, Padding -> "Periodic"]

Periodic padding in all dimensions for a matrix:

Wolfram Language code: ArrayFilter[fun, (⁠| | | | | -- | -- | -- | | 11 | 12 | 13 | | 21 | 22 | 23 |⁠), 1, Padding -> "Periodic"]

Show as a matrix:

Wolfram Language code: TraditionalForm[%]

With Padding->None, ArrayFilter only visits neighborhoods entirely inside the array:

Wolfram Language code: ArrayFilter[fun, {a, b, c, d}, 1, Padding -> None]

Use padded values with different paddings:

Wolfram Language code: ArrayFilter[fun, {a, b, c, d}, 1, Padding -> "Fixed"]

With Padding->None, empty lists are returned when the neighborhood size is larger than the input:

Wolfram Language code: ArrayFilter[fun, {a1, a2}, 1, Padding -> None]

A 2x2 matrix has no 3x3 neighborhoods:

Wolfram Language code: ArrayFilter[fun, {{a1, a2}, {b1, b2}}, 1, Padding -> None]

A 2x2 matrix with a 1x3 template:

Wolfram Language code: ArrayFilter[fun, {{a1, a2}, {b1, b2}}, {{1, 0, 1}}, Padding -> None]

Applications  (5)

Compute successive differences of elements:

Wolfram Language code: ArrayFilter[Last[#] - First[#]&, {a, b, c, d, e, f}, 1]

Compute a moving average with runs of 3 elements using a range-1 neighborhood:

Wolfram Language code: ArrayFilter[Mean, {a, b, c, d, e}, 1]

Compute a moving median of all values in each 3x3 neighborhood of a matrix:

Wolfram Language code: f[neigh_] := Median[Flatten[neigh]]; ArrayFilter[f, {{1, 2, 4}, {5, 3, 1}, {1, 4, 2}, {3, 2, 0}}, 1]

Compute a moving quantile for some data:

Wolfram Language code: data = RandomFunction[WienerProcess[], {0, 10, 0.1}]["Values"];
Wolfram Language code: mq = ArrayFilter[Quantile[#, 0.75]&, data, 1];
Wolfram Language code: ListLinePlot[{data, mq}]

Implement a 2D additive cellular automaton:

Wolfram Language code: ArrayPlot /@ NestList[ArrayFilter[Mod[Total[#, 2], 2]&, #, {1, 1}]&, BoxMatrix[0, {11, 11}], 5]

Properties & Relations  (1)

Templates with even dimensions effectively allow maximal overhang at the beginning:

Wolfram Language code: ArrayFilter[f, {a, b, c}, {1, 1}]
Wolfram Research (2015), ArrayFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/ArrayFilter.html.

Text

Wolfram Research (2015), ArrayFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/ArrayFilter.html.

CMS

Wolfram Language. 2015. "ArrayFilter." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArrayFilter.html.

APA

Wolfram Language. (2015). ArrayFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArrayFilter.html

BibTeX

@misc{reference.wolfram_2026_arrayfilter, author="Wolfram Research", title="{ArrayFilter}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/ArrayFilter.html}", note=[Accessed: 14-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_arrayfilter, organization={Wolfram Research}, title={ArrayFilter}, year={2015}, url={https://reference.wolfram.com/language/ref/ArrayFilter.html}, note=[Accessed: 14-November-2026]}