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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.
Examplesopen allclose all Basic Examples (3)Apply f to each element of a list and its range-1 neighbors:
Apply f to each element of a list and its range-2 neighbors:
Apply f to all 3x3 blocks of range-1 neighbors around each element:
Scope (4)Specify length-3 blocks using a template:
Specify length-3 blocks using a template where the center element is not considered:
Specify length-3 blocks using a template where only the left element is considered:
Use DeleteMissing to remove elements according to a specified template:
Options (6) Padding (6)By default, fixed padding is used for neighborhoods at the border:
Pad neighborhoods using a constant value:
Periodic padding in all dimensions for a matrix:
With Padding->None, ArrayFilter only visits neighborhoods entirely inside the array:
Use padded values with different paddings:
With Padding->None, empty lists are returned when the neighborhood size is larger than the input:
A 2x2 matrix has no 3x3 neighborhoods:
A 2x2 matrix with a 1x3 template:
Applications (5)Compute successive differences of elements:
Compute a moving average with runs of 3 elements using a range-1 neighborhood:
Compute a moving median of all values in each 3x3 neighborhood of a matrix:
Compute a moving quantile for some data:
Implement a 2D additive cellular automaton:
Properties & Relations (1)Templates with even dimensions effectively allow maximal overhang at the beginning:
Wolfram Research (2015), ArrayFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/ArrayFilter.html. TextWolfram Research (2015), ArrayFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/ArrayFilter.html.
CMSWolfram Language. 2015. "ArrayFilter." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ArrayFilter.html.
APAWolfram Language. (2015). ArrayFilter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ArrayFilter.html
BibTeX@misc{reference.wolfram_2025_arrayfilter, author="Wolfram Research", title="{ArrayFilter}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/ArrayFilter.html}", note=[Accessed: 12-July-2025 ]}
BibLaTeX@online{reference.wolfram_2025_arrayfilter, organization={Wolfram Research}, title={ArrayFilter}, year={2015}, url={https://reference.wolfram.com/language/ref/ArrayFilter.html}, note=[Accessed: 12-July-2025 ]}
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