ArrayReduce

reduces dimension n of array by applying f.

ArrayReduce[f,array,n₁;;n₂]

reduces dimensions n₁ through n₂.

ArrayReduce[f,array,{n₁,n₂,…}]

reduces dimensions n₁, n₂, etc.

ArrayReduce[f,array,{{n₁₁,n₁₂,…},{n₂₁,n₂₂,…},…}]

applies f to arrays formed by combining all dimensions n_ij to make each dimension i.

Details

Array reduction, also called array aggregation, is used to compute functions such as Mean, Total or StandardDeviation along specific dimensions of an array.
In ArrayReduce[f,array,n], f is applied to every vector along the n dimension of array. It can be seen as a transposition where dimension n becomes the last dimension, followed by the application of f on the lowest-level vectors:

If array has dimensions {d₁,d₂,…}, and if the function is transforming a vector into a scalar, the results is an array that has the same dimensions as array except for d_n, which is dropped.
In ArrayReduce[f,array,n₁;;n₂] and ArrayReduce[f,array,{n₁,n₂,…}], f is applied to every vector formed by combining and flattening the specified dimensions.
In ArrayReduce[f,array,{{n₁₁,n₁₂,…},{n₂₁,n₂₂,…},…}], f is applied to arrays of arbitrary ranks instead of vectors only.
ArrayReduce[f,array,{n₁,n₂,…}] is equivalent to ArrayReduce[f,array,{{n₁,n₂,…}}].

Compute the mean of every row of a matrix:

Compute the mean of every column of a matrix:

Define an array of rank 3:

Compute the standard deviation over the second dimension:

The resulting array is of rank 2, and the second axis has been removed:

Visualize the input and output arrays:

Define an array of rank 5:

Reduce the dimensions of the array by computing the total over dimensions 2 and 4:

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