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Surprising behavior of the two ways to implement a Filter

I’ve seen different ways to implement a Filter (see here and here). To my surprise, I’ve found that the first filter is more efficient than the second (as I’ve shown in the Mathematica Playground):
// Data is a matrix like {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}}
// On the first approach the filter is like {{7, 8}, {10, 11}, {11, 12}},
// On the second the filter is like {{1, 2}, {5, 6}, {9, 10}}
n = Length@Data;
f = ConstantArrayFilter[Data, Mod[{1, 2}, 2, -1]];

Using the first approach the number of evaluations is much higher than the second approach.
What I would have expected is the same order of evaluations both methods.
Is there any reason the second approach would be more efficient than the first one?


f is an AbstractArray, an instance of Complex[]{{a_, b_}, {c_, d_}, {e_, f_}}. Try
ArrayPlot[{{f, f}, {f, f}, {f, f}}]

to see that the {}s at the end of f cannot be used as a filter. To see why this is, try

It seems to me that the second case is quicker because it only applies the filter to the first two dimensions, so it is not as deep as the first case, which applies the filter to all three dimensions.

Alternatively, use a different constructor for f, like:
f = Array[ConstantArrayFilter, {n}][[{{2}}, { -1}

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[![Build Status](

## Description

To update frozen_array_compat to reflect recent changes to Eigen without breaking compatibility, we need to dump our frozen arrays in a backwards-compatible manner.

The frozen_array_compat library provides a method to easily convert a frozen array from Eigen to a normal Ruby array.

require «frozen_array_compat»

arr = Eigen::ArrayXd.frozen(‘

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