From 133b41b72a59fb2aba0f2ed460ed7eab0092adb9 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Tue, 12 Jul 2022 22:02:50 -0400 Subject: Simplify and explain multidimensional Windows definition --- docs/doc/windows.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'docs/doc') diff --git a/docs/doc/windows.html b/docs/doc/windows.html index d48db69b..08450842 100644 --- a/docs/doc/windows.html +++ b/docs/doc/windows.html @@ -148,4 +148,4 @@

The slices are naturally arranged along multiple dimensions according to their starting index. Once again the equivalence i⊏l↕x ←→ l↑i↓x holds, provided i and l have the same length.

If 𝕨 has length 0, then 𝕩 is not sliced along any dimensions. The only slice that results—the entire argument—is then arranged along an additional zero dimensions. In the end, the result is 𝕩, unchanged.

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Here's a more formal definition: 𝕩 is an array. 𝕨 is a number, or numeric list or unit, with 𝕨≤○≠≢𝕩. The result z has shape 𝕨∾¬⟜𝕨⌾((≠𝕨)⊸↑)≢𝕩, and element i⊑z is i⊑z ←→ 𝕩⊑˜+´¨(𝕨∾○(↕∘≠)≢𝕩)⊔i.

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Here's a more formal definition: 𝕩 is an array. 𝕨 is a number, or numeric list or unit, with length l←≠𝕨 so that l≤=𝕩. The result z has shape 𝕨 ∾ ¬⟜𝕨⌾(l⊸↑)≢𝕩, and element i⊑z is j⊑𝕩, with j←+´¨(l∾○↕=𝕩)⊔i. That is, the index list i starts with two length-l sequences that are added together to produce the first l values in j. We might also say that each of the first l values in j is split into two values in i.

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