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 --- doc/windows.md | 2 +- docs/doc/windows.html | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/windows.md b/doc/windows.md index baae3efc..f4ef0fe9 100644 --- a/doc/windows.md +++ b/doc/windows.md @@ -106,4 +106,4 @@ The slices are naturally arranged along multiple dimensions according to their s If `𝕨` has length `0`, then `𝕩` is not sliced along any dimensions. The only slice that resultsβ€”the entire argumentβ€”is then arranged along an additional zero dimensions. In the end, the result is `𝕩`, unchanged. -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 `π•¨βˆΎΒ¬βŸœπ•¨βŒΎ((≠𝕨)βŠΈβ†‘)≒𝕩`, and element `iβŠ‘z` is `iβŠ‘z` ←→ `π•©βŠ‘Λœ+´¨(π•¨βˆΎβ—‹(β†•βˆ˜β‰ )≒𝕩)βŠ”i`. +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 ∾ Β¬βŸœπ•¨βŒΎ(lβŠΈβ†‘)≒𝕩`, and element `iβŠ‘z` is `jβŠ‘π•©`, with `j←+´¨(lβˆΎβ—‹β†•=𝕩)βŠ”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`. 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 resultsβ€”the entire argumentβ€”is then arranged along an additional zero dimensions. In the end, the result is 𝕩, unchanged.

-

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 π•¨βˆΎΒ¬βŸœπ•¨βŒΎ((≠𝕨)βŠΈβ†‘)≒𝕩, and element iβŠ‘z is iβŠ‘z ←→ π•©βŠ‘Λœ+´¨(π•¨βˆΎβ—‹(β†•βˆ˜β‰ )≒𝕩)βŠ”i.

+

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 ∾ Β¬βŸœπ•¨βŒΎ(lβŠΈβ†‘)≒𝕩, and element iβŠ‘z is jβŠ‘π•©, with j←+´¨(lβˆΎβ—‹β†•=𝕩)βŠ”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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