From df5ddc0ed2fe48411645228c6e2d596be239a0c6 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Mon, 4 Jul 2022 22:25:39 -0400 Subject: A few edits more --- docs/doc/find.html | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) (limited to 'docs/doc/find.html') diff --git a/docs/doc/find.html b/docs/doc/find.html index 09632469..01efff6d 100644 --- a/docs/doc/find.html +++ b/docs/doc/find.html @@ -9,7 +9,7 @@ ↗️
    "xx" ⍷ "xxbdxxxcx"
 ⟨ 1 0 0 0 1 1 0 0 ⟩
-

More precisely 𝕨 needs to match a contiguous selection from 𝕩, which for strings means a substring. These subarrays of 𝕩 are also exactly the cells in the result of Windows. In fact we can use Windows to see all the arrays 𝕨 will be compared against.

+

More precisely, 𝕨 needs to match a contiguous selection from 𝕩, which for strings means a substring. These subarrays of 𝕩 are also exactly the cells in the result of Windows. So we can use Windows to see all the arrays 𝕨 will be compared against.

↗️
    2 ↕ "xxbdxxxcx"
 ┌─    
 ╵"xx  
@@ -32,7 +32,7 @@
     "string" (≢∘⊢↑⍷) "substring"  # APL style
 ⟨ 0 0 0 1 0 0 0 0 0 ⟩
-

If 𝕨 is larger than 𝕩, the result is empty, and there's no error even in cases where Windows would fail. One place this tends to come up is when applying First (⊑) the result: ⊑⍷ tests whether 𝕨 appears in 𝕩 at the first position, that is, whether it's a prefix of 𝕩. If 𝕨 is longer than 𝕩 it shouldn't be a prefix. First will fail but using a fold 0⊣´⥊∘⍷ instead gives a 0 in this case.

+

If 𝕨 is larger than 𝕩, the result is empty, and there's no error even in cases where Windows would fail. One place this tends to come up is when applying First (⊑) to the result: ⊑⍷ tests whether 𝕨 appears in 𝕩 at the first position, that is, whether it's a prefix of 𝕩. If 𝕨 is longer than 𝕩 it shouldn't be a prefix. First will fail but using a fold 0⊣´⍷ instead gives a 0 in this case.

↗️
    "loooooong" ⍷ "short"
 ⟨⟩
 
@@ -42,7 +42,7 @@
     0 ⊣´ "loooooong" ⍷ "short"
 0
-

This pattern also works in the high-rank case discussed below, testing whether 𝕨 is a multi-dimensional prefix starting at the lowest-index corner of 𝕩.

+

Adding a Deshape gives 0⊣´⥊∘⍷, which works with the high-rank case discussed below. It tests whether 𝕨 is a multi-dimensional prefix starting at the lowest-index corner of 𝕩.

Higher ranks

If 𝕨 and 𝕩 are two-dimensional then Find does a two-dimensional search. The cells used are also found in 𝕨≢⊸↕𝕩. For example, the bottom-right corner of 𝕩 below matches 𝕨, so there's a 1 in the bottom-right corner of the result.

↗️
    ⊢ a ← 7 (4|⋆˜)⌜○↕ 9   # Array with patterns
@@ -66,7 +66,7 @@
   0 0 1 0 0 0 1  
                 ┘
-

It's also allowed for 𝕨 to have a smaller rank than 𝕩; in this case leading axes of 𝕩 are mapped over so that axes of 𝕨 correspond to trailing axes of 𝕩. This is a minor violation of the leading axis principle, which would match axes of 𝕨 to leading axes of 𝕩 in order to make a function that's useful with the Rank operator, but such a function would be quite strange and hardly ever useful.

+

It's also allowed for 𝕨 to have a smaller rank than 𝕩; the axes of 𝕨 then correspond to trailing axes of 𝕩, so that leading axes of 𝕩 are mapped over. This is a minor violation of the leading axis principle, which would match axes of 𝕨 to leading axes of 𝕩 in order to make a function that's useful with the Rank operator, but such a function would be quite strange and hardly ever useful.

↗️
    0‿1‿0‿1 ⍷ a
 ┌─             
 ╵ 0 0 0 0 0 0  
-- 
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