From 2afb23928e1984d475cc460e1672e8f6fa0e4dbe Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Wed, 11 Aug 2021 17:21:31 -0400 Subject: Allow clicking on header to get fragment link --- docs/doc/shape.html | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) (limited to 'docs/doc/shape.html') diff --git a/docs/doc/shape.html b/docs/doc/shape.html index 99a4260e..80cfb45e 100644 --- a/docs/doc/shape.html +++ b/docs/doc/shape.html @@ -4,10 +4,10 @@ BQN: Array dimensions
(github) / BQN / doc
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Array dimensions

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Array dimensions

The function Shape (≢) returns an array's shape, and Rank (=) and Length (≠) return properties that can be derived from the shape. BQN's arrays are multidimensional, so that the shape is a list of natural numbers (the length along each axis), while the rank (length of the shape) and length (of the first axis) are numbers. In these functions, an atom is treated as a unit array, which has rank 0 and empty shape. A unit has no first axis, but its length is defined to be 1.

Rank can be defined as ≠∘≢ while Length can be defined with a fold to be 1⊣´≢.

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Examples

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Examples

The function Reshape (⥊) always returns an array of shape 𝕨, so we use it to make an array of shape 1‿3‿2‿6 in the example below (Take (↑) shares this property if (≠𝕨)≤=𝕩).

↗️
    ⊢ arr ← 1‿3‿2‿6 ⥊ '0'+↕10
 ┌─        
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     (= ≍ ≠) <↕10
 ⟨ 0 1 ⟩
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Units

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Units

A unit is an atom, or an array with no axes—rank 0. (See Enclose for more about unit arrays). Since it doesn't have any axes, its shape should have no elements. It should be the empty list ⟨⟩ (with a fill of 0, like all shapes). As there's no first element in the shape, it's not obvious what the length should be, and a stricter language would just give an error. However, there are some good reasons to use a length of 1. First, the total number of elements is 1, meaning that if the length divides this number evenly (as it does for non-unit arrays) then the only possible natural number it can be is 1. Second, many functions that take a list for a particular argument also accept a unit, and treat it as a length-1 array. For example, 5⥊a and ⟨5⟩⥊a are identical. Defining ≠5 to be 1 means that =s⥊a is always ≠s.

Despite this last point, it's important to remember that a unit isn't the same as a 1-element list. For example, the length-1 string "a" doesn't match <'a' but instead ⟨'a'⟩. And also bear in mind that having an empty shape doesn't make a unit an empty array. That would mean it has no elements, not one!

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