From 8342ba5e9392811dbc0514a97e847a44a5b330a2 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Mon, 6 Jun 2022 21:29:06 -0400 Subject: When I wrote all these docs did I really understand I'd have to edit them? --- docs/doc/reshape.html | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) (limited to 'docs/doc/reshape.html') diff --git a/docs/doc/reshape.html b/docs/doc/reshape.html index 963d03a3..68537bf0 100644 --- a/docs/doc/reshape.html +++ b/docs/doc/reshape.html @@ -58,8 +58,8 @@ -

The glyph ⥊ indicates BQN's facilities to reflow the data in an array, giving it a different shape. Its monadic form, Deshape, simply removes all shape information, returning a list of all the elements from the array in reading order. With a left argument, ⥊ is called Reshape and is a more versatile tool for rearranging the data in an array into the desired shape.

-

Because of its dependence on the reading order of an array, Reshape is less fundamental than other array operations. Using Reshape in the central computations of a program can be a sign of imperfect usage of arrays. For example, it may be useful to use Reshape to create a constant array or repeat a sequence of values several times, but the same task might also be accomplished more simply with Table ⌜, or by taking advantage of leading axis agreement in arithmetic primitives.

+

The glyph ⥊ indicates BQN's facilities to reflow the data in an array, giving it a different shape. Its monadic form, Deshape, simply removes all shape information, returning a list of all the elements from the array in index order. With a left argument, ⥊ is called Reshape and is a more versatile tool for rearranging the data in an array into the desired shape.

+

Because of its dependence on the index order of an array, Reshape is less fundamental than other array operations. Using Reshape in the central computations of a program can be a sign of imperfect usage of arrays. For example, it may be useful to use Reshape to create a constant array or repeat a sequence of values several times, but the same task might also be accomplished more simply with Table ⌜, or by taking advantage of leading axis agreement in arithmetic primitives.

Deshape

The result of Deshape is a list containing the same elements as the argument.

↗️
    ⊢ a ← +⌜´ ⟨100‿200, 30‿40, 5‿6‿7⟩
@@ -74,7 +74,7 @@
     ⥊ a
 ⟨ 135 136 137 145 146 147 235 236 237 245 246 247 ⟩
-

The elements are ordered in reading order—left to right, then top to bottom. This means that leading axes "matter more" for ordering: if one element comes earlier in the first axis but later in the second than some other element, it will come first in the result. In another view, elements are ordered according to their indices. In other words, deshaping the array of indices for an array will always give a sorted array.

+

The elements are ordered in reading order—left to right, then top to bottom. This means that leading axes "matter more" for ordering: if one element comes earlier in the first axis but later in the second than some other element, it will come first in the result. In another view, elements are ordered according to their indices, leading to the name index order for this ordering. To be precise, deshaping the array of indices for an array always gives a sorted array.

↗️
    ↕≢a
 ┌─                               
 ╎ ⟨ 0 0 0 ⟩ ⟨ 0 0 1 ⟩ ⟨ 0 0 2 ⟩  
@@ -87,8 +87,8 @@
     ⍋ ⥊ ↕≢a
 ⟨ 0 1 2 3 4 5 6 7 8 9 10 11 ⟩
-

This ordering is also known as row-major order.

-

Deshape turns a unit argument into a single-element list, automatically enclosing it if it's an atom. However, if you know 𝕩 is a unit, a more principled way to turn it into a list is to apply Solo (≍), which adds a length-1 axis before any other axes. If you ever add axes to the data format, Solo is more likely to continue working after this transition, unless there's a reason the result should always be a list.

+

This ordering is also known as row-major order in computing.

+

Deshape turns a unit argument into a single-element list, automatically enclosing it if it's an atom. However, if you know 𝕩 is a unit, a more principled way to turn it into a list is to apply Solo (≍), which adds a length-1 axis before any other axes. If you ever add axes to the data format, Solo is more likely to continue working after this transition, unless there's a reason the result should always be a list.

↗️
    ⥊ 2
 ⟨ 2 ⟩
     ≍ 2
@@ -121,7 +121,7 @@
     (⥊a) ≡ ⥊ 6‿2⥊a
 1
-

One common use is to generate an array with a specified shape that counts up from 0 in reading order, a reshaped Range. The idiomatic phrase to do this is ⥊⟜(↕×´), since it doesn't require writing the shape and its product separately.

+

One use is to generate an array with a specified shape that counts up from 0 in index order, a reshaped Range. The idiomatic phrase to do this is ⥊⟜(↕×´), since it doesn't require writing the shape and its product separately.

↗️
    2‿7 ⥊ ↕14
 ┌─                   
 ╵ 0 1 2  3  4  5  6  
@@ -171,12 +171,12 @@
   uU" 
      ┘
-

Above, the length given is ∘, a special value that indicates that a length that fits the argument should be computed. In fact, Reshape has four different special values that can be used. Every one works the same for a case like the one above, where the rest of the shape divides the argument length evenly. They differ in how they handle uneven cases, where the required length would fall between two whole numbers.

+

Above, the length given is ∘, a special value that indicates that a length fitting the argument should be computed. Reshape has four such special values that can be used. Every one works the same for a case like the one above, where the rest of the shape divides the argument length evenly. They differ in how they handle uneven cases, where the required length falls between two whole numbers.

These values are just BQN primitives of course. They're not called by Reshape or anything like that; the primitives are just chosen to suggest the corresponding functionality.

Here's an example of the four cases. If we try to turn five elements into two rows, ∘ gives an error, ⌊ drops the last element, ⌽ uses the first element again, and ↑ uses a fill element (like 6↑"abcde" would).

@@ -201,7 +201,7 @@ de " ┘ -

A computed length can be useful to input an array without using nested notation: for example, if you have a table with rows of three elements, you might write it as one long list, using ∘‿3⥊⟨…⟩ to get it back to the appropriate shape. ∘ is definitely the value to use here, as it will check that you haven't missed an element or something like that.

+

A computed length can be useful to input an array without using nested notation: for example, if you have a table with rows of three elements, you might write it as one long list, using ∘‿3⥊⟨…⟩ to get it back to the appropriate shape. ∘ is definitely the value to use here, as it will check that you haven't missed or added an element.

Computed Reshape might also be used in actual data processing: for example, to sum a list in groups of four, you might first reshape it using ↑‿4 for the shape, then average the rows. Here the code ↑ is useful because added fill elements of 0 won't change the sum, so that if the last group doesn't have four elements (9‿7 below), it will still be summed correctly.

↗️
    +´˘ ↑‿4 ⥊ ⟨0,2,1,1, 5,9,6,4, 3,3,3,3, 9,7⟩
 ⟨ 4 24 12 16 ⟩
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