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Ravel: Difference between revisions
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You can use ravel to squash a [[matrix]] down to one dimension. The elements are listed in reading order—left to right, top to bottom. | You can use ravel to squash a [[matrix]] down to one dimension. The elements are listed in reading order—left to right, top to bottom. | ||
< | <syntaxhighlight lang=apl> | ||
⎕←x ← 3 4⍴⍳12 ⍝ A matrix | ⎕←x ← 3 4⍴⍳12 ⍝ A matrix | ||
1 2 3 4 | 1 2 3 4 | ||
| Line 19: | Line 19: | ||
(,×/⍴x) ≡ ⍴,x ⍝ Or the product of the original shape | (,×/⍴x) ≡ ⍴,x ⍝ Or the product of the original shape | ||
1 | 1 | ||
</ | </syntaxhighlight> | ||
Ravelling a [[scalar]] yields a [[singleton]] [[vector]]. | Ravelling a [[scalar]] yields a [[singleton]] [[vector]]. | ||
< | <syntaxhighlight lang=apl> | ||
,3 | ,3 | ||
3 | 3 | ||
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⍴,3 ⍝ It's now a vector | ⍴,3 ⍝ It's now a vector | ||
1 | 1 | ||
</ | </syntaxhighlight> | ||
[[String]] notation cannot produce a single-character string since it produces a [[scalar]] character instead. Using Ravel on a list of characters in quotes ensures it will be a [[vector]] of characters. | [[String]] notation cannot produce a single-character string since it produces a [[scalar]] character instead. Using Ravel on a list of characters in quotes ensures it will be a [[vector]] of characters. | ||
< | <syntaxhighlight lang=apl> | ||
≢⍴ 'a' ⍝ Scalar character | ≢⍴ 'a' ⍝ Scalar character | ||
0 | 0 | ||
≢⍴ ,'a' ⍝ String | ≢⍴ ,'a' ⍝ String | ||
1 | 1 | ||
</ | </syntaxhighlight> | ||
[[Function axis|Axis specification]] may accept either a [[vector]] of two or more adjacent [[axis]] [[Index|indices]], or a single non-integer value. If multiple axes are given, they are merged into one axis whose length is the product of their lengths. If only one value is given, a new axis of length 1 is inserted in the indicated "gap" between axes. | [[Function axis|Axis specification]] may accept either a [[vector]] of two or more adjacent [[axis]] [[Index|indices]], or a single non-integer value. If multiple axes are given, they are merged into one axis whose length is the product of their lengths. If only one value is given, a new axis of length 1 is inserted in the indicated "gap" between axes. | ||
< | <syntaxhighlight lang=apl> | ||
⍴ ,[2 3] 5 4 3 2⍴0 | ⍴ ,[2 3] 5 4 3 2⍴0 | ||
5 12 2 | 5 12 2 | ||
⍴ ,[2.5] 5 4 3 2⍴0 | ⍴ ,[2.5] 5 4 3 2⍴0 | ||
5 4 1 3 2 | 5 4 1 3 2 | ||
</ | </syntaxhighlight> | ||
{{Works in|[[Dyalog APL]]}} | {{Works in|[[Dyalog APL]]}} | ||
== Description == | == Description == | ||
The ravel of an array < | The ravel of an array <syntaxhighlight lang=apl inline>A</syntaxhighlight> has shape <syntaxhighlight lang=apl inline>,×/⍴A</syntaxhighlight> and shares elements with <syntaxhighlight lang=apl inline>A</syntaxhighlight>. Thus Ravel may be modelled as a [[Reshape|reshaping]] function <syntaxhighlight lang=apl inline>{(×/⍴⍵)⍴⍵}</syntaxhighlight>. The [[element]] with [[index]] [[vector]] <syntaxhighlight lang=apl inline>I</syntaxhighlight> is moved to index <syntaxhighlight lang=apl inline>(⍴A)⊥I</syntaxhighlight> in [[index origin]] 0, or <syntaxhighlight lang=apl inline>⎕IO+(⍴A)⊥I-⎕IO</syntaxhighlight> in arbitrary index origin. | ||
As with any reshaping, the result of Ravel has the same [[prototype]] as the argument. | As with any reshaping, the result of Ravel has the same [[prototype]] as the argument. | ||