Ravel: Difference between revisions
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== Description == | == Description == | ||
The ravel of an array <source lang=apl inline>A</ | The ravel of an array <source lang=apl inline>A</source> has shape <source lang=apl inline>,×/⍴A</source> and shares elements with <source lang=apl inline>A</source>. Thus Ravel may be modelled as a [[Reshape|reshaping]] function <source lang=apl inline>{(×/⍴⍵)⍴⍵}</source>. The [[element]] with [[index]] [[vector]] <source lang=apl inline>I</source> is moved to index <source lang=apl inline>(⍴A)⊥I</source> in [[index origin]] 0, or <source lang=apl inline>⎕IO+(⍴A)⊥I-⎕IO</source> 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. |
Revision as of 09:07, 29 October 2019
Template:Primitive is a primitive function introduced in APL\360 which returns the ravel of an array. In the APL array model, an array's ravel is the vector containing all its elements in ravel order. It is equivalent to reshaping an array using its bound for the new shape. Reshaping the ravel using the original array's shape restores that array.
In some APLs an axis may be specified for Ravel in order to combine only some axes of an array, or insert a length-1 axis.
The name "ravel" references the process of undoing woven or knitted fabric, thus removing its structure and rendering it linear.
Examples
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.
⊢x ← 3 4⍴⍳12 ⍝ A matrix 1 2 3 4 5 6 7 8 9 10 11 12 ,x ⍝ Its ravel 1 2 3 4 5 6 7 8 9 10 11 12 ⍴,x ⍝ The shape is the total number of elements 12 (,×/⍴x) ≡ ⍴,x ⍝ Or the product of the original shape 1
Ravelling a scalar yields a singleton vector.
,3 3 3 ≡ ,3 ⍝ Not the same 0 ⍴,3 ⍝ It's now a vector 1
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.
≢⍴ 'a' ⍝ Scalar character 0 ≢⍴ ,'a' ⍝ String 1
Axis specification may accept either a vector of two or more adjacent axis 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.
⍴ ,[2 3] 5 4 3 2⍴0 5 12 2 ⍴ ,[2.5] 5 4 3 2⍴0 5 4 1 3 2
Description
The ravel of an array A
has shape ,×/⍴A
and shares elements with A
. Thus Ravel may be modelled as a reshaping function {(×/⍴⍵)⍴⍵}
. The element with index vector I
is moved to index (⍴A)⊥I
in index origin 0, or ⎕IO+(⍴A)⊥I-⎕IO
in arbitrary index origin.
As with any reshaping, the result of Ravel has the same prototype as the argument.
History
Ravel was present in the first version of APL\360[1] and has been included in every APL since.
External links
Lessons
Documentation
References
- ↑ Falkoff, A.D., and K.E. Iverson. "The APL\360 Terminal System". Research Report RC-1922, IBM, 1967-10-16.
Template:APL programming language