Ravel
Ravel (,
) 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
With axis
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.
See also
External links
Lessons
Documentation
- BQN (as Deshape)
References
- ↑ Falkoff, A.D., and K.E. Iverson. "The APL\360 Terminal System". Research Report RC-1922, IBM, 1967-10-16.
APL features [edit] | |
---|---|
Built-ins | Primitives (functions, operators) ∙ Quad name |
Array model | Shape ∙ Rank ∙ Depth ∙ Bound ∙ Index (Indexing) ∙ Axis ∙ Ravel ∙ Ravel order ∙ Element ∙ Scalar ∙ Vector ∙ Matrix ∙ Simple scalar ∙ Simple array ∙ Nested array ∙ Cell ∙ Major cell ∙ Subarray ∙ Empty array ∙ Prototype |
Data types | Number (Boolean, Complex number) ∙ Character (String) ∙ Box ∙ Namespace ∙ Function array |
Concepts and paradigms | Conformability (Scalar extension, Leading axis agreement) ∙ Scalar function (Pervasion) ∙ Identity element ∙ Complex floor ∙ Array ordering (Total) ∙ Tacit programming (Function composition, Close composition) ∙ Glyph ∙ Leading axis theory ∙ Major cell search ∙ First-class function |
Errors | LIMIT ERROR ∙ RANK ERROR ∙ SYNTAX ERROR ∙ DOMAIN ERROR ∙ LENGTH ERROR ∙ INDEX ERROR ∙ VALUE ERROR ∙ EVOLUTION ERROR |