Reshape: Difference between revisions

Reshape can be used to produce an array with a given shape and ravel:

       3 4 ⍴ ⍳12

1  2  3  4

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It appears to exhibit a form of [[Scalar extension|scalar]] or singleton extension:

       3 4 ⍴ 12

12 12 12 12

In fact it repeats an argument of any length, singleton or otherwise. This repetition applies with a vector result, or a higher rank.

       12 ⍴ 'abcde'

abcdeabcdeab

Reshape can also decrease the rank or [[bound]] of an array. One notable example is the use of an empty left argument <code>[[Zilde|⍬]]</code> to produce a [[scalar]]. The scalar is the first 0-[[cell]] of the right argument. In [[Nested array model|nested]] languages <code>⍬⍴</code> is like [[First]] except that it does not remove a layer of nesting.

       9 ⍴ ∘.+⍨ 1 2 1

2 3 2 3 4 3 2 3 2

Since Reshape itself is the fundamental way to create a multi-dimensional array in APL, the function as a whole cannot be modelled in terms of more fundamental primitives. However, we may express it in terms of a stricter reshaping function <code>shape</code>, which forms an array from its [[shape]] and [[ravel]] vectors, requiring both to have rank 1 and the number of elements in the ravel to be the product of the shape. <code>shape</code> is identical to Reshape on its domain, but it has a strictly smaller domain than Reshape. The extensions required to implement Reshape are that a scalar left argument must be allowed, and that the right argument must be converted to a vector with the appropriate length, truncating or repeating its elements.

Reshape ← {

     (1/⍺) shape (×/⍺) {(0=≢⍵)∨⍺≤≢⍵:⍺↑⍵ ⋄ ⍺∇,⍨⍵} ,⍵

{{Works in|[[Dyalog APL]],[[ngn/apl]]}}

The above implementation performs truncation and fill element generation using [[Take]], after extending the [[Ravel|ravelled]] right argument by [[Catenate|catenating]] it with itself until it is long enough. An implementation using indices instead of structural manipulation is also possible:

Reshape ← {

     ⎕IO←0

Reshape can be used to produce an [[identity matrix]] by reshaping a vector which is one longer than the desired side length.

       4 4 ⍴ 5↑1

1 0 0 0