Vector: Difference between revisions

A vector is an array with [[rank]] 1. Its shape is thus a [[singleton]], and its only element is equal to the array's [[bound]]. Outside of APL, such one-dimensional data might also be called a "list" or "array".

Results of the [[Shape]] and [[Ravel]] functions are always vectors. Because every array is defined by its shape and ravel (<source lang=apl inline>A ≡ (⍴A)⍴,A</code>), the multidimensional APL [[array model]] can be built up from only an understanding of vectors.

A [[simple array]] can also represented using [[nested]] vectors, where each vector represents a [[cell]] and the elements of a vector are the [[major cells]] of that cell. However, nested vectors are not equivalent to arrays because they are more permissive: the elements of a vector need not all have the same length, and may even be a mix of vectors and [[Simple scalar|simple scalars]]. Nonetheless, some APL-derived languages like [[K]] discard the multidimensional array model in favor of nested vectors.

Many APL functions, such as [[Reverse]], are most naturally defined on vectors. They may be extended to general arrays by applying along a specific axis (see [[function axis]]) or, in [[leading axis theory]], by treating an array as a vector of its [[major cells]] (an array can be converted to such a vector using <source lang=apl inline>⊂⍤¯1</code>). For many operations, such as [[scalar function]] [[reductions]] and most [[structural functions]], these extensions are equivalent. Reversing along the first axis of an array by reversing each vector [[subarray]] along that axis is identical to reversing the array's major cells. For more complicated operations like general reductions they are different: a reduction along the first axis (<source lang=apl inline>⌿</code> in most APLs) passes individual array elements to its operand while reducing the major cells (<source lang=apl inline>/</code> in [[J]]) passes entire cells, and performs fewer function calls.