Outer Product: Difference between revisions

{{Built-in|Outer Product|<nowiki>∘.</nowiki>}}, or '''Table''' is a [[monadic operator]], which will produce a [[dyadic function]] when applied with a [[dyadic function]]. In APL, the outer product is a generalisation of the [https://en.wikipedia.org/wiki/Matrix_multiplication matrix product], which allows not only multiplication, but any [[dyadic function]] given. In short, outer product allows you to apply a given function on each element of the left array with each element of the right array. Basically, a shortcut for constructing nested [https://en.wikipedia.org/wiki/For_loop for loop]s.

By right, a [[monadic operator]] should be a monograph (i.e. consist of only one character), and the operand should be on the left. However, due to [[legacy reason]], the outer product operator is not only a [[diagraph]] denoted as <source lang=apl inline>∘.</source>, the operand also appears on the right instead.

Notably, this syntactical inconsistency is resolved in [[BQN]], where the outer product operator <source lang=bqn inline>⌜</source> abides with the usual operator syntax. Also note that it is called table in BQN.

       ⍝ works for multi-dimensional array as well

Outer product is useful for solving problems that intuitively requires a [https://en.wikipedia.org/wiki/Time_complexity#Polynomial_time polynomial time] algorithm.  

However, this also indicates that such algorithm might not be the fastest solution.

2     (∪((2≤(+/∘.=⍨))(/⍨⍨)⊢)) x ⍝ point-free/tacit version

 

Using similar techniques, we can define a function that generate prime numbers by using an outer product of [[Residue]].

</source>

Again, using outer product might not yield the fastest solution. There are faster solutions such as [https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes Sieve of Eratosthenes].