# Outer Product: Difference between revisions

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m (remove reference to matrix multiplication, that should be for Inner Product instead) |
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{{Built-in|Outer Product|<nowiki>∘.</nowiki>}}, or '''Table''' is a [[monadic operator]], which will produce a [[dyadic function]] when applied with a [[dyadic function]]. | {{Built-in|Outer Product|<nowiki>∘.</nowiki>}}, or '''Table''' is a [[monadic operator]], which will produce a [[dyadic function]] when applied with a [[dyadic function]]. Outer product applies the [[operand]] function on each [[element]] of the left array with each element of the right array. It can be described as a shortcut for constructing nested [[wikipedia:for loop|for loop]]s. | ||

=== Syntax === | === Syntax === | ||

Outer Product differs from all other [[monadic operator]]s, which are written as a single [[glyph]], with the operand on the left. For [[backwards compatibility|historical reasons]], the outer product operator is a [[bi-glyph]] denoted as <source lang=apl inline>∘.</source>, and its appears on the right. | |||

This syntactical inconsistency is resolved in [[J]] and [[BQN]], where the outer product operator, called Table, and denoted <source lang=j inline>/</source> and <code>⌜</code> respectively, have the usual operator syntax. | |||

=== Examples === | === Examples === | ||

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=== Applications === | === Applications === | ||

Outer product is useful for solving problems that intuitively | Outer product is useful for solving problems that intuitively require a [[wikipedia:Time_complexity#Polynomial_time|polynomial time]] algorithm. This may also indicate that such an algorithm is not the fastest solution. | ||

For example, suppose we want to find duplicated elements in an non-[[nested array]]. Intuitively speaking, the easiest way to solve this problem is to compare each element of the array with all other elements, which is exactly what an outer product does. | For example, suppose we want to find duplicated elements in an non-[[nested array]]. Intuitively speaking, the easiest way to solve this problem is to compare each element of the array with all other elements, which is exactly what an outer product does. | ||

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primes 20 | primes 20 | ||

2 3 5 7 11 13 17 19 | 2 3 5 7 11 13 17 19 | ||

</source> | </source> | ||

Here there are faster solutions such as the [[wikipedia:Sieve of Eratosthenes|Sieve of Eratosthenes]]. | |||

== External links == | == External links == | ||