Outer Product: Difference between revisions

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Tone ("notably" is usually superfluous and "should be" is usually not neutral); wiki links
m (remove reference to matrix multiplication, that should be for Inner Product instead)
m (Tone ("notably" is usually superfluous and "should be" is usually not neutral); wiki links)
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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]]. 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.
{{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 ===
By right, a [[monadic operator]] should be a single [[glyph]], and the operand should be on the left. However, for [[backwards compatibility|historical reasons]], the outer product operator is not only a [[bi-glyph]] denoted as <source lang=apl inline>∘.</source>, the operand also appears on the right instead.
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.


Notably, 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, abide by the usual operator syntax.
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 requires a [https://en.wikipedia.org/wiki/Time_complexity#Polynomial_time polynomial time] algorithm.  
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.
However, this also indicates that such an algorithm might not be 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>
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].
Here there are faster solutions such as the [[wikipedia:Sieve of Eratosthenes|Sieve of Eratosthenes]].
== External links ==
== External links ==


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