Reduce: Difference between revisions
(Created page with "{{Built-ins|Reduce|/|⌿}}, also called '''Reduction''' or '''Insert''', is a primitive monadic operator which takes a dyadic function operand...") |
No edit summary |
||
| Line 8: | Line 8: | ||
In [[leading axis model]], Reduce only has the first-axis form, and it reduces the [[major cell|major cells]] of the entire array, not the individual elements. It does not enclose the result either. Instead, reduction over an axis other than the first is performed via the [[Rank (operator)|Rank operator]], which [[mix|mixes]] the results into a flat array. | In [[leading axis model]], Reduce only has the first-axis form, and it reduces the [[major cell|major cells]] of the entire array, not the individual elements. It does not enclose the result either. Instead, reduction over an axis other than the first is performed via the [[Rank (operator)|Rank operator]], which [[mix|mixes]] the results into a flat array. | ||
== Examples == | |||
Reduce is mainly used for aggregation, such as sum (using [[Add]]) or product (using [[Times]]). If used with [[Subtract]], it computes the alternating sum, since <math>a-(b-(c-(d-\cdots))) = a-b+c-d+\cdots</math>. Using with [[Divide]] gives similar effect, returning the alternating product. | |||
<source lang=apl> | |||
+/1 2 3 4 5 | |||
15 | |||
×/1 2 3 4 5 | |||
120 | |||
-/1 2 3 4 5 | |||
3 | |||
÷/1 2 3 4 5 | |||
1.875 | |||
</source> | |||
Reduction by [[Minimum]] or [[Maximum]] gives the minimum or maximum over several numbers. Same goes for [[And]], [[Or]], [[GCD]], [[LCM]], and XOR ([[Not Equal]] on [[Booleans]]). | |||
Reduction over an empty axis gives the [[identity element]] of the operand. | |||
<source lang=apl> | |||
+/⍬ | |||
0 | |||
+/2 3 0⍴0 | |||
0 0 0 | |||
0 0 0 | |||
</source> | |||
[[FinnAPL idiom library]] contains over 100 entries which use Reduce in some way. | |||
== External links == | == External links == | ||
Revision as of 05:57, 21 July 2020
/ ⌿
|
Reduce (/, ⌿), also called Reduction or Insert, is a primitive monadic operator which takes a dyadic function operand, inserts it between the elements of the argument, and evaluates it into a single array in right-to-left order. This operation is known as Fold, or more specifically foldr1, in other functional programming languages such as Haskell.
Description
When applied to a vector argument, f/x evaluates to the expression a f b f c f d … where a, b, c, d, … are the elements of x. In general, Reduce reduces one chosen axis (either implied by using the last-axis form f/ or first-axis f⌿, or explicitly by using function axis f/[x]) by evaluating each vector along the chosen axis into a scalar.
In nested array model, Reduce has a strong property that the reduced axis is removed from the shape of the argument, which forces it to enclose each non-simple result in the returned array.
In leading axis model, Reduce only has the first-axis form, and it reduces the major cells of the entire array, not the individual elements. It does not enclose the result either. Instead, reduction over an axis other than the first is performed via the Rank operator, which mixes the results into a flat array.
Examples
Reduce is mainly used for aggregation, such as sum (using Add) or product (using Times). If used with Subtract, it computes the alternating sum, since . Using with Divide gives similar effect, returning the alternating product.
+/1 2 3 4 5
15
×/1 2 3 4 5
120
-/1 2 3 4 5
3
÷/1 2 3 4 5
1.875
Reduction by Minimum or Maximum gives the minimum or maximum over several numbers. Same goes for And, Or, GCD, LCM, and XOR (Not Equal on Booleans).
Reduction over an empty axis gives the identity element of the operand.
+/⍬
0
+/2 3 0⍴0
0 0 0
0 0 0
FinnAPL idiom library contains over 100 entries which use Reduce in some way.
External links
Lessons
Documentation