Tally: Difference between revisions
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{{Built-in|Tally|≢}} is a [[primitive function|primitive]] [[monadic function]] which returns the number of [[major cell]]s in its [[argument]]. The Tally of an array is also the first [[element]] of its [[shape]], or 1 if it is a [[scalar]] (since a scalar is its own major cell by convention). Tally counts the first [[axis]] rather than the last because the number of major cells is more useful in [[leading axis theory]]. | {{Built-in|Tally|≢}} or '''Count''' is a [[primitive function|primitive]] [[monadic function]] which returns the number of [[major cell]]s in its [[argument]]. The Tally of an array is also the first [[element]] of its [[shape]], or 1 if it is a [[scalar]] (since a scalar is its own major cell by convention). Tally counts the first [[axis]] rather than the last because the number of major cells is more useful in [[leading axis theory]]. | ||
== Examples == | == Examples == | ||
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== History == | == History == | ||
Tally was introduced in [[ | Tally was introduced in [[A]] with the name "count" and symbol <source lang=j inline>#</source>. The same notation was carried forward to [[A+]], as well as [[J]] following [[Arthur Whitney]]'s suggestion. The primitive was present in [[NARS2000]] by 2010, with the name "Tally" and symbol <source lang=apl inline>></source><ref>NARS2000 Wiki. [http://wiki.nars2000.org/index.php?title=Tally&oldid=573 Tally]. Old revision: 2010-08-29.</ref>. The symbol <source lang=apl inline>≢</source> for Tally was introduced in [[Dyalog APL 14.0]], and quickly adopted by NARS2000. It was later added to [[GNU APL]] and has been included in many recent APLs based on Dyalog, such as [[ngn/apl]], [[dzaima/APL]], and [[APL\iv]]. | ||
Before the addition of Tally (and [[Zilde]]), there were numerous ways to get the length of a vector as a scalar: | |||
<source lang=apl> | |||
''⍴⍴v | |||
(⍴0)⍴⍴v | |||
(⍳0)⍴⍴v | |||
(⍴v)[0] | |||
×/⍴v ⍝ shortest and obscure | |||
0⊥⍴v ⍝ shortest and obscurest | |||
</source> | |||
== External links == | == External links == | ||
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* [http://wiki.nars2000.org/index.php/Tally NARS2000] | * [http://wiki.nars2000.org/index.php/Tally NARS2000] | ||
* J [http://www.jsoftware.com/help/dictionary/d400.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/number NuVoc] | * J [http://www.jsoftware.com/help/dictionary/d400.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/number NuVoc] | ||
{{APL built-ins}} | |||
== References == | |||
<references /> | |||
{{APL built-ins}}[[Category:Primitive functions]] |
Revision as of 13:43, 30 April 2020
≢
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Tally (≢
) or Count is a primitive monadic function which returns the number of major cells in its argument. The Tally of an array is also the first element of its shape, or 1 if it is a scalar (since a scalar is its own major cell by convention). Tally counts the first axis rather than the last because the number of major cells is more useful in leading axis theory.
Examples
Tally can compute the length of a numeric vector or string.
≢⍳12 12 ≢'string' 6
It gives the length of the first axis in a higher-rank array. Tally applied to an array's shape gives its rank.
≢5 4 3 2⍴1 'b' 3 'd' 5 ≢⍴5 4 3 2⍴1 'b' 3 'd' 4
The Tally of a scalar is always 1.
≢3.14 1
Description
Tally returns the length of the first axis of its argument if it has any axes (that is, if it is not a scalar), and 1 otherwise. This can be modelled easily with Shape and First:
Tally ← {⊃(⍴⍵),1}
An alternative implementation is to count the major cells by turning each into a scalar 1 with the Rank operator, then adding them up:
Tally ← +⌿ {1}⍤¯1
History
Tally was introduced in A with the name "count" and symbol #
. The same notation was carried forward to A+, as well as J following Arthur Whitney's suggestion. The primitive was present in NARS2000 by 2010, with the name "Tally" and symbol >
[1]. The symbol ≢
for Tally was introduced in Dyalog APL 14.0, and quickly adopted by NARS2000. It was later added to GNU APL and has been included in many recent APLs based on Dyalog, such as ngn/apl, dzaima/APL, and APL\iv.
Before the addition of Tally (and Zilde), there were numerous ways to get the length of a vector as a scalar:
''⍴⍴v (⍴0)⍴⍴v (⍳0)⍴⍴v (⍴v)[0] ×/⍴v ⍝ shortest and obscure 0⊥⍴v ⍝ shortest and obscurest