Tally: Difference between revisions

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m (→‎History: HOPL IV reference for older Tally alternatives)
m (Text replacement - "</source>" to "</syntaxhighlight>")
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       ≢'string'
       ≢'string'
6
6
</source>
</syntaxhighlight>
It gives the length of the first [[axis]] in a higher-rank array. Tally applied to an array's [[shape]] gives its [[rank]].
It gives the length of the first [[axis]] in a higher-rank array. Tally applied to an array's [[shape]] gives its [[rank]].
<source lang=apl>
<source lang=apl>
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       ≢⍴5 4 3 2⍴1 'b' 3 'd'
       ≢⍴5 4 3 2⍴1 'b' 3 'd'
4
4
</source>
</syntaxhighlight>
The Tally of a [[scalar]] is always 1.
The Tally of a [[scalar]] is always 1.
<source lang=apl>
<source lang=apl>
       ≢3.14
       ≢3.14
1
1
</source>
</syntaxhighlight>


== Description ==
== Description ==
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<source lang=apl>
<source lang=apl>
Tally ← {⊃(⍴⍵),1}
Tally ← {⊃(⍴⍵),1}
</source>
</syntaxhighlight>
An alternative implementation is to count the major cells by turning each into a scalar 1 with the [[Rank operator]], then adding them up:
An alternative implementation is to count the major cells by turning each into a scalar 1 with the [[Rank operator]], then adding them up:
<source lang=apl>
<source lang=apl>
Tally ← +⌿ {1}⍤¯1
Tally ← +⌿ {1}⍤¯1
</source>
</syntaxhighlight>


== History ==
== History ==


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]].
Tally was introduced in [[A]] with the name "count" and symbol <source lang=j inline>#</syntaxhighlight>. 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>></syntaxhighlight><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>≢</syntaxhighlight> 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:<ref>[[Roger Hui]] and [[Morten Kromberg]]. [https://dl.acm.org/doi/abs/10.1145/3386319 ''APL since 1978'']. §2.1 Tally. ACM [[HOPL]] IV. 2020-06.</ref>
Before the addition of Tally (and [[Zilde]]), there were numerous ways to get the length of a vector as a scalar:<ref>[[Roger Hui]] and [[Morten Kromberg]]. [https://dl.acm.org/doi/abs/10.1145/3386319 ''APL since 1978'']. §2.1 Tally. ACM [[HOPL]] IV. 2020-06.</ref>
Line 46: Line 46:
×/⍴v    ⍝ shortest and obscure
×/⍴v    ⍝ shortest and obscure
0⊥⍴v    ⍝ shortest and obscurest
0⊥⍴v    ⍝ shortest and obscurest
</source>
</syntaxhighlight>


== External links ==
== External links ==

Revision as of 10:39, 11 September 2022

≢

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. <source lang=apl> 

     ≢⍳12

12 

     ≢'string'

6 </syntaxhighlight> It gives the length of the first axis in a higher-rank array. Tally applied to an array's shape gives its rank. <source lang=apl> 

     ≢5 4 3 2⍴1 'b' 3 'd'

5 

     ≢⍴5 4 3 2⍴1 'b' 3 'd'

4 </syntaxhighlight> The Tally of a scalar is always 1. <source lang=apl> 

     ≢3.14

1 </syntaxhighlight>

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: <source lang=apl> Tally ← {⊃(⍴⍵),1} </syntaxhighlight> An alternative implementation is to count the major cells by turning each into a scalar 1 with the Rank operator, then adding them up: <source lang=apl> Tally ← +⌿ {1}⍤¯1 </syntaxhighlight>

History

Tally was introduced in A with the name "count" and symbol <source lang=j inline>#</syntaxhighlight>. 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>></syntaxhighlight>[1]. The symbol <source lang=apl inline>≢</syntaxhighlight> 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:[2] <source lang=apl> ⍴⍴v (⍴0)⍴⍴v (⍳0)⍴⍴v (⍴v)[0] ×/⍴v ⍝ shortest and obscure 0⊥⍴v ⍝ shortest and obscurest </syntaxhighlight>

External links

Lessons

Documentation

References

  1. ↑ NARS2000 Wiki. Tally. Old revision: 2010-08-29.
  2. ↑ Roger Hui and Morten Kromberg. APL since 1978. §2.1 Tally. ACM HOPL IV. 2020-06.
APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
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Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
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Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
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Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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