Tally: Difference between revisions

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* [http://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Tally.htm Dyalog]
* [http://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Tally.htm Dyalog]
* [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}}
{{APL built-ins}}

Revision as of 10:11, 19 November 2019

≢

Tally (≢) 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 J using the symbol #, and adopted in APL by Dyalog APL 14.0. It was later added to NARS2000 and GNU APL and has been included in many recents APLs based on Dyalog, such as ngn/apl, dzaima/APL, and APL\iv.

External links

Lessons

Documentation

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
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
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
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
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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