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.
External links
Lessons
Documentation
References
- ↑ NARS2000 Wiki. Tally. Old revision: 2010-08-29.
| 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
|