Sort

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Sort Up and Sort Down are monadic functions that order the major cells of an array in ascending or descending order. Traditionally these functions are performed using Grade in APL: for example the FinnAPL idiom library gives X[⍋X] and X[⍒X] to sort X ascending and descending, respectively. In several dialects or other array languages they are defined as primitives, but with widely varying glyphs: ∧∨ Extended Dyalog APL, Kap, and BQN, <> in dzaima/APL, and ≤≥ in Dyalog APL Vision, as well as ^ for ascending sort in K9 and Goal.

In Dyalog APL there are several recognized idioms for sorting: for ascending sorting, {⍵[⍋⍵]} and {⍵[⍋⍵;]} to sort rank 1 and 2 arrays specifically, and {(⊂⍋⍵)⌷⍵} to sort any rank (all idioms have the same performance; the rank-specific ones were defined first and are shorter). The same idioms are recognized for descending sorting, replacing ⍋ with ⍒.

Sorting with Grade is easiest using the Select (⊇) or From function, which for example allows the ascending sort function on any rank to be written as the train ⍋⊇⊢ in dzaima/APL. Using Reverse Compose ⍛ as implemented in Kap or Dyalog APL Vision, it can be written ⍋⍛⊇. In J, it's implemented as Sort By (/: for ascending) with Commute, /:~.

A dedicated sorting implementation can be substantially faster than grade and selection both because sorting is generally faster than grade (particularly for long vectors with small-width elements, where an index may take more storage space than an element) and because selection is cache-unfriendly. For small-range data, a moveless variant of counting sort is possible for sorting but not grading.[1] Flags for sorted data, which can be used to optimize various operations on the flagged array, can more easily be set with a dedicated sorting function.[2]

Documentation

References

  1. ↑ Marshall Lochbaum. Implementation of ordering functions. BQN implementation notes.
  2. ↑ Marshall Lochbaum. Sortedness flags in primitive implementation. BQN implementation notes.
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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