Grade
Grade (⍋, ⍒) is a pair of ambivalent primitive functions related to sorting. Instead of sorting the given array directly, Grade returns a permutation vector whose length equals the number of major cells, so that indexing into the argument gives the sorted array. The glyph <syntaxhighlight lang=apl inline>⍋</source> is called Grade Up and gives the ascending sort order, while <syntaxhighlight lang=apl inline>⍒</source> is called Grade Down and gives the descending sort order.
Monadic form
Monadic Grade returns the sorting order of the major cells of the argument. Indexing into the original argument gives the sorted array; indexing into another array gives the result commonly known as Sort By.
<syntaxhighlight lang=apl>
⎕←A←↑'foo' 'bar' 'baz' ⍝ A character matrix
foo bar baz
⍋A ⍝ Grade up its rows
2 3 1
A[⍋A;] ⍝ Move the rows to sorted order (ascending)
bar baz foo
⍒A ⍝ Grade down its rows
1 3 2
A[⍒A;] ⍝ Move the rows to sorted order (descending)
foo baz bar
B←15 10 5
A[⍋B;] ⍝ Sort A by B
baz bar foo </source>
Grade performs stable sorting, so that the indices of the repeated major cells are sorted by the order of appearance. Because of this, Grade Down produces the reverse of Grade Up only if all the major cells are unique.
<syntaxhighlight lang=apl>
S←6 10 10 3 2 15 ⋄ T←S,¨⍳6
⍝ Note that the order of two 10s are preserved in both cases
(⍋S) (T[⍋S])
┌───────────┬────────────────────────────┐ │5 4 1 2 3 6│┌───┬───┬───┬────┬────┬────┐│ │ ││2 5│3 4│6 1│10 2│10 3│15 6││ │ │└───┴───┴───┴────┴────┴────┘│ └───────────┴────────────────────────────┘
(⍒S) (T[⍒S])
┌───────────┬────────────────────────────┐ │6 2 3 1 4 5│┌────┬────┬────┬───┬───┬───┐│ │ ││15 6│10 2│10 3│6 1│3 4│2 5││ │ │└────┴────┴────┴───┴───┴───┘│ └───────────┴────────────────────────────┘ </source>
Dyalog APL supports total array ordering when comparing nested arrays of possibly different shape and type. Grade is the only built-in function which can perform comparisons between arbitrary arrays of previously unknown order (Interval Index requires the left argument to be sorted beforehand).
<syntaxhighlight lang=apl>
⎕←A←(1(⍪2 3)) (1 3) (⊂0 1 2)
┌─────┬───┬───────┐ │┌─┬─┐│1 3│┌─────┐│ ││1│2││ ││0 1 2││ ││ │3││ │└─────┘│ │└─┴─┘│ │ │ └─────┴───┴───────┘
⍋A
3 1 2
</source>
Dyadic form
Dyadic Grade is limited to simple character array arguments. The left argument specifies the collation order to use when sorting the right argument.
If the left argument is a vector, the sorting order is simply the order of appearance in the left argument. In other words, <syntaxhighlight lang=apl inline>X⍋Y</source> equals <syntaxhighlight lang=apl inline>⍋X⍳Y</source>, and same for <syntaxhighlight lang=apl inline>⍒</source>.
<syntaxhighlight lang=apl>
⎕A⍋'ZAM,.BIA' ⍝ Alphabetical order, garbage goes last
2 8 6 7 3 1 4 5
(⌽⎕A)⍋'ZAM,.BIA' ⍝ Reverse alphabetical order, garbage still goes last
1 3 7 6 2 8 4 5 </source>
If the left argument is a higher-rank array, sorting is done in multiple stages. The last axis of X takes highest precedence, then the next-to-last, and so on, giving ties to all characters that appear at the same index over the current axis. A notable application is case-insensitive sorting.
<syntaxhighlight lang=apl>
Data
ABLE aBLE ACRE ABEL aBEL ACES
Coll
ABCDEFGHIJKLMNOPQRSTUVWXYZ abcdefghijklmnopqrstuvwxyz
Coll⍋Data
4 5 1 2 6 3
Data[Coll⍋Data;]
ABEL aBEL ABLE aBLE ACES ACRE </source>
J does not implement dyadic grade, but provides Sort By as the dyadic counterparts of <syntaxhighlight lang=j inline>/:</source> and <syntaxhighlight lang=j inline>\:</source> instead.
External links
Documentation
- Dyalog Grade Up Monadic, Grade Down Monadic, Grade Up Dyadic, Grade Down Dyadic
- APLX Grade Up, Grade Down
- J Dictionary Grade Up, Grade Down, NuVoc Grade
- BQN
Other
- APL Cultivation lesson
- Dyadic Grade by Roger Hui, Dyalog Blog
- abrudz/Sort library: Examples of sorting variations (Classic, Natural, Danish, Finnish, German) using dyadic grade