Vocabulary/slashco
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/: y Grade Up Verb
\: y Grade Down Verb
Rank Infinity -- operates on x and y as a whole, by items of y -- WHY IS THIS IMPORTANT?
The permutation that sorts the items of y into ascending (/:) or descending (\:) order (numerical or lexicographical)
The atom at position i of (/: y) is the index in y of the ith-largest value of y.
] Wk=: ;:'Su Mo Tu We Th Fr Sa'
+--+--+--+--+--+--+--+
|Su|Mo|Tu|We|Th|Fr|Sa|
+--+--+--+--+--+--+--+
] p=: /: Wk
5 1 6 0 4 2 3
p { Wk
+--+--+--+--+--+--+--+
|Fr|Mo|Sa|Su|Th|Tu|We|
+--+--+--+--+--+--+--+
] Wko=: > Wk
Su
Mo
Tu
We
Th
Fr
Sa
p { Wko NB. also works with unboxed list
Fr
Mo
Sa
Su
Th
Tu
We
Common uses
Invert the permutation q
Note that p{q is the permutation product of permutations p and q
] q=: 10?10
8 7 6 9 5 2 0 4 1 3
] p=: /:q
6 8 5 9 7 4 2 1 0 3
p{q
0 1 2 3 4 5 6 7 8 9
Details
1. The permutations (/: y) and (\: y) produce a stable sort (identical keys stay in order).
2. Grading uses intolerant comparison.
3. Any array can be ordered. The first atom in a row is the most significant for ordering purposes; any item of rank higher than 1 is flattened into a list before ordering.
- Characters are ordered according to the Unicode collating sequence. (For bytes, this is the same as the ordering given by a.).
- Symbols are ordered according to the order of the character lists they represent (if one string is a prefix of the other, the shorter string comes first)
- Complex values are ordered on real part first, then imaginary part.
Boxes are ordered according to their contents.
The order of priority for ordering-up is:
- Type: numeric or empty, symbol, character (byte or unicode), and boxed, are so ordered
- Rank: lower comes before higher
- Values: compared after padding with fills to the same shape
Use These Combinations
Combinations using /: y that have exceptionally good performance include:
What it does Type;
Precisions;
RanksSyntax Variants;
Restrictions
Benefits;
Bug Warnings
Find ordinal numbers of y (the relative rank of each item of y in the sort order /:@/: y note \: is not special better than /:^:2 y Find the index of the xth-largest value of y x is a Boolean or integer atom, y is an integer or floating-point list x ({ /:) y not \: Partitions y using a randomly-selected pivot, so time and space results are variable, even for unchanging arguments
x /: y y /: y Sort Up (Using) Verb
x \: y y \: y Sort Down (Using) Verb
Rank Infinity -- operates on x and y as a whole, by items -- WHY IS THIS IMPORTANT?
Sorts x using the order given by y.
i. e. applies to list x the permutation that sorts list y into ascending (/:) or descending (\:) order (whether numerical or lexicographical). Formally, (x /: y is ((/: y) { x).
If x and y are the same, the noun is sorted into order
Wk=: ;:'Su Mo Tu We Th Fr Sa' NB. As defined above (100+i.7) /: Wk 105 101 106 100 104 102 103
Common uses
1. Sort a list y
sort=: /:~ NB. (/:~ y) is the same as: (y /: y) sort Wk +--+--+--+--+--+--+--+ |Fr|Mo|Sa|Su|Th|Tu|We| +--+--+--+--+--+--+--+
Note: Verb sort_z_ is defined in stdlib.ijs as
sort=: /:~ :/:
sort is a
- Standard Library word(s) residing in the 'z'-locale
- Defined in the factory script stdlib.ijs which is located in ~system/main/stdlib.ijs
- View the definition(s) in a JQt session by entering: open '~system/main/stdlib.ijs'
This uses Monad-Dyad (:) to define two separate verbs (/:~) and (/:) for monadic and dyadic usage of the verb: sort.
2. Find the ordinal number of each item of y, that is, the position each item would have if the array were sorted.
/:@/: 3 1 4 1 5 9 2 0 3 1 4 5
Details
1. If x is an atom, x /: y is a one-atom list.
2. Sorting uses intolerant comparison.
3. y may have fewer items than x. The result is ((/: y) { x).
Use These Combinations
Combinations using x /: y that have exceptionally good performance include:
What it does Type;
Precisions;
RanksSyntax Variants;
Restrictions
Benefits;
Bug Warnings
Find xth-largest value of y x is a Boolean or integer atom, y is an integer or floating-point list x ({ /:~) y not \: Partitions y using a randomly-selected pivot, so time and space results are variable, even for unchanging arguments