Vocabulary/ampdot
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[x] u&.v y Under (Dual) Conjunction
Rank -- depends on the rank of v -- WHY IS THIS IMPORTANT?
Executes v on the argument(s) cell-by-cell.
- For each cell, u is applied to the result(s) of v
- Then v^:_1 (i.e. the obverse of v) is applied to the result of u — giving the result for that cell.
Finally the results for all cells are collected into the end result.
In mathematical terms:
- Verb v defines a transformation of the argument(s) (x and) y into the v-domain
- Next, verb u operates on the transformed argument(s)
- Lastly the result is transformed back from the v-domain to the original domain.
We say that u is applied under v .
Example: Apply (i.) to the contents of each box separately, and re-box each result separately
] y =: 1;2;2 3 +-+-+---+ |1|2|2 3| +-+-+---+ u =: i. v =: > u&.v y +-+---+-----+ |0|0 1|0 1 2| | | |3 4 5| +-+---+-----+
Common uses
1. The most common use of &. is [x] u&.> y which applies the verb u inside each box of the arguments. This follows the rules above: u&.> has rank 0 regardless of u, so each box is opened separately, operated on, and then reboxed.
Examples:
Convert a list of boxed strings to uppercase
] z =: ;:'alpha bravo charlie' +-----+-----+-------+ |alpha|bravo|charlie| +-----+-----+-------+ toupper&.> z +-----+-----+-------+ |ALPHA|BRAVO|CHARLIE| +-----+-----+-------+
Add the contents of corresponding boxes
]l =. 1;2 3;4 5 6 +-+---+-----+ |1|2 3|4 5 6| +-+---+-----+ ]r =. 3 1 4;1 5;9 +-----+---+-+ |3 1 4|1 5|9| +-----+---+-+ l +&.> r +-----+---+--------+ |4 2 5|3 8|13 14 15| +-----+---+--------+
The standard library defines the name each as &.>
(<'Mr. ') , each 'Smith';'Jones' +---------+---------+ |Mr. Smith|Mr. Jones| +---------+---------+
each is a
- Standard Library word(s) residing in the 'z'-locale.
- Defined in the factory script stdlib.ijs.
- View definition(s) by entering in the J session: open'stdlib'
2. A useful trick is to use each when one or more arguments are not boxed. Since > y leaves y unchanged if it is not boxed, an unboxed argument will be processed as individual unboxed atoms:
i.&.> 3 4 NB. i. on each atom, boxing results separately +-----+-------+ |0 1 2|0 1 2 3| +-----+-------+ 3 3 4 {. each 'Washington';'Sheffield';'Hereford' +---+---+----+ |Was|She|Here| +---+---+----+ 100 + each 3;1 4;1 5 9 NB. Add 100 inside each box +---+-------+-----------+ |103|101 104|101 105 109| +---+-------+-----------+
Related Primitives
Under (&.:)
More Information
1. Under (Dual) (&.) differs from Under (&.:) in that u&.v applies u under v cell-by-cell, whereas u&.:v applies u under v to the entire argument(s) (x and) y .
2. Let mv be the monadic rank of v. Then:
- u&.v y is the same as (u&.:v)"mv y
- x u&.v y is the same as (u&.:v)"mv y
Use These Combinations
Combinations using &. y that have exceptionally good performance include:
What it does Type;
Precisions;
RanksSyntax Variants;
Restrictions
Benefits;
Bug Warnings
Join contents of boxed items along first axis ,&.>/ y Bug warning: Atomic replication is inaccurate. OK if contents of same rank. Better to use <@; y Join contents of boxed items along last axis ,.&.>/ y Bitwise operations on bytes byte u&.(a.&i.) y (u y) -: u"0 y avoids conversion to integer (m b.)/&.(a.&i.) y
x (m b.)&.(a.&i.) y
m is 16 to 31