Vocabulary/tildeco

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~: y Nub Sieve

Rank Infinity -- operates on x and y as a whole, by items of y -- WHY IS THIS IMPORTANT?



A Boolean vector with one value per item of y . Which is 1 if the item does not match any previous item.

Therefore, 1s in the result indicate the positions of the unique items of y.

   z=: 'abracadabra'
   ~.z	NB. Nub z - the unique values
abrcd
   ~:z	NB. Nub Sieve z
1 1 1 0 1 0 1 0 0 0 0
   (~:z) # z   NB. another way to get the unique values
abrcd

Common Uses

1. Wherever data is held in 2 parallel lists, Nub Sieve (~:) yields a vector capable of pruning the second list to match the Nub (~.) of the first.

   NAME=: 'Joe' ; 'Bob' ; 'Jim' ; 'Mary' ; 'Jim'
   AGE=: 25 60 32 21 33

   ] z=. ~: NAME	NB. "sieve" to apply to AGE
1 1 1 1 0
   ] NAME=: ~. NAME
+---+---+---+----+
|Joe|Bob|Jim|Mary|
+---+---+---+----+
   ] AGE=: z # AGE
25 60 32 21

Related Primitives

Nub (~. y)


Details

1. ~: y is a member of the i. family. 1. ~: y uses tolerant comparison. Use ~:!.0 y for intolerant comparison. Because of tolerant comparison, the number of 1s in ~: y may depend on the order of the items of y. 1. ~. y is equivalent to (~: y) # y. 1. The result of ~: y is always a list.


x ~: y Not-Equal

Rank 0 0 -- operates on individual atoms of x and y, producing a result of the same shape -- WHY IS THIS IMPORTANT?



The Boolean result of comparing two items, or lists of items, atom by atom.

Use NotMatch (x -.@-: y) to see if two entire nouns are different.

   ]z=: i.5
0 1 2 3 4
   3 ~: z
1 1 1 0 1
   z ~: z
0 0 0 0 0
   z ~: |.z
1 1 0 1 1

Not-Equal (~:) works between boxed items too:

   z=: 'alpha' ; 'bravo' ; 'charlie'
   z ~: |.z
1 0 1
   z ~: <'bravo'
1 0 1

To avoid x~:y giving length error, the Shape Of ($) x and y must follow the rules for Plus (+).


Common Uses

1. To construct criteria for conditional expressions in verb definitions

 if. '.' ~: y do. return. end.
NB. instead of:
 if. -. '.' = y do. return. end.

Related Primitives

Equal (x = y), Larger Than (x > y), Larger Or Equal (x >: y), Less Than (x < y), Less Or Equal (x <: y), Match (x -: y)


More Information

1. See the rules for equality for a discussion of tolerant comparison and nonnumeric arguments.


Performance Note

Comparisons are fastest when the precisions are identical. If an atom is compared against an array, it helps to choose the right precision for the atom.

   0. ~: %: i. 10  NB. float list: faster than 0 ~:
   00 ~: i. 10  NB.  integer list: faster than 0 ~:

Use These Combinations

Combinations using x ~: y that have exceptionally good performance include those shown in Searching and Matching Items: Fast List Operations (FLOs), as well as the following:

What it does Type;

Precisions;
Ranks

Syntax Variants;

Restrictions

Benefits;

Bug Warnings

Boolean reductions on infixes Boolean x +./\ y x positive

*. = ~: in place of +.

much faster than alternatives
Mean on infixes integer and floating-point x (+/%#)\ y x positive

*. = ~: in place of +

much faster than alternatives
Boolean reductions on partitions Boolean x +//. y = <. >. +. * *. ~: in place of + avoids building argument cells
Polynomial Multiplication (Boolean) Boolean x ~://.@(*./) y

x ~://.@(+./) y
x +//.@(*./) y
x +//.@(+./) y

avoids building argument cells
Boolean reductions along diagonals Boolean +.//. y *. = ~: < <: > >: in place of +. avoids building argument cells