Vocabulary/idot
>> << Down to: Dyad Back to: Vocabulary Thru to: Dictionary
i. y Integers
Rank 1 -- operates on lists of y, producing a result of variable shape for each one -- WHY IS THIS IMPORTANT?
Returns an ascending (or descending) sequence of integers, wrapped to the shape specified by (|y).
i. 6 0 1 2 3 4 5 i. 2 3 0 1 2 3 4 5 i. 6 1 0 1 2 3 4 5
If an atom of y is negated, this specifies reversal along that dimension.
i. _6 5 4 3 2 1 0 i. 2 _3 2 1 0 5 4 3 i. _2 3 3 4 5 0 1 2 i. _2 _3 5 4 3 2 1 0
If y is all-positive, then y is the shape of the table (i.y).
That is, if shape is any given positive integer list, then (i.shape) is the same as: shape $ i. (*/shape)
shape=: 2 3 i.shape 0 1 2 3 4 5 shape $ i. (*/shape) 0 1 2 3 4 5
Common uses
0. A video has been made showing common uses of the Integers monadic verb
1. Make a sample numeric matrix for miscellaneous test purposes
] z=: i. 3 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 +/ z 15 18 21 24 27 +/"1 z 10 35 60
2. Generate the identity permutation
e.g. see the samples in Anagram Index (A.)
N=: 4 ] i=: i.N NB. the identity permutation on N points 0 1 2 3
3. Make a "self-indexing" numeric matrix for investigating the behavior of a given J primitive, e.g. Transpose (|:).
"self-indexing" here means that each atom represents its own array index
ii=: ] {. [: i. 10 #~ # NB. utility verb for generating a test matrix
] z=: ii 2 3 4
0 1 2 3
10 11 12 13
20 21 22 23
100 101 102 103
110 111 112 113
120 121 122 123
Use These Combinations
Combinations using i. y that have exceptionally good performance are shown in Miscellaneous Functions.
x i. y Index Of
Rank Infinity -- operates on x and y as a whole, by items of x -- WHY IS THIS IMPORTANT?
Finds the first occurrence of y in x
'abracadabra' i. 'a' 0 'abracadabra' i. 'acd' NB. several search terms at once 0 4 6 7 < 2^i.5 0 0 0 1 1 NB. 1, 2 and 4 are smaller than 7 (7 < 2^i.5) i. 1 3 NB. inequality satisfied starting with list element no 3 7 (< i. 1:) 2^i.5 3
If list x doesn't contain y, then (i.) returns (#x)
If you subsequently use this value to index x then J signals index error
'abcdef' i. 'k'
6
6 { 'abcdef'
|index error
Use (i.) with a table x (i.e. a list of lists) to find the first row of x that matches y
This is a special case of internal rank
] x=: > 'alpha' ; 'bravo' ; 'charlie' alpha bravo charlie x i. 'charlie' 2
y must match the entire row of x (including any trailing fill letters) for (i.) to find it. Otherwise (i.) returns (#x) (signifying "not found"), concealing your error.
So be sure to get the search term y right!
#x 3 x i. 'bravo' NB. i.e. not found 3 $x NB. shape of table (width is seven chars) 3 7 x i. 'bravo ' NB. y needs to be the full width of x (including the two trailing blanks) 1
Related Primitives
Index Of Last (x i: y)
More Information
1. x i. y is a member of the i.-family.
2. The internal rank of x i. y uses items whose rank is the rank of items of x.
3. If rix is the rank of an item of x, the shape of the result is (-rix)}.$y
4. If x and y are of different classes, or if their items couldn't possibly match because of differing shapes, no error is signaled: each search simply fails to match.
5. To find all occurrences of y in x, not just the first, use Equal (=) or Match (-:) , together with Indices (I.) to convert the resulting Boolean list into indices.
'abracadabra' = 'a' 1 0 0 1 0 1 0 1 0 0 1 I. 'abracadabra' = 'a' 0 3 5 7 10 'abracadabra' I.@:= 'a' 0 3 5 7 10
6. The variant x i.!.0 y has better performance on numeric arrays. See discussion here
7. The variant x i.!.1 y has better performance when the cells of x and y are known to be lists of integers sorted in nondescending order. The results are unpredictable if the arguments are not sorted.
Use These Combinations
Combinations using x i. y that have exceptionally good performance include:
What It Does Type;
Precisions;
RanksSyntax Primitives permitted in place of f Variants;
Restrictions
Benefits;
Bug Warnings
Find first place where x f y is true Permitted: Boolean, integer, floating point, byte, symbol (not unicode).
x and y need not be the same precision.x (f i. 1:) y x i.&1@:f y = ~: < <: > >: e. E. Permitted: (f!.0) (parentheses obligatory!) to force exact comparison.
J recognizes FLO only if f returns an atom or list.Avoids computing entire x f y
Bug warning: if f is e. it does (,@e.) rather than e. regardless of ranks of argumentsFind first place where x f y is false x (f i. 0:) y x i.&0@:f y = ~: < <: > >: e.
What it does Type;
Precisions;
RanksSyntax Variants;
Restrictions
Benefits;
Bug Warnings
Find first/last match m&i. y i: in place of i. for last match
!.0 for exact comparison
Find index of first/last cell of y that does/does not match an m-item (e. i. 1:)&m y i: in place of i. for last cell
0: for mismatch
Bug warning: it does (,@e.) rather than e. Translate characters from q to p byte (p {~ q i. ]) y also ((q i.]) { p"_) y and (q&i. { p"_) y Find index of first/last occurrence of largest/smallest value integer or floating-point list (i. <./) y
(i. >./) y
or i: it actually does (i. >.!.0/) etc.; is faster than 0 ({ /:~) 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
16 ≤ m ≤ 31 i. on sorted lists integer cells of rank 1 x i.!.1 y supports IRS with i.!.1"n Faster; results unpredictable if atoms of argument-cells are not in nondescending order