hits ← patn {w←'*'} ##.match array ⍝ find with wildcards.
A generalisation of ⍷, which takes account of "wildcard" items in its left argu-
ment pattern vector. The result is a boolean array, the same shape as the right
argument, showing where each occurrence of [patn] is found.
By default, the wildcard is character '*' but an alternative scalar may be sup-
plied as a second item of a left argument pair. See example below.
In common with primitive function find (⍷), overlapping strings are matched.
NB: From Dyalog v13.0, this functionality is provided by system operator ⎕S.
Technical notes:
Notice in the following that the subject array ⍵ may be of higher rank.
The first two lines:
p x←{⍵'*'}⍣(1=≡,⍺),⍺ ⍝ pattern and wildcard.
v←1↓¨{(x≡¨⍵)⊂⍵}x,p ⍝ wildcard-separated segments.
establish the pattern and wildcard items before splitting the pattern into wild-
card-separated vectors. For example:
'red*green*blue' match 'credit green bored blues' ⍝ tracing ...
...
v
┌───┬─────┬────┐
│red│green│blue│
└───┴─────┴────┘
The third line:
h←↑v⍷¨⊂⍵ ⍝ hits, one row (leading subarray) per segment.
produces a simple boolean "hits array" of rank one more than the subject array ⍵
where subarrays along the leading axis are hits per pattern segment.
⍵⍪h
c r e d i t g r e e n b o r e d b l u e s
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ← hits for 'red'
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ← .. .. 'green'
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 ← .. .. 'blue'
Using reduction along the vector of trailing axes, the hits arrays are refined
right-to-left so that at each step of the reduction, the right argument repres-
ents hits of trailing pattern segments. For example,
c r e d i t g r e e n b o r e d b l u e s
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 ← mask for 'blue'
c r e d i t g r e e n b o r e d b l u e s
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ← hits for green*blue
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0
c r e d i t g r e e n b o r e d b l u e s
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ← hits for green*blue
· · · · · · · · · · · · · · · · · · · · · · · ·
c r e d i t g r e e n b o r e d b l u e s
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 ← second occurrence ignored
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ← mask for green*blue
· · · · · · · · · · · · · · · · · · · · · · · ·
c r e d i t g r e e n b o r e d b l u e s
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ← hits for red*green*blue
1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
· · · · · · · · · · · · · · · · · · · · · · · ·
A slight complication arises with overlapping patterns:
'ban*and' match 'abandon' ⍝ tracing ...
...
v ⍝ pattern segments.
┌───┬───┐
│ban│and│
└───┴───┘
...
⍵⍪h ⍝ pattern segment hits.
a b a n d o n
0 1 0 0 0 0 0
0 0 1 0 0 0 0
In this case, the string 'ban*and' does not occur within 'abandon'. The upper
row of the hits matrix should really be shifted, so that the start of the second
hit coincides with the end of the first:
a b a n d o n
0 0 0 0 1 0 0 ← shifted hit after 'ban'
0 0 1 0 0 0 0 ← 'and' does not follow 'ban'
We could do this inside the reduction by shifting the left argument right; ap-
plying the mask; and then shifting the result back again for the next step. How-
ever, a more efficient way is to shift the right argument left, which doesn't
require a second shift back again.
a b a n d o n
0 1 0 0 0 0 0 ← hit for 'ban'
0 0 0 0 0 0 0 ← hit for 'and' shifted off left-hand side.
We can't just use Dyalog's primitive rotatation function ⌽ for the shifting as
1s rotated off the left hand side would reappear on the right. To avoid this, we
append a sufficient number of columns of zeros to the right of the array; rotate
and then drop the same number of colums from the right. This means that any 1s
shifted beyond the left edge of the array are lost, as required:
sl←{ ⍝ array shifted left.
a←¯1↓⍴⍵ ⍝ leading axes.
x←⌈/⍺ ⍝ maximum shift.
p←⍵,(a,x)⍴0 ⍝ 0-padded on right.
s←⍉a⍴⍺ ⍝ subarray of vector rotations.
(-(0×a),x)↓s⌽p ⍝ shifted array.
} ⍝ :: a ← r ∇ a
Note that this shifting and the following propogation of 1s to the left, to form
the mask, may be done outside the reduction.
m←⌽∨\⌽r sl h ⍝ shifted mask 1 .. 1 0 .. 0
Then hit/mask pairs form the items of the vector to be reduced:
}/↓⍉↑vec¨h m ⍝ hits and masks.
Examples:
botter ← 3 13⍴'betty botter bought a bit better butter'
betty botter
bought a bit
better butter
'b*t' match botter
1 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 0 0 0 1 0 0 0 0 0
(2 ¯1 1 8)¯1 match 2 7 1 8 2 8 1 8 2 8 ⍝ ¯1 is wildcard
1 0 0 0 1 0 0 0 0 0
'12*56*9'match ⎕D ⍝ multiple wildcards
0 1 0 0 0 0 0 0 0 0
(2⍴¨¨ '12*56*9' '*') match 2⍴¨⎕D ⍝ nested arguments.
0 1 0 0 0 0 0 0 0 0
display A ← 2 2 20⍴'<<aa>> <<bbb>>' ⍝ Higher rank argument ...
┌┌→───────────────────┐
↓↓<<aa>> <<bbb>><<aa>>│
││ <<bbb>><<aa>> <<bbb│
││ │
││>><<aa>> <<bbb>><<aa│
││>> <<bbb>><<aa>> <<b│
└└────────────────────┘
display '<<*>>'match A ⍝ ... higher rank result.
┌┌→──────────────────────────────────────┐
↓↓1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0│
││0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0│
││ │
││0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0│
││0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0│
└└~──────────────────────────────────────┘
'a*b*d'match'aaaabbbccd' ⍝ overlapping patterns
1 1 1 1 0 0 0 0 0 0
See also: find
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