Re: Potential problem in diadic iota (⍳) or in Pick (⊃)

[Christian Robert]

An other proof (I think) without invoking the "fasteach" operator...


      ∇test2;z;t;d;shpz;⎕RL;r
⎕RL←0
d←3
Loop:
z←(d,d) ⍴ (d×d)?(d×d)
shpz←⍴z
t←shpz ⍴ ((∪,z) ⍳ ,z) ⊃ ¨ {⍵×2} ¨⊂ ,z
t←shpz ⍴ t
''
d,("False" "True")[(⎕io+r←z≡t÷2)]
z (t÷2)
→(r≠1)/Fail
d←d+1
→(d<10)/Loop
Fail:
∇
      test2

 3 True
 3 6 2   3 6 2
 4 8 7   4 8 7
 1 9 5   1 9 5

 4 True
  2  7 15 14    2  7 15 14
  5  3 10 13    5  3 10 13
  8 12  6  1    8 12  6  1
 11  4  9 16   11  4  9 16

 5 True
 16 20 23 13 12   16 20 23 13 12
 14 15  8 18  5   14 15  8 18  5
  3  6  2  7  4    3  6  2  7  4
 10 21 24 19 25   10 21 24 19 25
  9 17 11  1 22    9 17 11  1 22

 6 True
  4 28 14 23 16 12    4 28 14 23 16 12
 26 29 17  2 10  9   26 29 17  2 10  9
 15 19 20 18 27 33   15 19 20 18 27 33
  5 30  6  8  1 25    5 30  6  8  1 25
 31 21 36 11 34 22   31 21 36 11 34 22
  7  3 32 24 35 13    7  3 32 24 35 13

 7 True
 45 11 25 24 33 39  4   45 11 25 24 33 39  4
  1 38 17 10  7 46 40    1 38 17 10  7 46 40
 28 19  6 48 22 44 42   28 19  6 48 22 44 42
 30 35 26 18  2 49 14   30 35 26 18  2 49 14
 34 16 12 13 31 27 32   34 16 12 13 31 27 32
 29  5 20  9 47 23 15   29  5 20  9 47 23 15
 36 43  8 41  3 21 37   36 43  8 41  3 21 37

 8 False
 50  4  6 53 47  7 35 13    1  2  3  4  5  6  7  8
 28 45 48 40 38 23 27 22    9 10 11 12 13 14 15 16
 63 12 36 49  3 26 25 51   17 18 19 20 21 22 23 24
 54 57 41 58 18  2  5 37   25 26 27 28 29 30 31 32
  9 11 29 16 17 24 52 30   33 34 35 36 37 38 39 40
 56 34 59 42 61 55  1 14   41 42 43 44 45 46 47 48
 19 60 21 33 20 10 32 31   49 50 51 52 53 54 55 56
 44 43 64  8 15 46 39 62   57 58 59 60 61 62 63 64


Xtian.


On 2020-08-06 20:50, Christian Robert wrote:
> Can someone help me debug this function (fasteach). I'm not the author
> but from what I've read it may be a faster than the "each" Operator especially
> when a few unique numbers in a large array
>
>
>        ∇z←test;⎕RL;t;i;r
> ⎕RL←0
> i←20
> Loop:
> t←? 1000 ⍴ i
> i,r←t ≡ 2÷⍨ {⍵×2} fasteach t
> →(r=0)/Fail
> i←i+1
> →Loop
> Fail:
> ''
> 'Failed with t←? 1000 ⍴', (⍕i)
> ''
> z←t
> ∇
>
>        ∇z←(F fasteach) A;shp;vec;nub;res;idx
> shp←⍴A               ⍝ Shape and ...
> vec←,A               ⍝ ... ravel of arg.
> nub←∪ vec            ⍝ Vector of unique elements.
> res←F¨nub            ⍝ Result for unique elts.
> idx←nub ⍳ vec        ⍝ Indices of arg in nub ...
> z←shp ⍴ idx ⊃¨⊂ res  ⍝ ... distribute result.
> ∇
>
>
>        test
> 20 1
> 21 1
> 22 1
> 23 1
> 24 1
> 25 1
> 26 1
> 27 1
> 28 1
> 29 1
> 30 1
> 31 1
> 32 1
> 33 1
> 34 1
> 35 1
> 36 1
> 37 1
> 38 1
> 39 1
> 40 1
> 41 1
> 42 1
> 43 1
> 44 1
> 45 1
> 46 1
> 47 1
> 48 1
> 49 1
> 50 1
> 51 1
> 52 1
> 53 1
> 54 1
> 55 1
> 56 1
> 57 1
> 58 1
> 59 1
> 60 1
> 61 1
> 62 1
> 63 1
> 64 0
>
> Failed with t←? 1000 ⍴64
>
> 31 12 9 10 50 26 19 11 47 34 58 45 46 9 64 54 4 4 38 25 12 54 29 24 45 44 32 13 
> 57 54 48 40 27 43 50 51 37 11 14 15 3 32 5 31 55 64 36 11 6 5 13 21 5 47 37 39 
> 58 30 39 46 51 46 12 58 43 28 52 59 2
>        4 56 10 18 11 48 60 36 49 10 14 54 56 63 9 18 52 37 4 5 33 63 61 1 31 19 
> 9 28 12 17 56 59 35 46 57 60 29 22 52 15 23 44 2 36 27 7 52 22 56 41 63 64 32 
> 33 35 30 15 49 29 45 12 59 52 55 55 16
>        17 3 24 12 63 37 14 20 13 4 24 40 55 30 10 28 13 64 41 21 52 32 23 11 50 
> 8 35 16 19 20 61 38 51 14 39 29 8 11 63 61 47 56 63 9 50 5 13 62 24 58 39 12 39 
> 26 51 57 57 22 6 3 13 52 56 54 10 52
>        18 20 12 49 14 4 13 23 37 27 50 37 60 11 54 49 10 54 47 26 45 50 7 22 54 
> 5 18 30 2 17 64 17 29 11 36 62 37 6 17 57 63 27 44 46 27 43 20 27 14 52 20 39 
> 12 49 29 44 39 26 40 2 61 13 36 39 58 12
>        62 50 19 27 4 6 27 5 63 29 33 59 38 48 54 12 43 41 26 37 20 50 50 43 27 
> 11 59 29 21 56 9 49 44 21 63 31 6 63 55 45 33 53 51 41 51 45 40 44 3 45 56 34 
> 14 62 44 54 13 15 43 12 24 32 11 44 27 14
>        44 27 49 36 57 21 64 45 16 45 61 55 38 8 37 33 27 25 34 19 60 9 27 46 50 
> 42 55 4 19 29 13 21 53 22 64 8 41 56 2 10 17 14 25 27 35 64 18 44 61 17 49 15 
> 40 63 27 29 25 28 19 34 3 43 9 47 25 25
>        25 7 33 61 15 60 55 13 30 64 46 5 23 48 44 45 12 62 36 18 9 48 46 60 59 
> 28 37 42 62 48 35 60 35 28 18 24 62 14 7 12 44 37 62 13 61 51 47 22 19 45 17 42 
> 39 34 11 52 13 11 63 19 34 19 62 7 35
>        44 19 46 54 19 27 50 60 30 17 46 34 13 14 24 53 61 52 44 23 64 7 10 11 
> 52 10 11 26 25 12 40 17 31 25 57 7 31 25 48 55 57 39 45 60 11 12 19 8 53 6 8 22 
> 54 39 52 50 61 2 32 29 60 3 22 19 45 49
>        38 55 46 23 55 28 15 20 49 6 63 13 51 20 27 57 60 61 30 35 54 40 13 7 49 
> 44 62 1 43 59 47 34 36 27 1 6 10 12 38 60 7 6 1 16 46 47 22 15 49 35 41 29 20 
> 30 3 39 50 22 49 46 9 36 20 32 23 12 63
>        25 51 53 34 3 18 52 52 38 23 37 9 59 64 1 37 60 39 11 17 4 42 19 17 40 
> 28 38 45 19 63 9 5 26 37 62 30 43 17 63 38 25 42 55 53 10 5 33 34 48 35 2 55 20 
> 20 60 52 63 59 44 18 2 50 37 22 9 29 12
>        2 55 3 15 28 30 37 16 2 10 46 43 59 60 26 62 8 54 30 15 11 33 53 15 42 
> 44 8 26 55 12 57 3 1 54 20 61 60 17 50 59 30 48 53 49 55 46 31 38 24 34 6 15 35 
> 40 17 14 47 38 25 23 53 15 40 22 2 18 15
>        54 4 56 38 14 64 12 46 60 8 37 62 48 16 22 51 31 43 41 36 50 63 19 22 17 
> 37 38 51 4 32 7 25 44 49 17 42 9 26 57 60 49 24 2 5 29 59 35 42 47 10 61 9 11 
> 59 9 14 24 18 49 25 56 20 29 31 36 25 53
>        42 48 60 9 56 64 31 55 42 27 47 57 6 15 6 33 54 47 11 37 63 63 46 42 1 
> 61 22 8 5 2 62 61 5 5 2 59 62 50 63 45 21 5 28 40 58 2 50 50 4 28 8 26 29 4 21 
> 43 60 24 45 39 23 52 40 56 60 40 19 21 55
>        7 37 5 53 26 9 55 25 13 46 62 13 51 40 17 10 49 25 57 35 55 18 5 45 26 
> 19 38 45 2 17 48 45 19 45 43 64 10 28 17 16 20 54 20 13 56 49 21 62 56 44 35 46 
> 52 24 35 18 63 53 30 45 8 37 63 37 19 16
>        33 64 27 31 7 41 15 7 2 28 44 31 54 43 25 26 43 23 2 15 27 44 23 50 29 
> 19 11 31 49 36 51 17 15 47 57 27 51 11 58 55 28 3 19 59 55 53 16 25 28 25 21 3 
> 28 42 2 52 60 13 11 47 37 39 2 3 60 10 17
>
> I don't know why it fail here.
>
> I suspect an error either in "idx←nub ⍳ vec" or
> in "idx ⊃¨⊂ res"
>
> eg: in diadic iota (⍳) or in Pick (⊃)
>
> will continue to search,
> If someone can confirm it may help...
>
> Xtian.