Interesting. Don't have access to a J interpreter right now, but could we
express this along the lines of
At=: ((,'@') <@; <)@,"0
conv2 =: +//. At ($:"_1 _`(*/))@.(1...@$@[)
Even if it's this simple, I'm surprised we require the recursion, given J's
native array capabilities.
-Dan
Please excuse typos; composed on a handheld device.
-----Original Message-----
From: "R.E. Boss" <[email protected]>
Date: Wed, 3 Mar 2010 16:05:24
To: 'Programming forum'<[email protected]>
Subject: Re: [Jprogramming] convolution
> Van: [email protected] [mailto:programming-
> [email protected]] Namens Aai
(...)
>
> Not a general solution, but the 3 convolutions can be computed as follows.
>
> pp=: +//.@(*/) NB. 1D
>
> ppp=: +//.@(pp"1/) NB. 2D
>
> pppp=: +//.@(ppp"2/) NB. 3D
>
>
> 1D
> h (conv-:pp) f
> 1
>
> 2D
> h (conv-:ppp) f
> 1
>
> 3D
> h (conv-:pppp) h
> 1
Nice solution.
conv1=: 4 : 0
if. 1 = #$x do. x +//.@(*/) y return. end.
t=.<:#$x
x +//.@ (conv1 "t/) y
)
g1-:h1 conv1 f1
1
g2-:h2 conv1 f2
1
g3-:h3 conv1 f3
1
see below for hi, fi, gi
R.E. Boss
h1=: _8 2 _9 _2 9 _8 _2
f1=: 6 _9 _7 _5
g1=: _48 84 _16 95 125 _70 7 29 54 10
h2=:".;._2]0 :0
_8 1 _7 _2 _9 4
4 5 _5 2 7 _1
_6 _3 _3 _6 9 5
)
f2=:".;._2]0 :0
_5 2 _2 _6 _7
9 7 _6 5 _7
1 _1 9 2 _7
5 9 _9 2 _5
_8 5 _2 8 5
)
g2=:".;._2]0 :0
40 _21 53 42 105 1 87 60 39 _28
_92 _64 19 _167 _71 _47 128 _109 40 _21
58 85 _93 37 101 _14 5 37 _76 _56
_90 _135 60 _125 68 53 223 4 _36 _48
78 16 7 _199 156 _162 29 28 _103 _10
_62 _89 69 _61 66 193 _61 71 _8 _30
48 _6 21 _9 _150 _22 _56 32 85 25
)
h3=:_3[\".;._2]0 :0
_6 _8 _5 9
_7 9 _6 _8
2 _7 9 8
7 4 4 _6
9 9 4 _4
_3 7 _2 _3
)
f3=: _2[\".;._2]0 :0
_9 5 _8
3 5 1
_1 _7 2
_5 _6 6
8 5 8
_2 _6 _4
)
g3=: _4[\".;._2]0 :0
54 42 53 _42 85 _72
45 _170 94 _36 48 73
_39 65 _112 _16 _78 _72
6 _11 _6 62 49 8
_57 49 _23 52 _135 66
_23 127 _58 _5 _118 64
87 _16 121 23 _41 _12
_19 29 35 _148 _11 45
_55 _147 _146 _31 55 60
_88 _45 _28 46 _26 _144
_12 _107 _34 150 249 66
11 _15 _34 27 _78 _50
56 67 108 4 2 _48
58 67 89 32 32 _8
_42 _31 _103 _30 _23 _8
6 4 _26 _10 26 12
)
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