20 TX 16 NB. in a 20x20 plane, 16 iterations ran with error: |assertion failure: TX | b-:a I can't tell why, but maybe if I change some a=.'s to a=:'s I can find where it goes astray.
Linda -----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Roger Stokes tSent: Tuesday, November 13, 2012 10:36 A. To: programm...@jsoftware.com Subject: Re: [Jprogramming] Matrix Transformations based on local submatrices There is a version of Conway's "Life" in J in Rosetta Code, and reproduced below. g It uses Cut ;. but shifting the plane or rotating the torus is more than a hundred times faster. The timings I get for 100 iterations on a random 100x100 matrix are: Rosetta 3.421 seconds shifting 0.030 " rotating 0.028 " Evidence follows, transcript of session: NB. Conway's "Life" NB. ======================================== NB. Rosetta Code method NB. ======================================== pad=: 0,0,~0,.0,.~] life=: (_3 _3 (+/ e. 3+0,4&{)@,;._3 ])@pad NB. =============================================== NB. Lincolnshire Method, by shifting NB. ================================================ sh =: |. !. 0 E =: 0 _1 & sh W =: 0 1 & sh N =: 1 & sh S =: _1 & sh NS =: N + S EW =: E + W NeCo =: NS + (+ NS) @: EW NB. neighbour-count evol =: ((3 = ]) +. ([ *. 2 = ])) NeCo NB. =================================================== NB. Test for correctness by comparing with Rosetta NB. =================================================== rp =: 3 : 0 NB. make y-by-y matrix with r-pentomino at SE corner w =. (y,y) $ 0 w =. 1 (0 1 ; 0 2; 1 0; 1 1; 2 1) } w 4 4 |. w ) TX =: 4 : 0 NB. y iterations of r-pentomino in x-by-x matrix T =. rp x a =. life ^:y T NB. Rosetta method b =. evol ^:y T NB. shifting method assert. b -: a 'OK' ) 20 TX 16 NB. in a 20x20 plane, 16 iterations OK NB. ==================================================== NB. a variation, rotating instead of shifting NB. (life on a torus rather than a bounded plane) NB. ==================================================== adverb =: 1 : ('sh =. u' , LF, 'evol f.') revo =: |. adverb NB. ================================================ NB. timings NB. ================================================ randmat =: 3 : '(y, y) $ ? (y * y) # 2' OBS =: 3 : 0 NB. y-by-y matrix M =: randmat y R =. 0 2 $ a: do =. (10j5 & ":) @: (4 & (6!:2)) R =. R, 'Rosetta 100' ; do 'life ^: 100 M' R =. R, 'evol 100 ' ; do 'evol ^: 100 M' R =. R, 'revo 100 ' ; do 'revo ^: 100 M' R ) OBS 100 +-----------------------+ |Rosetta 100| 3.42198| +------------+----------| |evol 100 | 0.03048| +------------+----------| |revo 100 | 0.02817| +-----------------------+ ----- Original Message ----- From: "Alex Giannakopoulos" <aeg...@blueyonder.co.uk> To: "J Programming forum" <programm...@jsoftware.com> Sent: Tuesday, November 13, 2012 11:43 AM Subject: [Jprogramming] Matrix Transformations based on local submatrices > OK, I'm trying to do some work with matrices that involves transformations > based on local properties of a matrix (neighbouring elements). > This is the sort of thing you may find in image-processing > "edge-detection", etc, or in some cellular automata of the type of > Conway's > "Life". > > In other words, I want to be able to supply a matrix, and have it so > processed that the result is a new matrix where each new element was > determined by a function which processed the old elements neighbours. > > Any direction, relevant help pages, etc, much appreciated. > If anyone would go as far as offering some sample code that would be > great, > too! > As a trivial example, suppose I want to calculate the sum of the > neighbours > of each element > Say we have a matrix m0 =. 3 3 $ >:i.9 > What I want is the verb "neighbours" whereby > neighbours m0 > 11 19 13 > 23 40 27 > 17 31 19 > > Obviously, I am maily interested in how to extract the "neighbours" > submatrix, without resorting to explicit looping, if that is possible. > To make it a bit more interesting, how would I extract the neighbours if > the matrix was a torus or infinite tiling, such that: > neighb-torus m0 > 44 43 42 > 41 40 39 > 38 37 36 > > Thanks for any suggestions! > Alex > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
