So can you give an example of something that can be expressed simply in APL/J/K ...

smabie · on Aug 15, 2020

Here's Conway's Game of Life by Arthur Whitney (creator of K):

  life:{3=a-x*4=a:2{+(0+':x)+1_x,0}/x}

I'm guessing a numpy implementation would be between one and two orders of magnitude more verbose, even if you're just comparing the number of operations.

worc3131 · on Aug 15, 2020

It doesn't quite seem fair to compare numpy to one of the most famous K code golf's ever created, but here is my attempt, 140 characters compared to Arthur's 30, so 5 times longer. Not worry about padding the edges would cut it to 100. I don't think the gap is as wide as you think it is.

  def life(M):
    MP = np.pad(M,[(1,1),(1,1)])
    N = sum(np.roll(MP,(i,j),(0,1))
             for i in [1,0,-1]
             for j in [1,0,-1])
    return (3==N-MP*(4==N))[1:-1,1:-1]

Speedtest (presumably memory bound):

  100 x 100 matrix, numpy  0.2ms, K  0.2ms
  200 x 200 matrix, numpy  0.5ms, K  0.8ms
  500 x 500 matrix, numpy  5.2ms, K  8.0ms
  1000x1000 matrix, numpy 20.0ms, K 36.0ms
  5000x5000 matrix, numpy  0.5s , K  1.2s

Interestingly the K code is designed to return a boolean matrix, but operates much more slowly for me on a boolean matrix compared to an integer matrix, with the result that:

  q)\t klife M

Takes 1.2 seconds whilst

  q)\t klife klife M

Takes 24 seconds. So whilst the idea seems to be that klife is used with scan/over to run a number of iterations, it's actually a bad idea to run it more than once.