new algorithm for wilcoxon signed-rank test

[Jason Stover]

I put this on pspp-dev, since now we're talking about a new algorithm.

Very creative, Ben. It's definitely worth a paper if it isn't already
published.

I've read through the code of ranksum6 below, and it passed the few
tests I ran. Walking through the algorithm, it always seems to give
the correct value.

But I would have to think more about the algorithm to convince myself
it will always be correct. Or see a written explanation. ('sorry Ben,
I know how you feel about being able figure out what code is supposed
to do just by reading it.)

-Jason

----- Forwarded message from Ben Pfaff <address@hidden> -----

To: Ben Pfaff <address@hidden>, John Darrington <address@hidden>,
        Michel Boaventura <address@hidden>,
        address@hidden
From: Ben Pfaff <address@hidden>
...
Actually, here's a solution that is even better.  A test program using it
calculates (correctly) and prints *all* the values for 1 <= N <= 30, 1 <= W <=
N*(N+1)/2, in under .2 seconds *total*.

The runtime of this algorithm is O(N*W) and it uses O(W) space.


int ranksum6(int N, int W)
{
  int *array;
  int max;
  int total;

  assert (N >= 0);
  if (N == 0)
    return 0;
  else if (W <= 0)
    return 1 << N;
  else if (W > N * (N + 1) / 2)
    return 0;
  else if (N == 1)
    return 1;

  array = calloc (sizeof *array, W + 1);
  array[W] = 1;

  max = W;
  total = 0;
  for (; N > 1; N--)
    {
      int max_sum = N * (N + 1) / 2;
      int i;

      if (max_sum < max)
        max = max_sum;

      for (i = 1; i <= max; i++)
        if (array[i] != 0)
          {
            int new_W = i - N;
            if (new_W <= 0)
              total += array[i] * (1 << (N - 1));
            else
              array[new_W] += array[i];
          }
    }
  total += array[1];
  free (array);
  return total;
}


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