linkage benchmarking script

## Deterministic benchmark for linkage.m optimization

addpath ("inst");

sizes = [50, 100, 200, 400, 600];
methods = {"single", "complete", "average", "weighted"};
num_runs = 5;

printf ("=== Linkage Benchmark ===\n\n");

results = {};
idx = 1;

for n = sizes
  rand ("seed", 12345);
  X = rand (n, 5);

  for m = 1:length (methods)
    method = methods{m};

    orig_times = zeros (1, num_runs);
    for run = 1:num_runs
      tic;
      Z1 = linkage_original (X, method);
      orig_times(run) = toc;
    endfor
    orig_best = min (orig_times);

    opt_times = zeros (1, num_runs);
    for run = 1:num_runs
      tic;
      Z2 = linkage (X, method);
      opt_times(run) = toc;
    endfor
    opt_best = min (opt_times);

    err = norm (Z1 - Z2);
    if (err > 1e-12)
      printf ("ERROR: n=%d, %s - diff=%.2e\n", n, method, err);
    endif

    speedup = orig_best / opt_best;
    results{idx, 1} = n;
    results{idx, 2} = method;
    results{idx, 3} = orig_best;
    results{idx, 4} = opt_best;
    results{idx, 5} = speedup;
    idx += 1;

    printf ("n=%3d, %s: orig=%.4fs, opt=%.4fs, speedup=%.2fx\n", ...
            n, method, orig_best, opt_best, speedup);
  endfor
endfor

fid = fopen ("linkage_benchmark_results.csv", "w");
fprintf (fid, "n,method,original,optimized,speedup\n");
for i = 1:size (results, 1)
  fprintf (fid, "%d,%s,%.6f,%.6f,%.2f\n", ...
           results{i,1}, results{i,2}, results{i,3}, results{i,4}, results{i,5});
endfor
fclose (fid);

speedups = cell2mat (results(:, 5));
printf ("\n=== Summary ===\n");
printf ("Average speedup: %.2fx\n", mean (speedups));
printf ("Min: %.2fx, Max: %.2fx\n", min (speedups), max (speedups));