From your description what you need to do is:

  A1 = F1(a1, a2, a3, ...., an)
  B1 = F2(b1, b2, b3, ...., bn)
  C1 = F3(c1, c2, c3, ...., cn)
on the face of it, that doesn't appear to be O(n^2). You transpose the original matrix so that (a1, a2, ...) etc. are Perl arrays, presumably for the convenience of F1 etc. -- which seems reasonable, though the work to pull a column into a row seems about the same as processing the column directly (unless elements are accessed more than once by the respective Fn.

I assume the issue here is scale. But I regret this humble engineer is struggling to understand where to look for improvement. (Assuming a multi-core processor I can see that processing columns in parallel makes sense -- especially if the original matrix were in shared memory !) You don't say where the matrix comes from... I wonder if it's possible to transpose it as it's read in ?

So... can you post some code ? Preferrably reduced to show the key logic... and give some idea of the true scale ?

Of course, the general advice is to profile what you have, to identify where the time is really being spent.

In reply to Re: An efficient, scalable matrix transformation algorithm by gone2015
in thread An efficient, scalable matrix transformation algorithm by Luftkissenboot

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