test_mult_ndxsd.m

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% Here we give an example of how we can multiply two tables using two 1D indices

foo = 1;
ns = 2*ones(1,20);
if foo
  bigdom = [3 4 7 8 10];
  smalldom = [4 10];
else
  bigdom = 1:5;
  smalldom = [3 5];
end

% compute using dpot
bigpot = dpot(bigdom, ns(bigdom), rand(ns(bigdom)));
smallpot = dpot(smalldom, ns(smalldom));
newbigpot = divide_by_pot(bigpot, smallpot);
%newbigpot = multiply_by_pot(bigpot, smallpot);
S = struct(bigpot); bigT = S.T;
S = struct(smallpot); smallT = S.T;
S = struct(newbigpot); newbigT = S.T;

% naive implementation
if ~foo
i = 1;
for e=1:ns(5)
  for c=1:ns(4) % c chnages fastest
    smallndx = subv2ind(ns(smalldom), [c e]);
    assert(isequal(smallndx, i))
    offset = (c-1)*4 + (e-1)*16;
    for a=1:ns(1)
      for b=1:ns(2)
	for d=1:ns(4)
	  bigndx = subv2ind(ns(bigdom), [a b c d e]);
	  base = subv2ind(ns(bigdom), [a b 1 d 1]); % clamp the outer loop to its 1st iteration
	  assert(isequal(offset + base, bigndx))
	  newbigT2(bigndx) = bigT(bigndx) * smallT(smallndx);
	end
      end
    end % next a
    i = i + 1;
  end
end
assert(approxeq(newbigT, newbigT2))
end

[small_ndx, diff_ndx] = mk_ndx(bigdom, smalldom, ns);

%%%% Use offset and base to do multiplication

newbigT3 = zeros(ns(bigdom));
S = length(small_ndx);
D = length(diff_ndx);
for i=1:S 
  for j=1:D
    k = small_ndx(i) + diff_ndx(j) + 1;
    newbigT3(k) = bigT(k) * smallT(i);
  end
end
assert(approxeq(newbigT, newbigT3))

% Use 2D indices
ndx = 1 + repmat(diff_ndx, S, 1) + repmat(small_ndx(:), 1, D); % ndx(i,j) = k above
newbigT4(ndx(:)) = bigT(ndx(:)) .* repmat(smallT(:), D, 1);
assert(approxeq(newbigT, newbigT4))

% for i, for j is better for cache locality
% but the repmat method implements for j, for i (both give equivalent results)

tmp.small = small_ndx;
tmp.diff = diff_ndx;
newbigT5 = mult_by_table_ndx(bigT, smallT, tmp);
assert(approxeq(newbigT, newbigT5))