test_marg_ndxsd.m

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% Here we give an example of how we can marginalize a table

foo = 1;
ns = 2*ones(1,20);
if foo
  bigdom = [3 4 7 8 10 11];
  smalldom = [];
else
  bigdom = 1:5;
  smalldom = [3 5];
end

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

if ~foo
for c=1:C
  for e=1:E
    smallndx = subv2ind(smallsz, [c e]);
    offset = (c-1)*4 + (e-1)*16;
    s = 0;
    for a=1:A
      for b=1:B
	for d=1:D
	  bigndx = subv2ind(bigsz, [a b c d e]);
	  base = subv2ind([A B C D E], [a b 1 d 1]) % clamp the outer loop to its 1st iteration
	  assert(isequal(offset + base, bigndx))
	  s = s + bigT(bigndx);
	end
      end
    end
    smallT2(smallndx) = s;
  end
end
assert(approxeq(smallT, smallT2))


i = 1;
for c=1:C
  for e=1:E
    offset(i) = (c-1)*4 + (e-1)*16;
    i = i + 1;
  end
end
% This can be done faster by
%
%  c e
% [0 0       [4
%  1 0        16]
%  0 1   * 
%  1 1]
%
% where 4 = A*B, 16 = A*B*C*D
end

[small_ndx, diff_ndx] = mk_ndx(bigdom, smalldom, ns);
% small_ndx = offset, diff_ndx = base-1
S = length(small_ndx);
D = length(diff_ndx);
smallT4 = zeros(S,1);
for i=1:S
  s = 0;
  for j=1:D
    k = diff_ndx(j) + small_ndx(i) + 1;
    s = s + bigT(k);
  end
  smallT4(i) = s;
end
assert(approxeq(smallT, smallT4))


% Use 2D indices
ndx = 1 + repmat(diff_ndx, S, 1) + repmat(small_ndx(:), 1, D); % ndx(i,j) = k above

for i=1:S
  s = 0;
  for j=1:D
    k = ndx(i,j);
    s = s + bigT(k);
  end
  smallT5(i) = s;
end
assert(approxeq(smallT, smallT5))

smallT6 = sum(bigT(ndx), 2);    
assert(approxeq(smallT, smallT6))



tmp.small = small_ndx;
tmp.diff = diff_ndx;
smallT7 = marg_table_ndx(bigT, 0, tmp);
assert(approxeq(smallT, smallT7))