I can think of three ways to go about this
Simple loop
Just loop over all the 2D indices you have, and use colons to access the remaining dimensions:
for jj = 1:size(twoDinds,1)
M(twoDinds(jj,1),twoDinds(jj,2),:,:) = rand;
end
Vectorized calculation of Linear indices
Skip sub2ind
and vectorize the computation of linear indices:
% generalized for arbitrary dimensions of M
sz = size(M);
nd = ndims(M);
arg = arrayfun(@(x)1:x, sz(3:nd), 'UniformOutput', false);
[argout{1:nd-2}] = ndgrid(arg{:});
argout = cellfun(...
@(x) repmat(x(:), size(twoDinds,1),1), ...
argout, 'Uniformoutput', false);
twoDinds = kron(twoDinds, ones(prod(sz(3:nd)),1));
% the linear indices
inds = twoDinds(:,1) + ([twoDinds(:,2) [argout{:}]]-1) * cumprod(sz(1:3)).';
Sub2ind
Just use the ready-made tool that ships with Matlab:
inds = sub2ind(size(M), twoDinds(:,1), twoDinds(:,2), argout{:});
Speed
So which one's the fastest? Let's find out:
clc
M = nan(4,4,2,2);
sz = size(M);
nd = ndims(M);
twoDinds = [...
1 2
4 3
3 4
4 4
2 1];
tic
for ii = 1:1e3
for jj = 1:size(twoDinds,1)
M(twoDinds(jj,1),twoDinds(jj,2),:,:) = rand;
end
end
toc
tic
twoDinds_prev = twoDinds;
for ii = 1:1e3
twoDinds = twoDinds_prev;
arg = arrayfun(@(x)1:x, sz(3:nd), 'UniformOutput', false);
[argout{1:nd-2}] = ndgrid(arg{:});
argout = cellfun(...
@(x) repmat(x(:), size(twoDinds,1),1), ...
argout, 'Uniformoutput', false);
twoDinds = kron(twoDinds, ones(prod(sz(3:nd)),1));
inds = twoDinds(:,1) + ([twoDinds(:,2) [argout{:}]]-1) * cumprod(sz(1:3)).';
M(inds) = rand;
end
toc
tic
for ii = 1:1e3
twoDinds = twoDinds_prev;
arg = arrayfun(@(x)1:x, sz(3:nd), 'UniformOutput', false);
[argout{1:nd-2}] = ndgrid(arg{:});
argout = cellfun(...
@(x) repmat(x(:), size(twoDinds,1),1), ...
argout, 'Uniformoutput', false);
twoDinds = kron(twoDinds, ones(prod(sz(3:nd)),1));
inds = sub2ind(size(M), twoDinds(:,1), twoDinds(:,2), argout{:});
M(inds) = rand;
end
toc
Results:
Elapsed time is 0.004778 seconds. % loop
Elapsed time is 0.807236 seconds. % vectorized linear inds
Elapsed time is 0.839970 seconds. % linear inds with sub2ind
Conclusion: use the loop.
Granted, the tests above are largely influenced by JIT's failure to compile the two last loops, and the non-specificity to 4D arrays (the last two method also work on ND arrays). Making a specialized version for 4D will undoubtedly be much faster.
Nevertheless, the indexing with simple loop is, well, simplest to do, easiest on the eyes and very fast too, thanks to JIT.