ndgrid on cell array of vectors

hi guys,

i need your help in solving the following question:

Given a cell array of vectors where each index represent a range of elements in dimension i, how can you apply ndgrid of the vectors?

To ease the question, here is an example:

Thanks in advance.

Answer 1

[Guillaume]

What you are asking for is the cartesian product of the sets.

If your cell array only contains two sets (each with arbitrary size):

c1 = {{[1 2],[2 3]}, {[10 11], [11 12]}}
assert(numel(c1) == 2, 'only works with two sets')
[idx1, idx2] = ndgrid(1:numel(c1{1}), 1:numel(c1{2});
c2 = arrayfun(@(i1, i2) [c1{1}(i1), c1{2}(i2)], idx1(:), idx2(:), 'UniformOutput', false);
c2 = vertcat(c2{:})

A completely generic version that works with any number of sets:

c1 = {{[1 2],[2 3]}, {[10 11], [11 12]}, {4, 5, [6 7]}} %3 sets here
indices = cell(1, numel(c1));   %output variable for ndgrid
ndgridin = cellfun(@(c) 1:numel(c), c1, 'UniformOutput', false); %input arrays for ndgrid
[indices{:}] = ndgrid(ndgridin{:}); %get ngrid result
indices = cellfun(@(idx) reshape(idx, [], 1), indices, 'UniformOutput', false); %reshape ndgrid outputs into columns
catfun = @(nset, subsets) [arrayfun(@(n, i) c1{n}{i}, nset, subsets, 'UniformOutput', false)];
c2 = arrayfun(@(varargin) catfun(1:numel(c1), [varargin{:}]), indices{:}, 'UniformOutput', false);
c2 = vertcat(c2{:})

[jack]

thx

Answer 2

[Walter Roberson]

ndgrid indices and use the indices to index the cell array.