problem with combvec, allcomb

How to use combvec for a huge set (a1 to a100)?

Example a1=[1 3 4], a2=[5 7], a3=[7 9 1], .... a100=[8 9 6 2]

[Walter Roberson]

How many output rows do you calculate you will form?

[zon]

100 in this case

[Walter Roberson]

Then I am confused by your notation. Are you working with a set with 100 elements and you need to find all the combinations of the 100 taken up to 4 at a time? Or are you working with 100 sets and you need to generate all the combinations in which one element is taken from the first set, one from the second, and so on up to one from the 100th set ? Or do you have a set of elements and you want 100 random combinations of them? Or do you have a set of elements and you want to process them 100 combinations at a time, then another 100, etc. ?

[zon]

Another example: a1=[1] a2=[3] a3=[2 6 4] a4=[8 9]. The required output is:

1 1 1 1 1 1
3 3 3 3 3 3
2 6 4 2 6 4
8 8 8 9 9 9

The order of cols. does not matter.

[Walter Roberson]

The number of results you will get will be the product of the number of elements in the sets. That could be quite a lot!!

Answer 1

[Andrei Bobrov]

a = {1,3,[2 6 4],[8 9]};

c = cell(size(a));
[c{:}] = ndgrid(a{end:-1:1});
c2 = sortrows(cell2mat(cellfun(@(x)x(:),c,'un',0)),1);
out = fliplr(c2)';

ADD

n = cellfun(@numel,a);
t = max(n)./n;
while any(rem(t,1) ~= 0)
    t = t*2;
end
c = cellfun(@(x,y)repmat(x,1,y),a,num2cell(t),'un',0);
out = cat(1,c{:});

[Matt Fig]

There seems to be a problem with this solution. For example:

a = {[1 1],[7 4 5 6],[9 8]}

Shouldn't we get this?

     1     1     1     1
     7     4     5     6
     9     8     9     8

Also, I think that it can be fixed for small sets, but the OP seems to want something like this:

N = 100;  % Even with N = 30 we will have problems (NDGRID)!
M = 4;    % Or more?
a = cellfun(@(x) randi(10,1,randi(M)),cell(1,N),'Un',0);

That surely will fail with NDGRID.

[Andrei Bobrov]

Hi Matt! I added version (ADD).

[Rik]

Comment posted as flag by @Hang Zhang:

combvec全组合

(machine translation of the Chinese characters: "full combination")

Answer 2

[Matt Fig]

This will solve your problem.

function M = expand_vects(A)
% A is a cell array of 1-by-n vectors where n need not 
% be the same in every element.

L = cellfun('length',A);
B = lcms(L);
M = zeros(length(L),B);

for ii = 1:length(L)
    M(ii,:) = reshape(A{ii}(ones(1,B/L(ii)),:).',1,B);
end

Note that to use it you first need to get this file from the FEX.

Once you have the files in place, call like this:

>> A = {1,3,[2,6,4],[8,9]};  % Use a cell array
>> M = expand_vects(A)

M =

       1     1     1     1     1     1
       3     3     3     3     3     3
       2     6     4     2     6     4
       8     9     8     9     8     9

[Matt Fig]

You can forgo the FEX function and just use this. (I found that recursively calling LCM is just as fast or faster than the FEX function.)

function M = expand_vects(A)
% A is a cell array of 1-by-n vectors where n need not 
% be the same in every element.

L = cellfun('length',A);
LC = length(L);
% B = lcms(L);  % Available on the FEX.  Or use below loop.
B = L(1);
for ii = 2:LC
    B = lcm(B,L(ii));
end

M = zeros(LC,B);
L = B./L;

for ii = 1:LC
    M(ii,:) = reshape(A{ii}(ones(1,L(ii)),:).',1,B);
end

[Matt Fig]

Well.....

Simply make yourself a cell array and pass it in:

a1 = 1;
a2 = 3;
a3 = [3 4 5];
A = {a1,a2,a3};

Nasty problems like this are the reason we don't make variables a1,a2,a3,a4.....an in the first place.....

Other reasons to avoid doing this found here.