How generate combination list of 4 independent vectors?

Hello,

I have a question. I am trying to generate list of 4 vectors. For example v1=[ 1; 2; 3, 4]; v2=[ 5; 6; 7]; v3=[ 8; 9]; v4=[ 10] will generate matrix with 24 rows (number of possible combinations) and with 4 columns.

I tried to use 4 for-loops, but when input vectors have more elements (200 elements for each vector), the algorithm is starting to be slow. I would like to ask you for a help. Is there any other possible way or a matlab function to create this thing?

Thank You, Dominik.

M1_idx=[1; 2; 3; 4]; M2_idx=[5; 6; 7]; M3_idx=[8; 9]; M4_idx=[10];

[r1,c1] = size(M1_idx);
[r2,c2] = size(M2_idx);
[r3,c3] = size(M3_idx);
[r4,c4] = size(M4_idx);

K_mat = zeros(r1*r2*r3*r4,c1+c2+c3+c4);

for i=1:r1
   for j=1:r2 
       for k=1:r3
           for l=1:r4
                K_mat((i-1)*r2*r3*r4 + (j-1)*r3*r4 + (k-1)*r4 + l,:) = [M1_idx(i) M2_idx(j) M3_idx(k) M4_idx(l)];   
           end
       end
   end
end

[Stephen23]

"...when input vectors have more elements (200 elements for each vector), the algorithm is starting to be slow."

This is not really a surprise, have you calculated how much memory that would require?:

>> bits = 200*200*200*200 * 64
bits =  102400000000
>> num2sip(bits/8) % bytes
ans = 12.8 G

Does your computer have enough memory to hold four of arrays of that size? And then one array of size

>> num2sip(4*bits/8) % bytes
ans = 51.2 G

so you would need more than 100 GB of memory in total. I don't know of many desktop computers with that much memory. What calculations do you imagine doing on arrays of that size?

You could save memory by using an integer class, e.g. uint8 only requires 13 GB or so.

[Dominik Vana]

I know, I am trying to search solution in 3D space based on values from 4 sensors. It is part of my Master's thesis.

Answer 1

[Stephen23]

A simple solution for a fixed number of vectors:

v1 = [1;2;3;4];
v2 = [5;6;7];
v3 = [8;9];
v4 = [10]; 
[x1,x2,x3,x4] = ndgrid(v1,v2,v3,v4);
M = [x1(:),x2(:),x3(:),x4(:)]

M = 24×4

1 5 8 10 2 5 8 10 3 5 8 10 4 5 8 10 1 6 8 10 2 6 8 10 3 6 8 10 4 6 8 10 1 7 8 10 2 7 8 10 3 7 8 10 4 7 8 10 1 5 9 10 2 5 9 10 3 5 9 10

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A general efficient solution which expands to any number of vectors (which should be stored in one cell array, as using numbered variables invariably leads to inefficient code):

C = {v1,v2,v3,v4}; % the vectors should be stored in one cell array.
N = numel(C);
[C{:}] = ndgrid(C{:});
M = reshape(cat(N+1,C{:}),[],N) % thanks to Guillaume.

M = 24×4

1 5 8 10 2 5 8 10 3 5 8 10 4 5 8 10 1 6 8 10 2 6 8 10 3 6 8 10 4 6 8 10 1 7 8 10 2 7 8 10 3 7 8 10 4 7 8 10 1 5 9 10 2 5 9 10 3 5 9 10

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[Guillaume]

The cell2mat(cellfun(..)) could be replaced by:

M = reshape(cat(numel(C)+1, C{:}), [], numel(C))

which I suspect would be faster.

[Stephen23]

@Guillaume: agreed, that is a very neat approach. I modifed my answer to suit.

Answer 2

[Bálint Udvardy]

Try to use the 'combvec' function. It generates all possible conbinations of the given vectors. For your case it can be called as:

K_mat=combvec(v1',v2',v3',v4')';

Or for the latter:

K_mat=combvec(M1_idx',M2_idx',M3_idx',M4_idx')';

The transpositions were added due to the fact that the function requires a column vectors; the last transposition assures only provides better readibility of the result.

Hope I could help. ;)

[Dominik Vana]

Thank you Balint, I tried it, but your suggestion is slower than my solution for larger vectors.