How generate combination list of 4 independent vectors?
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Dominik Vana
el 29 de Feb. de 2020
Comentada: Dominik Vana
el 1 de Mzo. de 2020
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
2 comentarios
Stephen23
el 1 de Mzo. de 2020
Editada: Stephen23
el 1 de Mzo. de 2020
"...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.
Respuesta aceptada
Stephen23
el 1 de Mzo. de 2020
Editada: Stephen23
el 1 de Mzo. de 2020
A simple solution for a fixed number of vectors:
>> [x1,x2,x3,x4] = ndgrid(v1,v2,v3,v4);
>> M = [x1(:),x2(:),x3(:),x4(:)]
M =
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
4 5 9 10
1 6 9 10
2 6 9 10
3 6 9 10
4 6 9 10
1 7 9 10
2 7 9 10
3 7 9 10
4 7 9 10
A general 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}; % vectors should be stored in one cell array.
>> [C{:}] = ndgrid(C{:});
>> M = cell2mat(cellfun(@(m)m(:),C,'uni',0))
M =
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
4 5 9 10
1 6 9 10
2 6 9 10
3 6 9 10
4 6 9 10
1 7 9 10
2 7 9 10
3 7 9 10
4 7 9 10
1 comentario
Guillaume
el 1 de Mzo. de 2020
The cell2mat(cellfun(..)) could be replaced by:
M = reshape(cat(numel(C)+1, C{:}), [], numel(C))
which I suspect would be faster.
Más respuestas (1)
Bálint Udvardy
el 29 de Feb. de 2020
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. ;)
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