How generate combination list of 4 independent vectors?

3 次查看（过去 30 天）
Dominik Vana
Dominik Vana 2020-2-29
编辑： Stephen23 2025-7-29
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 个评论
Stephen23
Stephen23 2020-3-1
编辑：Stephen23 2020-3-1
"...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
Dominik Vana 2020-3-1
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.

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

Stephen23
Stephen23 2020-3-1
编辑：Stephen23 2025-7-29
Ran in:
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
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
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
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
  2 个评论
Guillaume
Guillaume 2020-3-1
The cell2mat(cellfun(..)) could be replaced by:
M = reshape(cat(numel(C)+1, C{:}), [], numel(C))
which I suspect would be faster.
Stephen23
Stephen23 2025-7-27
@Guillaume: agreed, that is a very neat approach. I modifed my answer to suit.

请先登录，再进行评论。

更多回答（1 个）

Bálint Udvardy
Bálint Udvardy 2020-2-29
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. ;)
  1 个评论
Dominik Vana
Dominik Vana 2020-3-1
Thank you Balint, I tried it, but your suggestion is slower than my solution for larger vectors.

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Creating and Concatenating Matrices 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by