用于迭代选择矩阵列的 Octave 或 Matlab 代码

Question

I have a matrix A composed of 4 columns C1, C2, C3 and C4. I would like to have all the matrices (vectors) that can be generated from matrix A without repetitions of columns and where the order of the columns does not matter, ie matrix B = [C1 C2] = [C2 C1] . More precisely I would like to obtain the following matrices / vectors: [C1]; [C2]; [C3]; [C4]; [C1 C2]; [C1 C3]; [C1 C4]; [C2 C3]; [C2 C4 ]; [C3 C4]; [C1 C2 C3]; [C1 C2 C4]; [C1 C3 C4]; [C2 C3 C4]; [C1 C2 C3 C4]. Can you please help me with an Octave code that can do this task.

Thanks in advance

George

Answer 1

Here is MATLAB code to do it using logical indexing and arrayfun:

n = size(A,2); % number of columns
x = logical(dec2bin(1:2^n-1)-'0'); % logical array of all possible combinations
C = arrayfun(@(k)A(:,x(k,:)),1:size(x,1),'uni',false); % build the combinations

Result will be in the cell array C. Basically, each row of the dec2bin result is used for logical indexing into the columns of A. Note that this method is only practical for relatively small values of n. For large n the memory requirements quickly become overwhelming.