How can I construct a matrix with its column elements as matrix operations?

Hello everyone,

I want to construct a M X N matrix with results imported from other matrices.

For example, I have 3 matrices

I want to construct a matrix with first column input as A+B, second column as B+C and third column as C+A

----> Yellow column as A+B, Orange column as B+C, Blue column as C+A

Basically I want a matrix of all possible combinations. Please help me. Thank you.

Regards,

Azhar Uddin Mohammed

[Guillaume]

Assuming you have more than three matrices, how are all the matrices that you want to combine stored?

Hopefully all in a cell array or as a 3d matrix and not as individual variables?

[Azhar Uddin]

As individual variables

[Guillaume]

That's not a particularly good idea.

Anyway, what's the naming pattern? and how do you know how many individual variables to combine?

Answer 1

[Guillaume]

Assuming your column vectors are stored in cell array C:

combs = num2cell(nchoosek(1:numel(C), 2), 2);
S = cellfun(@(comd) C{comb(1)} + C{comb(2)}, combs, 'UniformOutput', false);
M = [S{:}];

Or, if your column vectors are actually columns of a matrix M1:

combs = num2cell(nchoosek(1:size(M1, 2), 2), 2);
S = cellfun(@(comb) sum(M1(:, comb), 2), combs, 'UniformOutput', false);
M2 = [S{:}];

[Azhar Uddin]

That is the perfect answer I wanted. Column vectors are actually columns of a matrix. But I need to know one more thing. Can I make the first row display the combination performed for any particular column. For example, first column is a combination of A+B, then A+B should appear in first row to make identification easy. Is it possible?

Answer 2

[the cyclist]

Rather than storing the original variables as A,B,C; can you you store them as A{1}, A{2}, A{3}? If so, then it is easy:

M = 4;
N = 3;

% Make up some data
for nn = 1:N
    A{nn} = rand(M,1);
end

% Preallocate memory
M = zeros(M,N*(N-1)/2);

% Combine
cc = 0;
for n1=1:N
for n2=n1+1:N
    cc = cc+1;
    M(:,cc) = A{n1}+A{n2};
end
end

It was not clear how the sorting should be in the general case, so you might need to adapt this.

Answer 3

[Matt J]

Assuming A,B, and C are column vectors,

 S=[A,B,C];
 S_new = S + circshift(S,[0,1]);