Column multiplication in the same matrix

I have a 3 by 3 matrix and would like to loop and multiply column 1 with all other columns but not itself and also column 2 with other columns but not itself and column 3 with other columns but not itself.

x11 = [1 2 3; 4 5 3; 2 8 3];

[m12, n12] = size(x11);

for i = 1:m12

    for j = 1:n12
         x1x1(i, j)=x11(i, j).*x11(i, j)
    end
end

Answer 1

[Star Strider]

Try this:

x11 = [1 2 3; 4 5 3; 2 8 3];
[m12, n12] = size(x11);

for k1 = 1:n12
    x11t = x11;                                             % Copy ‘x11’
    idx = setdiff(1:n12, k1)                                % Columns To Be Multiplied
    x11t(:,idx) = bsxfun(@times, x11(:,idx), x11(:,k1))     % Assign Multiplied ‘Columns To Be Multiplied’ To Appropriate Columns Of ‘x11t’
    x1x1(:,:,k1) = x11t;                                    % Store In Output Array
end

It appears to do what you want.

[Mahmoud Solomon]

Thanks for the respond but I am not getting the desire result. The resulting matrix should look like this [2 6 3; 20 15 12; 16 24 6]. Again, column 1 multiplies columns 2 and 3 and column 3 multiplies column 1.

[Star Strider]

Change the ‘x1x1’ assignment to:

x1x1(:,k1) = x11t(:,rem(2*n12+k1,n12)+1)                % Store In Output Array

That puts the correct columns of ‘x11t’ into ‘x1x1’ in each iteration.

[Mahmoud Solomon]

Nice Sir. It works. Thanks again.

[Star Strider]

As always, my pleasure.

[Mahmoud Solomon]

Sir... I need to generalize the solution to that problem. I have been trying but it's not working. What I want to achieve is when a column is used once, it should be removed from the original matrix thereby reducing the number of column by one. So, column 1 is used to multiple columns 2 to n. The next multiplication should be done between column 2 and 3 up to n, and in that order. Remember, nCr = n!/(n-r)!r!.

[Star Strider]

It seems that my original solution (link) will do what you want.

If you begin with an (NxM) matrix, you would end up with a (NxMxM) 3D matrix, or perhaps (Nx(M-1)xM), depending upon what you want. I know of no other way to do that.

[Mahmoud Solomon]

Thanks again.

[Star Strider]

As always, my pleasure.

Answer 2

[Elias Gule]

Here you go:

[nr,nc] = size(x11);
for col = 1 : nc
  col_data = x11(:,col);
  col_prod = bsxfun(@times,col_data,x11(:,~all(ismember(x11,col_data))));
  col_prod   % you can store this in another array
end

[Mahmoud Solomon]

Thanks for the respond but I am not getting the desire result. The resulting matrix should look like this [2 6 3; 20 15 12; 16 24 6]. Again, column 1 multiplies columns 2 and 3 and column 3 multiplies column 1.

[Elias Gule]

ok. I see what you mean. You are basically multiplying the columns of a matrix while ignoring the currently selected column.

x11 = [1 2 3; 4 5 3; 2 8 3];
[nr,nc] = size(x11);
for col = 1 : nc
col_data = x11(:,col);
tempX11  = x11(:,~all(ismember(x11,col_data)));
col_prod = tempX11(:,1).*tempX11(:,2);
col_prod   % you can store this in another array
end

Answer 3

[Elias Gule]

I believe this works as expected:

x11 = [1 2 3; 4 5 3; 2 8 3];
[nr,nc] = size(x11);
for col = 1 : nc
 col_data = x11(:,col);
 tempX11  = x11(:,~all(ismember(x11,col_data)));
 col_prod = tempX11(:,1).*tempX11(:,2);
 col_prod   % you can store this in another array
end

[Mahmoud Solomon]

It also worked but the result is not in a matrix format. I will work that out. Anyway, thanks.

[Yuanli Guo]

@Mahmoud Solomon Hi Mahmoud, do you know how to store these arrays in one matrix? I'm having the same problem now. Thank you^^