# Combination of rows of two different matrices

5 views (last 30 days)
J AI on 23 Jul 2020
Commented: Fangjun Jiang on 24 Jul 2020
Sorry if this is a repeated question but I failed to find an answer myself. I have two matrices:
A = [-0.6, -0.2;
-60, 2;
6, -20];
B = [-0.4, -0.8;
-40, 8;
4, -80];
I want to find all the possible combinations of sum of each row (sum of individual elements of a row) of A with each row of B, i.e., my desired result is (order does not matter):
ans = [-1, -1;
-40.6, 7.8;
3.4, -80.2;
-60.4, 1.2;
-100, 10;
-56, -78;
5.6, -20.8;
-34, -12;
10, -100];
which is a matrix resulting from possible combinations of A and B.
(Please no for loops. It is pretty trivial then.)
EDIT: I have used 2 columns and 3 rows as an example. Looking for more general solution, i.e., for n number of columns and m number of rows.

Fangjun Jiang on 23 Jul 2020
Edited: Fangjun Jiang on 23 Jul 2020
Feels non-ideal. Any better solution?
>> C=A(:,1)+B(:,1)';
D=A(:,2)+B(:,2)';
reshape([C(:),D(:)],[],2)
ans =
-1.0000 -1.0000
-60.4000 1.2000
5.6000 -20.8000
-40.6000 7.8000
-100.0000 10.0000
-34.0000 -12.0000
3.4000 -80.2000
-56.0000 -78.0000
10.0000 -100.0000
better one
>> m=size(A,1);
ind1=repmat(1:m,1,m);
ind2=repelem(1:m,m);
A(ind1,:)+B(ind2,:)
ans =
-1.0000 -1.0000
-60.4000 1.2000
5.6000 -20.8000
-40.6000 7.8000
-100.0000 10.0000
-34.0000 -12.0000
3.4000 -80.2000
-56.0000 -78.0000
10.0000 -100.0000
##### 2 CommentsShowHide 1 older comment
J AI on 23 Jul 2020
Great work! Thanks a lot

Bruno Luong on 23 Jul 2020
Edited: Bruno Luong on 23 Jul 2020
A = [-0.6, -0.2;
-60, 2;
6, -20];
B = [-0.4, -0.8;
-40, 8;
4, -80];
Single statement
reshape(permute(A,[3 1 2])+permute(B,[1 3 2]),[],size(A,2))
or a variation
reshape(reshape(A,1,size(A,1),[])+reshape(B,size(B,1),1,[]),[],size(A,2))
Gives
ans =
-1.0000 -1.0000
-40.6000 7.8000
3.4000 -80.2000
-60.4000 1.2000
-100.0000 10.0000
-56.0000 -78.0000
5.6000 -20.8000
-34.0000 -12.0000
10.0000 -100.0000
>>
Fangjun Jiang on 24 Jul 2020
Brilliant, Bruno Luong! I learned implicit expansion in a whole new dimension.

R2020a

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