Adding each row of a matrix to another matrix

Is there a linear operation for adding the individual rows of a matrix to another matrix, something like a tensor product but for summing? if not, would repmat be better here? This is my implimentation:

For a numeric Example:

A1 =rand(4, 2);
A2 =rand(2, 2);
A12=zeros(size(A1,1)*size(A2,1),size(A1,2));
startind=1+size(A1,1)*(0:(size(A2,1)-1));
endind=startind+size(A1,1)-1;
for i=1:size(A2,1)
    A12(startind(i):endind(i),:)=A2(i,:)+A1;
end

For a symbolic Example:

A1 =sym('A1', [4 2]);
A2 =sym('A2', [2 2]);
A12=sym('A12', [size(A1,1)*size(A2,1),size(A1,2)]);
startind=1+size(A1,1)*(0:(size(A2,1)-1));
endind=startind+size(A1,1)-1;
for i=1:size(A2,1)
    A12(startind(i):endind(i),:)=A2(i,:)+A1;
end

[Image Analyst]

I don't have the symbolic toolbox so I'm not sure what you're doing, but wouldn't it just be

A12 = A1 + A1;

Give a small numerical example so we can see what you're starting with for A1 and A2, and what you'd like to end up with for A12.

[SciFiPhysics Guy]

Thanks for the reply, I have included a numeric example. Maybe a better way to word the question is: Is there a linear operation to broadcast one row in a matrix to another matrix? So more like A2(1,:)+A1 then repeating that for each row in A2.

Answer 1

[Voss]

A1 =rand(4, 2);
A2 =rand(2, 2);

% the original method
A12=zeros(size(A1,1)*size(A2,1),size(A1,2));
startind=1+size(A1,1)*(0:(size(A2,1)-1));
endind=startind+size(A1,1)-1;
for i=1:size(A2,1)
    A12(startind(i):endind(i),:)=A2(i,:)+A1;
end
A12_original = A12;

% another method
A12 = repmat(A1,size(A2,1),1)+repelem(A2,size(A1,1),1);
% check
isequal(A12,A12_original)

ans = logical
   1

% another method
[ii,jj] = meshgrid(1:size(A2,1),1:size(A1,1));
A12 = A2(ii,:)+A1(jj,:);
% check
isequal(A12,A12_original)

ans = logical
   1

[SciFiPhysics Guy]

This is great, thanks so much! I was also wondering if anyone might know if there is something like a tensor product but for summing.

[Voss]

I'm not sure about an analogy to kron but for summation, but here's another way to do the operation in question (where the matrices have the same number of columns and the summation is done with all pairs of rows), this time with no indexing or repmat/repelem:

A1 = rand(4,2);
A2 = rand(2,2);

A12 = reshape(permute(A1,[1 3 2])+permute(A2,[3 1 2]),[],size(A1,2));

A12 = 8×2

0.3120 0.5850 0.7758 0.4788 1.1809 0.9340 1.1380 0.4903 0.2080 1.0628 0.6717 0.9565 1.0768 1.4117 1.0339 0.9681

% check
A12_original = repmat(A1,size(A2,1),1)+repelem(A2,size(A1,1),1);
isequal(A12,A12_original)

ans = logical
   1

[SciFiPhysics Guy]

That's great! I was just playing with the permute function and couldn't figure out the reshape portion of it. Thanks alot!

I'm thinking there isn't anything like kron for summing, but this permute function seems perfect.