Adding each row of a matrix to another matrix

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SciFiPhysics Guy
SciFiPhysics Guy 2022-4-21
评论： SciFiPhysics Guy 2022-4-22
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
  2 个评论
Image Analyst
Image Analyst 2022-4-21
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
SciFiPhysics Guy 2022-4-21
编辑：SciFiPhysics Guy 2022-4-21
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.

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采纳的回答

Voss
Voss 2022-4-21
Ran in:
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
  3 个评论
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Voss
Voss 2022-4-22
Ran in:
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
SciFiPhysics Guy 2022-4-22
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.

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