Adding each row of a matrix to another matrix

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SciFiPhysics Guy 2022-4-21

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1702060-adding-each-row-of-a-matrix-to-another-matrix

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

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Image Analyst 2022-4-21

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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 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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Answer 1

Voss 2022-4-21

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https://ww2.mathworks.cn/matlabcentral/answers/1702060-adding-each-row-of-a-matrix-to-another-matrix#answer_947975

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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

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Voss 2022-4-22

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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