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Adding each row of a matrix to another matrix

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SciFiPhysics Guy
SciFiPhysics Guy el 21 de Abr. de 2022
Comentada: SciFiPhysics Guy el 22 de Abr. de 2022
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 comentarios
Image Analyst
Image Analyst el 21 de Abr. de 2022
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 el 21 de Abr. de 2022
Editada: SciFiPhysics Guy el 21 de Abr. de 2022
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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Respuesta aceptada

Voss
Voss el 21 de Abr. de 2022
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 comentarios
Voss
Voss el 22 de Abr. de 2022
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 el 22 de Abr. de 2022
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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