Adding each row of a matrix to another matrix
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SciFiPhysics Guy
am 21 Apr. 2022
Kommentiert: SciFiPhysics Guy
am 22 Apr. 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 Kommentare
Image Analyst
am 21 Apr. 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.
Akzeptierte Antwort
Voss
am 21 Apr. 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)
% another method
[ii,jj] = meshgrid(1:size(A2,1),1:size(A1,1));
A12 = A2(ii,:)+A1(jj,:);
% check
isequal(A12,A12_original)
3 Kommentare
Voss
am 22 Apr. 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));
% check
A12_original = repmat(A1,size(A2,1),1)+repelem(A2,size(A1,1),1);
isequal(A12,A12_original)
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