replacing for loop with more efficient code

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Lukas Müller
Lukas Müller 2019-1-10
评论： Anusha Sridharan 2019-1-11
Hi, given symmetric matrices für i=1,...,m, positiv definite and symmetric and ,
I want to compute with .
I solved this with the following for loop:
for i=1:m
M_row=X*A(:,(i-1)*n+1:i*n)*inv_S;
for j=i:m %since M is symmetric
M(i,j)=trace(M_row*A(:,(j-1)*n+1:j*n));
end
end
Is there a more efficient way to solve this in matlab? with vectorization?
  2 个评论
Bruno Luong
Bruno Luong 2019-1-11
OP wants to compute
M(i,j) = Trace(X * A(:,:,i) * inv(S) * A(:,:,j))
where A(:,:,i), X and S are n x n symmetric, matrices, S and X are definite positive. i=1,...m
His original code that needs to be optimized is
M = zeros(m,m);
inv_S = inv(S);
for i=1:m
M_row=X*A(:,(i-1)*n+1:i*n)*inv_S;
for j=i:m %since M is symmetric
M(i,j)=trace(M_row*A(:,(j-1)*n+1:j*n));
end
end

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采纳的回答

Bruno Luong
Bruno Luong 2019-1-10
% Generate test matrices
m = 5;
n = 10;
S = rand(n,n);
S = 0.5*(S + S.');
X = rand(n,n);
X = 0.5*(X + X.');
A = zeros(n,n,m);
for k=1:m
Ak = rand(n,n);
Ak = 0.5*(Ak + Ak.');
A(:,:,k) = Ak;
end
AA = reshape(A,[n n m]);
M = zeros(m,m);
for i=1:m
Ti = S\(AA(:,:,i)*X);
M(i,:) = Ti(:).'*reshape(AA(:,:,:),[],m);
end
  1 个评论
Bruno Luong
Bruno Luong 2019-1-11
The loop can be replaced by vectorized code if you use this mtimesxmtimesx FEX
AA = reshape(A,[n n m]);
Ti = mtimesx(mtimesx(inv(S),AA),X);
M = reshape(Ti,[],m).' *reshape(AA(:,:,:),[],m)

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更多回答（1 个）

Lukas Müller
Lukas Müller 2019-1-10
Thanks for you fast answer. So I guess it doesnt work without at least one for loop. Still way better then before thanks a lot :)

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