4D matrix multiplication

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Kamran 2021-10-15

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https://ww2.mathworks.cn/matlabcentral/answers/1564551-4d-matrix-multiplication

评论： Kamran 2021-10-20

I do the following in 4 loops and it takes ages to complete. Is there a way this code could be made more efficeint, without using parallel processing toolbox?

'steer' is a 136x101x101x16 matrix

'R' is a 136x16x16 matrix

'pow' and 'F' are 101x101 matrices.

pow = zeros(grdpts_y, grdpts_x); %grdpts_y, grdpts_x = 101
for l=1:nf  %nf = 136
    F = zeros(grdpts_y,grdpts_x); 
        for i=1:grdpts_x
            for j=1:grdpts_y
              F(i,j) = F(i,j) + 1./(squeeze(steer(l,i,j,:))'*squeeze(R(l,:,:))*squeeze(steer(l,i,j,:)));  
            end
        end
    F = F.*conj(F);
    pow = pow + F;    
end

Thanks in advance,

Kamran

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采纳的回答

Matt J 2021-10-15

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https://ww2.mathworks.cn/matlabcentral/answers/1564551-4d-matrix-multiplication#answer_809406

编辑：Matt J 2021-10-18

在 MATLAB Online 中打开

steer=reshape( permute(steer,[2,3,4,1]),101^2,[],136  );
R=permute(R,[2,3,1]);
F=1./sum( pagemtimes(conj(steer),R).*steer, 2);
F=reshape( abs(F).^2 ,101,101,[]);
pow=sum(F,3);

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Matt J 2021-10-19

编辑：Matt J 2021-10-19

在 MATLAB Online 中打开

In your new version, F will always be real, non-negative, so I don't know why you would still be computing conj(F).

steer=reshape( permute(steer,[2,3,4,1]),101^2,[],136  );
Vec_n=cell(1,nf);
for l=1:nf
            [Vec, Val] = eig(squeeze(R(l,:,:)));
            [Val Seq] = sort(max(Val));
            Vec_s = Vec(:,Seq(nstat ,nstat));
            Vec_n{l}= Vec(:,Seq(1:nstat-1));
end
Vec_n=cat(3,Vec_n{:});
F=1./sum( abs(pagemtimes(conj(steer),Vec_n)).^2, 2);
F=reshape( abs(F).^2 ,101,101,[]);
pow=sum(F,3);