How can calcuate the lines of code efficiently?

Question

Amir Torabi 2019-12-4

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/494796-how-can-calcuate-the-lines-of-code-efficiently

评论： Ahmad Nadeem 2021-7-14

Hello. This code calculates the Laplacian. I am looking for reducing the time running of it. My main aim is improving the performance of loop running time.

Thanks

%%%code
nx=512;
ny=nx;
dx=1;
dy=dx;
format long;
nxny=nx*ny;
r=zeros(1,nx);
r(1:2)=[2,-1];
T=toeplitz(r);
E=speye(nx);
grad=-(kron(T,E)+kron(E,T));%Tensor
%-- for periodic boundaries
for i=1:nx
    ii=(i-1)*nx+1;
    jj=ii+nx-1;
    grad(ii,jj)=1.0;
    grad(jj,ii)=1.0;
    kk=nxny-nx+i;
    grad(i,kk)=1.0;
    grad(kk,i)=1.0;
end%for
grad = grad /(dx*dy);

1 个评论
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Ahmad Nadeem 2021-7-14

hello brother!

I want to contact you. Can you please share your email or any other ID?

Thank You

Best Regards

Ahmad Nadeem

Hongik University, Seoul, South Korea

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Answer 1

Stephan 2019-12-4

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/494796-how-can-calcuate-the-lines-of-code-efficiently#answer_404695

Yes, you can if you avoid using a loop and vectorize your code - see here:

tic
%%%code
nx=512;
ny=nx;
dx=1;
dy=dx;
format long;
nxny=nx*ny;
r=zeros(1,nx);
r(1:2)=[2,-1];
T=toeplitz(r);
E=speye(nx);
grad=-(kron(T,E)+kron(E,T));%Tensor
%-- for periodic boundaries
ii=(0:nx-1).*nx+1;
jj = ii+nx-1;
grad(ii,jj)=1.0;
grad(jj,ii)=1.0;
kk=(nxny-nx+1):nxny;
grad(1:nx,kk)=1.0;
grad(kk,1:nx)=1.0;
grad = grad /(dx*dy);
toc
Elapsed time is 0.145899 seconds.

Your code:

tic
%%%code
nx=512;
ny=nx;
dx=1;
dy=dx;
format long;
nxny=nx*ny;
r=zeros(1,nx);
r(1:2)=[2,-1];
T=toeplitz(r);
E=speye(nx);
grad=-(kron(T,E)+kron(E,T));%Tensor
%-- for periodic boundaries
for i=1:nx
    ii=(0:nx-1).*nx+1;
    jj=ii+nx-1;
    grad(ii,jj)=1.0;
    grad(jj,ii)=1.0;
    kk=nxny-nx+i;
    grad(i,kk)=1.0;
    grad(kk,i)=1.0;
end 
toc
Elapsed time is 11.333450 seconds.

Are the results correct? - to check this we call one of the results grad1 and subtract grad1 from grad:

nx=512;
ny=nx;
dx=1;
dy=dx;
format long;
nxny=nx*ny;
r=zeros(1,nx);
r(1:2)=[2,-1];
T=toeplitz(r);
E=speye(nx);
grad=-(kron(T,E)+kron(E,T));%Tensor
%-- for periodic boundaries
for i=1:nx
    ii=(0:nx-1).*nx+1;
    jj=ii+nx-1;
    grad(ii,jj)=1.0;
    grad(jj,ii)=1.0;
    kk=nxny-nx+i;
    grad(i,kk)=1.0;
    grad(kk,i)=1.0;
end 
ii=(0:nx-1).*nx+1;
jj = ii+nx-1;
grad(ii,jj)=1.0;
grad(jj,ii)=1.0;
kk=(nxny-nx+1):nxny;
grad(1:nx,kk)=1.0;
grad(kk,1:nx)=1.0;
grad1 = grad /(dx*dy);
expect_all_zeros = grad1-grad
expect_all_zeros =
   All zero sparse: 262144×262144