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How can calcuate the lines of code efficiently?

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Amir Torabi
Amir Torabi on 4 Dec 2019
Commented: Amir Torabi on 5 Dec 2019
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);

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Accepted Answer

Stephan
Stephan on 4 Dec 2019
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
Appears to work fine...

  3 Comments

Amir Torabi
Amir Torabi on 4 Dec 2019
kk in your code first code is an empty array!.
Stephan
Stephan on 4 Dec 2019
Sure, for me not. Check it with
whos kk
For me kk is 1x512 sized. Also if it would be empty, why are the results the same like in the code you provided?
Amir Torabi
Amir Torabi on 5 Dec 2019
i checked it again. yes your answer is correct. Thanks.

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