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Hi, I am working with a program like this:

E0=10

A = zeros(10000,10000);

for k = 1:10000

for j = 1:10000

A(k,j)=E0*exp(-10^(-6.5)*((k-5000)^2+(j-5000)^2));

end

end

for k=1:10:9990

for j=1:10:9990

X=rand*pi;

for h=1:10

for l=1:10

A(k+l-1,j+h-1) = A(k+l-1,j+h-1) *exp(+1i*X);

end

end

end

end

as you can imagine it is very slow, but I can't reduce matrix size and I would like to find a way to speed up the programme, thanks.

one way we can write:

for k=1:10:9990

for j=1:10:9990

X=rand*pi;

for h=1:10

for l=1:10

A(k+l-1,j+h-1)=E0*exp(-10^(-6.5)*((k+l-1-5000)^2+(j+l-1-5000)^2));

A(k+l-1,j+h-1) = A(k+l-1,j+h-1) *exp(+1i*X);

end

end

end

end

That should be the same, are there others?

Moreover I have noticed that if i repeat the programme with a for loop, each cycle is slower than the previous one, how can I overcome this?

Thanks

Dana
on 2 Oct 2020

Edited: Dana
on 2 Oct 2020

%% Using loops

tic

E0=10;

A = zeros(10000,10000);

for k = 1:10000

for j = 1:10000

A(k,j)=E0*exp(-10^(-6.5)*((k-5000)^2+(j-5000)^2));

end

end

for k=1:10:9990

for j=1:10:9990

X=rand*pi;

for h=1:10

for l=1:10

A(k+l-1,j+h-1) = A(k+l-1,j+h-1) *exp(+1i*X);

end

end

end

end

disp('Using loops:')

toc

%% Vectorizing

tic

E0=10;

N = 10000;

m = 10;

nX = N/m;

XX = pi*rand(nX);

x = ((1:N).'-N/2).^2;

A = E0*exp(-10^(-6.5)*(x+x.'));

krX = kron(exp(1i*XX),ones(m));

A = A.*krX;

disp('Vectorizing:')

toc

which yields output on my machine:

Using loops:

Elapsed time is 11.358504 seconds.

Vectorizing:

Elapsed time is 0.577795 seconds.

By the way, I did the vectorization assuming that using 9990 as the upper bounds for k and j in your second loop structure was an error on your part. With how you did it, the bottom-right 10x10 block of A wouldn't be mutiplied by a random number. If you wanted it to be, you should instead use 9991 (or really any number from 9991 up to 10000) as the upper limits. If, on the other hand, how you had it was how you wanted, then immediately after the line where XX is defined in the vectorization code, you should do XX(nX,nX)=0.

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