Speed up a programme with for loops?

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

Answer 1

[Dana]

You can vectorize this easily for huge computational savings:

%% 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.

[Alberto Paniate]

Thanks, yes huge computational saving.

Regarding the 9990 part, I have seen it and I should use 9991 even if it is not a big deal for my purpose.