get ridoff "for loops" while defining matrices elements, incl. improvement and reference

Hello Community,

is it possible to write a code which is faster than my version?

function D = Dp(N)
D = (zeros(N-1,N-1));
for i=1:N-1
    for j=1:N-1
        if i ~= j
            D(i,j)= -.5 * sin(j*pi/N)^2/sin(i*pi/N)^2 *(-1)^(i+j)/(sin(pi*(i+j)/(2*N))*sin(pi*(i-j)/(2*N)));
        else
            D(i,j) =  3/2 * cos(pi*i/N)/sin(pi*i/N)^2;
        end
    end
end
end

the reference i should inplement is:

my "optimized" version:

function D = Dp(N)
D = (zeros(N-1,N-1));
for i=1:N-1
    for j=1:N-1
        if i ~= j
            D(i,j)= -.5 * sin(j*pi/N)^2/sin(i*pi/N)^2 *(-1)^(i+j)/(sin(pi*(i+j)/(2*N))*sin(pi*(i-j)/(2*N)));
        else
        end
    end
end
D = D + diag(1.5 * cos(pi*(1:N-1)/N)./sin(pi*(1:N-1)/N).^2);
end

Answer 1

[Pranav Verma]

Hi Marko,

Since you want to initilialise each and every element of your matrix with a different value, you'll have to visit each element of the matrix in any case. You can try vectorising your code to remove the nested loops using meshgrid/ndgrid but this may not necessarily provide an improvement in performance (running time).

Below are some useful threads where the code has been vectorized to remove the nested loops:

https://www.mathworks.com/matlabcentral/answers/116079-how-to-vectorized-a-nested-for-loop

https://www.mathworks.com/matlabcentral/answers/385839-how-can-i-vectorize-this-function-with-nested-for-loop

https://www.mathworks.com/matlabcentral/answers/59231-how-to-vectorize-this-code-to-eliminate-nested-for-loops

PS: I tried to run your code using parfor but that deprecated the performance due to overhead.

Thanks