Solving linear equations with large times

I am new to using matlab. I have a simple linear equation of Ax=B in loops;

where A is a complex matrix (1000x1000), and A will be changed with the parameters f, delta_p and delta_dopp in my code, i.e. A=A(f, delta_p, delta_dopp); B is a simple invariant column matrix (1000x1).

Cause I need to solve the linear equation almost about ~10^6 times. And matirx A is changing inside the loops (f, delta_p, delta_dopp are cycle indicators). When I using x=A\B solving the eqution, it should take me a lot of time. For example, it takes me one hour running 5e4 times.

I hope that someone can suggest a faster and better method? (Especially for the x=A\B method).

This is distribution of matrix A:

Thanks a lot!

[KSSV]

Have you checked the time taken by one step?

[剑豪 戴]

It takes about 0.063 seconds in one step. I also need time to build the matrix A. x=A\B takes 0.03 seconds. And in my one hour example, the x=A\B should take 50 minutes (use profile getting)

[KSSV]

If you have GPU, you may try running on that. Read about gpuArray.

[剑豪 戴]

ok, thanks! But I still have a question, I have tried gpu before. I need to use besselj function to build my matrix A. Can it work right if I use gpu? (for the besselj()).

Oh, I should see the MATLAB Functions with gpuArray Arguments. Or I should make a bessel function by myself

[KSSV]

Yes it should be supported. You may check it here: https://in.mathworks.com/help/matlab/referencelist.html?type=function&capability=gpuarrays

[剑豪 戴]

Thanks a lot!

Answer 1

[Hiro Yoshino]

It seems that your matrix is sparse - it would be worth while using some techniques for sparse matrix operetions where you can find methods for linear problems.

https://www.mathworks.com/help/matlab/math/sparse-matrix-operations.html

https://www.mathworks.com/help/matlab/sparse-matrices.html

[剑豪 戴]

Thanks！I will try it

[剑豪 戴]

When I use the sparse matrix, the time was shortened from one hour to 15 minutes. It' s very helpful. But there is another question. Through the Profiler, I found an assignment statement taking much time. It is in my getting matrix A function.

such like,

A(1:21, 1:21)=C(1:21,1:21)

Hopefully!

[Hiro Yoshino]

put in one lines before A = C as follows:

A = zeros(size(C));

[剑豪 戴]

Thanks！