How can I vectorize my code and use fsolve to solve thousands of non-linear equations simulataneously?

Dear Sir/Madam,

Please see the following piece of code: %%%%%%%%%%

M=4; lamda_lin=0.1;

sr_vect=0:729; rp_vect=0:729; rd_vect=0:729;

beta_opt_matrix = generate_beta_opt_grid(sr_vect,rp_vect,rd_vect,lamda_lin,M);

function beta_opt_matrix = generate_beta_opt_grid(sr_vect,rp_vect,rd_vect,lamda_lin,M)

beta_opt_matrix = zeros(length(sr_vect),length(rp_vect),length(rd_vect));% initialization of matrix

%gereration of 3D data space and finding \beta_{opt}

for i = 1:length(sr_vect) for j = 1:length(rp_vect) for k= 1:length(rd_vect) beta_opt_matrix(i,j,k) = find_beta_opt(sr_vect(i),rp_vect(j),rd_vect(k),lamda_lin,M); end end end

%%%

I use find_beta_opt function passing scalars to a non-liner equation and solving it. This is taking lot of time.

how can I vectorize the above code and use fsolve to solve for 729*729*729 grid points simultaneously.

Kindly reply, Thanks very much in advance, sainath.

Answer 1

[José-Luis]

What does a long time mean? You realize you are trying to solve almost 400 million systems of non-linear equations. That is bound to take a while. You could try parallelization.

doc parfor

For instance:

beta_opt_matrix = NaN * ones(730,730,730);
parfor ii=1:730^3;
    [sr rp rd] = ind2sub([730 730 730],ii);
    beta_opt_matrix(sr,rp,rd) = find_beta_opt(sr-1, rp-1, rd-1, lambda, M);
end