Question

I’ve been working on speeding up the following function, but with no results:

function beta = beta_c(k,c,gamma)
beta = zeros(size(k));
E = @(x) (1.453*x.^4)./((1 + x.^2).^(17/6));
for ii = 1:size(k,1)
    for jj = 1:size(k,2)
        E_int = integral(E,k(ii,jj),10000);
        beta(ii,jj) = c*gamma/(k(ii,jj)*sqrt(E_int));
    end
end
end

Up to now, I solved it this way:

function beta = beta_calc(k,c,gamma)
k_1d = reshape(k,[1,numel(k)]);
E_1d =@(k) 1.453.*k.^4./((1 + k.^2).^(17/6));
E_int = zeros(1,numel(k_1d));
parfor ii = 1:numel(k_1d)
E_int(ii) = quad(E_1d,k_1d(ii),10000);
end
beta_1d = c*gamma./(k_1d.*sqrt(E_int));
beta = reshape(beta_1d,[size(k,1),size(k,2)]);
end

Seems to me, it didn’t really enhance performances. What do you think about this?

Would you mind to shed a light?

I thank you in advance.

EDIT

I am gonna introduce some theoretical background involving my question.
Generally, beta is to be calculated as follows

Therefore, in the reduced case of unidimensional k array, E_int may be calculated as

E = 1.453.*k.^4./((1 + k.^2).^(17/6));
E_int = 1.5 - cumtrapz(k,E);

or, alternatively as

E_int(1) = 1.5;
for jj = 2:numel(k)
E =@(k) 1.453.*k.^4./((1 + k.^2).^(17/6));
E_int(jj) = E_int(jj - 1) - integral(E,k(jj-1),k(jj));
end

Nonetheless, k is currently a matrix k(size1,size2).

Answer 1

Here’s another approach, parallelize, because it’s easy using spmd or parfor. Instead of integral consider quad, see this link for examples…