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Too slow using int, want to replace with integral2 or integral 3?

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Sharif Khalil
Sharif Khalil el 29 de Jun. de 2018
Editada: Sharif Khalil el 29 de Jun. de 2018
I am trying to solve a double integral in Matlab using two int functions, the equation is in spherical coordinate. It takes too long and sometimes gives an out of memory message, is there a way to solve this integration in the spherical coordination using integral2 or integral3 built-in functions?
if true
% code
end
syms theta phi real
sin_alpha = sin(theta)*cos(phi);
sin_beta = sin(theta)*sin(phi);
Term1 = repmat((0:4-1)*sin_beta,4,1);
Term2 = repmat((0:4-1)*sin_alpha,4,1)';
AF_Field = sum(sum(exp(1i*(Term1+Term2)),2));
U = abs((AF_Field)).^2; % Radiation Intensity
L1 = 0; L2 = pi; % limits for theta
L3 = 0; L4 = 2*pi; % limits for phi
I1 = int(U*sin(theta),theta,L1,L2); % theta-integral
I = int(I1,phi,L3,L4); % phi-integral
Prad = double(I);

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