Replace symsum/vpasum with numerical method

Hi,

the following code is running, but relatively slow.

I therefore want to replace the symbolic calculation completely with a numeric one.

Tried to solve this with arrayfun, but didn't manage that either.

Maybe someone can give me a hint:

syms t m kappa N i
N = 500;
rb = 100;
ra = 90;
a = 20;
h = 10;
kappa = rb/ra;
u0 = 4*pi*10^-7;
t = a/ra;
m = a/rb;
[kappa,t] = meshgrid(1:0.05:3,0:0.05:0.95);
eq1 = 1./(2.*N.*log(kappa)).*vpasum(log((1+m.^2-2.*m.*cos(i.*2.*pi./N))./(1^2+t.^2-2.*t.*cos(i.*2.*pi./N))),i,0,N-1);
var = double((eq1).*100);
surf(t,kappa,var)

Answer 1

[Walter Roberson]

%syms t m kappa N i
N = 500;
rb = 100;
ra = 90;
a = 20;
h = 10;
kappa = rb/ra;
u0 = 4*pi*10^-7;
t = a/ra;
m = a/rb;
[kappa,t] = meshgrid(1:0.05:3,0:0.05:0.95);
i = reshape(0:N-1,1,1,[]);
temp = log((1+m.^2-2.*m.*cos(i.*2.*pi./N))./(1^2+t.^2-2.*t.*cos(i.*2.*pi./N)));
eq1 = 1./(2.*N.*log(kappa)) .* sum(temp,3);
var = double((eq1).*100);
surf(t, kappa, var, 'edgecolor', 'none');
xlabel('t'); ylabel('\kappa');

[Roman Jamy]

Works like a charm. Thank you!