how to assign indexes to a function handle?

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I'm trying to approximate the double integral of the functions fun_1 and fun_2 over the given region. In the case of one single f it seems ok. But I want to use a vector f insted of a single number to have a vector of TL values. I don't know how to handle this problem. Note that when M >0 and n is a larg number it takes long time to calculate.
The code is:
gamma = 1.4;
R = 286;
T = 273.15;
rho_1 = 1.229;
c_1 = sqrt(gamma*R*T);
rho_2 = rho_1
c_2 = c_1
h = 0.00163;
rho_s = 2750;
M = 0;
m = rho_s*h;
eta = 0.01;
E = 72e9;
v = 0.30;
D = E*h^3/(12*(1-v^2));
f_c1 = c_1^2/(2*pi)*(m/D)^0.5;
f_c2 = c_2^2/(2*pi)*(m/D)^0.5;
n = 1500;
f = linspace(55,7700,n);
for i=1:numel(f)
omega(i) = 2*pi*f(i);
phi_2 = @(phi_1,beta) acos(c_2/c_1.*cos(phi_1).*(1+M.*cos(beta).*cos(phi_1)).^-1);
tau = @(phi_1,beta) ((0.5*(rho_2*c_2/(rho_1*c_1))^0.5...
+0.5*(rho_1*c_1/(rho_2*c_2))^0.5*sin(phi_2(phi_1,beta))./(sin(phi_1).*(1.0...
+M*cos(beta).*cos(phi_1)))+0.5*eta*m*omega(i)*(rho_1*c_1*rho_2*c_2)...
^-0.5.*(f(i)/f_c2).^2.*sin(phi_1).*cos(phi_2(phi_1,beta)).^4).^2.0...
+(0.5*m*omega*sin(phi_2(phi_1,beta))*(rho_1*c_1*rho_2*c_2)^-0.5...
.*(1-(f/f_c2).^2.*cos(phi_2(phi_1,beta)).^4)).^2).^-1;
fun_1 = @(phi_1,beta) tau(phi_1,beta).*sin(phi_1).*cos(phi_1);
q_1(i) = integral2(fun_1,12*pi/180,90*pi/180,0,2*pi);
fun_2 = @(phi_1,beta) sin(phi_1).*cos(phi_1);
q_2 = integral2(fun_2,12*pi/180,90*pi/180,0,2*pi);
tau_avg = q_1/q_2;
TL = -10*log10(tau_avg);
end

Risposta accettata

Star Strider
Star Strider il 23 Set 2021
But I want to use a vector "f" insted of a single number to have a vector of "TL" values.
I cannot run that because there are insufficient data provided, and the online Run feature is currently down for scheduled maintenance.
Otherwise, the integral2 function cannot integrate arrays, although integral can. The way to deal with that problem with respect to a double integral is essentially:
f = randn(1, 25);
fcn = @(x,y) sin(2*pi*f.*x) .* exp(0.1*f.*y);
int2 = integral(@(y) integral(@(x) fcn(x,y), 0, 1, 'ArrayValued',1), -1, 0, 'ArrayValued',1);
This returns a vector the size of ‘f’.
.
  9 Commenti
Mohammad SD
Mohammad SD il 24 Set 2021
@Star Strider Your suggestion helped me a lot and I was able to solve my problem. This is the paper that explain the theory behind:
Thank you.
Star Strider
Star Strider il 24 Set 2021
As always my pleasure!
That paper sounds interesting, however I have no idea what it refers to. It would be interesting to have the PDF file to read.
.

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