Numerical Integration by Simpsons method - matlab

Question

I am trying to solve this integration by simpsons method and plot the result in a figure.The figure is taking only the value of P0= -6 from the for loop. When I set I(K,P) it gives the error:
Attempted to access P0(0); index must be a positive integer or logical
How can I solve it?
alpha = 45;
beta = 185;
gamma_e = 116;
% Gain values
G_ei = -18.96;
G_ee = 18.52;
G_sr = -0.26;
G_rs = 16.92;
G_es = 2.55;
G_re = 4.67;
G_se = 0.73;
G_sn = 2.78;
G_esre = G_es*G_sr*G_re;
G_srs = G_sr*G_rs;
G_ese = G_es*G_se;
G_esn = G_es*G_sn;
t_0 = 0.085; % corticothalamic loop delay in second
r_e = 0.086; % Excitatory axon range in metre
f = linspace(-40,40,500); % f = frequency in Hz
w = 2*pi*f; % angular frequency in radian per second
delt_P = 0.5;
L=zeros(1,500);
Q=repmat(L,1);
P=repmat(L,1);
%%%%%%%%%%%%% integration %%%%%%%%%%%%
a = -80*pi;
b = 80*pi;
n=500;
I=repmat(L,1);
P_initial = repmat(L,1);
P_shift = repmat(L,1);
p = repmat(L,1);
for k = 1:length(w)
for P0 = [6 -6]
L_initial = #(w1) (1-((1i*w1)/alpha))^(-1)*(1-((1i*w1)/beta))^(-1);
Q_initial = #(w1) (1/(r_e^2))*((1-((1i*w1)/gamma_e))^(2) - (1/(1-G_ei*L_initial(w1)))*....
(L_initial(w1)*G_ee + (exp(1i*w1*t_0)*(L_initial(w1)^2*G_ese +L_initial(w1)^3*G_esre))/(1-L_initial(w1)^2*G_srs)));
P_initial = #(w1) (pi/r_e^4)* (abs((L_initial(w1)^2*G_esn)/((1-L_initial(w1)^2*G_srs)*....
(1-G_ei*L_initial(w1)))))^2 * abs((atan2((imag(Q_initial(w1))),(real(Q_initial(w1)))))/imag(Q_initial(w1)));
G = 150*exp(- (f - P0).^2./(2*(delt_P).^2));
P2 = #(w1) G(k) + P_initial(w1);
L_shift = #(w1) (1-((1i*(w(k)-w1))/alpha))^(-1)* (1-((1i*(w(k)-w1))/beta))^(-1);
Q_shift = #(w1) (1/(r_e^2))*((1-((1i*(w(k)-w1))/gamma_e))^(2) - (1/(1-G_ei*L_shift(w1)))*...
(L_shift(w1)*G_ee + (exp(1i*(w(k)-w1)*t_0)*(L_shift(w1)^2*G_ese +L_shift(w1)^3*G_esre))/(1-L_shift(w1)^2*G_srs)));
P_shift = #(w1) (pi/r_e^4)* (abs((L_shift(w1)^2*G_esn)/((1-L_shift(w1)^2*G_srs)*(1-G_ei*L_shift(w1)))))^2 *....
abs((atan2((imag(Q_shift(w1))),(real(Q_shift(w1)))))/imag(Q_shift(w1)));
p = #(w1) P2(w1)*P_shift(w1); % Power spectrum formula for P(w1)*p(w-w1)
I(k) = simprl(p,a,b,n);
end
end
figure(1)
plot(f,I,'r--')
figure(2)
plot(f,G,'k')

Answer 1

At the moment you only use the results for P0 = -6 as you save them in I(k). First you save the result for P0 = 6 later you overwrite it and save the other. The results of P0 = 6are neither used nor saved. If you write your code as follows this will be clarifyied.
for k = 1:length(w)
L_shift = #(w1) (1-((1i*(w(k)-w1))/alpha))^(-1)* (1-((1i*(w(k)-w1))/beta))^(-1);
Q_shift = #(w1) (1/(r_e^2))*((1-((1i*(w(k)-w1))/gamma_e))^(2) - (1/(1-G_ei*L_shift(w1)))*...
(L_shift(w1)*G_ee + (exp(1i*(w(k)-w1)*t_0)*(L_shift(w1)^2*G_ese +L_shift(w1)^3*G_esre))/(1-L_shift(w1)^2*G_srs)));
P_shift = #(w1) (pi/r_e^4)* (abs((L_shift(w1)^2*G_esn)/((1-L_shift(w1)^2*G_srs)*(1-G_ei*L_shift(w1)))))^2 *....
abs((atan2((imag(Q_shift(w1))),(real(Q_shift(w1)))))/imag(Q_shift(w1)));
for P0 = [6 -6]
G = 150*exp(- (f - P0).^2./(2*(delt_P).^2));
P2 = #(w1) G(k) + P_initial(w1);
p = #(w1) P2(w1)*P_shift(w1);
I(k) = simprl(p,a,b,n);
end
end
You can't access I(k,P) as I is an vector not an matrix. However this will give you Index exceeds matrix dimensions. You could save the results for P0 = -6 in one variable and P0 = 6 in the other variable as the results in your code do not depent on each other.