How to make my code run faster?

Hello, I just wanted to know, how do I make this code run faster?

tic

for z_0=0.1:0.05:0.8

for R_0=0.01:0.05:1

for N=0:1:5

load('am_z.mat')

syms D_guess; x_h=1; x_w=3.9/7.4; theta0= 0; theta1= 1; u= 1; AM=0.968740; BM=0.969441; alpha_h_Ih=0.25; alpha_h_xh=0.25; alpha_h_xw =0.25; alpha_h_theta=0.25; alpha_h_Yh= 0.25; alpha_w_Iw= 1/3; alpha_w_xh=1/3; alpha_w_xw= 1/3; alpha_h_am=1- alpha_h_Ih- alpha_h_xh; alpha_h_bm=1- alpha_h_Yh- alpha_h_xh; Y_h=1; Y_w=1; %z_0=0.5; R_0=0.5; N=1;

%% Defining the functions t_w=(Y_w-D_guess)*(1-exp(-(alpha_w_xh*u*sqrt(x_h))/(alpha_w_Iw)));

I_h=Y_h+D_guess+t_w;

p =z_0*(1-sqrt(z));

u_h0= alpha_h_Ih*log(I_h)+alpha_h_xh*log(x_h)+alpha_h_xw*sqrt(x_w)+alpha_h_theta*sqrt(theta0); %u_h when theta=0

u_h1= alpha_h_Ih*log(Y_h+D_guess)+alpha_h_xh*log(x_h)+alpha_h_xw*sqrt(x_w)+alpha_h_theta*sqrt(theta1); %u_h when theta=1

v_h=alpha_h_Ih*log(Y_h+D_guess)+alpha_h_xh*log(x_h)+ alpha_h_am*log(am);

R = R_0+alpha_h_Yh*log(Y_h)+alpha_h_xh*log(x_h)+alpha_h_bm*log(BM);

%%%Seperation of the equation into three parts:

%% %Part 2: for j=1:1:35; %A loop for 'j' to create the first integration and summation that contains variable 'j'

kappa_computed(j)= alpha_h_xw*sqrt(x_w)-alpha_h_am.*log(am(j))-alpha_h_Ih*(log(Y_h+D_guess)-log(I_h));

   fun1= @(kappa_computed)(u_h0-kappa_computed)*((kappa_computed^((N-2)/2))*exp(-kappa_computed/2))/(2^(N/2)...
       *gamma(N/2))*Pram(j); %The integration of the first function contiaining k 

   fun2= @(kappa_computed)(v_h(j))*((kappa_computed^((N-2)/2))*exp(-kappa_computed/2))/(2^(N/2)...
       *gamma(N/2))*Pram(j); %The integration of the second function contiaining k 

   integral_1= int(fun1,0,kappa_computed(j)); %Computing the integration of the function fun1

   integral_2= int(fun2,kappa_computed(j),Inf);%Computing the integration of the function fun2

   i_n_t1(j)=integral_1; %Creating an array called 'i_n_t1' to store the value of the first function 'integral_1'

   i_n_t2(j)=integral_2; %Creating an array called 'i_n_t2' to store the value of the first function 'integral_2'

    j=j+1; %Incrementing the value of 'j'

end

 num1= sum(i_n_t1); %Sum of all the variable in the array 'i_n_t1' saved as 'num1'

 num2= sum(i_n_t2); %Sum of all the variable in the array 'i_n_t2' saved as 'num2'

 for i=1:1:33; 

pt_1=(1-p(i))*u_h1*Prz(i); %First function that contains varaiable 'i'

sum_p1(i)= pt_1;       %Creating an array called 'sum_p1' to store the value of the first function 'pt_1'

pt_2=num1*p(i)*Prz(i); %Second function that contains varaiable 'i' that is multiplied by the 
%previous function 'num1'

pt_3=num2*p(i)*Prz(i);  %Second function that contains varaiable 'i' that is multiplied by the 
%previous variable 'num2

sum_p2(i)=pt_2; %Creating an array called 'sum_p2' to store the value of the first function 'pt_2'

sum_p3(i)=pt_3; %Creating an array called 'sum_p3' to store the value of the first function 'pt_3'

   i=i+1; %Incrementing the value of 'i'

 end

sum1=sum (sum_p1); %Sum of all the variable in the array 'sum_p1'

sum2=sum(sum_p2); %Sum of all the variable in the array 'sum_p2' saved as 'sum2'

sum3=sum(sum_p3); %Sum of all the variable in the array 'sum_p3' saved as 'sum3'

%% EU_h= sum1+sum2+sum3;

eqn=EU_h==R; D_computed=solve(eqn,D_guess)

 end
 end
end 
toc

Answer 1

[mizuki]

First, use code profiler to identify which part of your code takes much time to execute. Then, consider vectorization/using parallel computing (replace for with parfor using Parallel Computing Toolbox).

https://jp.mathworks.com/help/matlab/matlab_prog/profiling-for-improving-performance.html

[Sarah Kandeel]

Thanks, I will try that.