While loop in function

This is my function code:

function [i, epsilon_a,x_sol] = secant_hyy(f,epsilon_c,x_var_1,x_var_2)
syms x;
i = 3;
x_sol(1) = x_var_1;
x_sol(2) = x_var_2;

while 1
    x_sol(i) = x_sol(i-1) - subs(f,x_sol(i-1)) * (x_sol(i-2)-x_sol(i-1)) / (subs(f,x_sol(i-2))-subs(f,x_sol(i-1)));
    epsilon_a(i) = ((x_sol(i)-x_sol(i-1)) / x_sol(i) )* 100 ;
    fprintf("x_sol %f değeri: %f \n ",i,x_sol(i));
    fprintf("x_sol %f hata oranı %f \n ",i,epsilon_a(i));
    if epsilon_a(i) < 1
        break;
    end
    i = i + 1;  
    
    
end
end

This is the main code:

clear; 
clc;
%known veriables
syms x
f(x) = exp(-x) - x;
eqn = f(x) == 0;
mat_sol = solve(eqn,x);
x_var_1 = 1; 
x_var_2 = 2;
epsilon_c = 1;
[i, epsilon_a,x_sol] = secant_hyy(f,epsilon_c,x_var_1,x_var_2);

This is the solution:

x_sol 3.000000 değeri: 0.487142

x_sol 3.000000 hata oranı -310.558199

>!The code results only calculates for first i value and loop doesn't work. I didn't get where the error was.

Answer 1

[Voss]

The first iteration of the while loop produces an epsilon_a(i) of -310.558, which is less than 1, so the loop terminates (the termination criterion is epsilon_a(i) < 1).

If you change the termination criterion to abs(epsilon_a(i)) < 1, then the loop iterates a few times and maybe gives the result you are hoping for?

% This is the main code:
clear; 
clc;
%known veriables
syms x
f(x) = exp(-x) - x;
eqn = f(x) == 0;
mat_sol = solve(eqn,x);
x_var_1 = 1; 
x_var_2 = 2;
epsilon_c = 1;
[i, epsilon_a,x_sol] = secant_hyy(f,epsilon_c,x_var_1,x_var_2);

x_sol 3.000000 değeri: 0.487142 
 x_sol 3.000000 hata oranı -310.558199 
 x_sol 4.000000 değeri: 0.583780 
 x_sol 4.000000 hata oranı 16.553853 
 x_sol 5.000000 değeri: 0.567386 
 x_sol 5.000000 hata oranı -2.889254 
 x_sol 6.000000 değeri: 0.567143 
 x_sol 6.000000 hata oranı -0.043003 
 

function [i, epsilon_a,x_sol] = secant_hyy(f,epsilon_c,x_var_1,x_var_2)
    
syms x;
i = 3;
x_sol(1) = x_var_1;
x_sol(2) = x_var_2;

while 1
    x_sol(i) = x_sol(i-1) - subs(f,x_sol(i-1)) * (x_sol(i-2)-x_sol(i-1)) / (subs(f,x_sol(i-2))-subs(f,x_sol(i-1)));
    epsilon_a(i) = ((x_sol(i)-x_sol(i-1)) / x_sol(i) )* 100 ;
    fprintf("x_sol %f değeri: %f \n ",i,x_sol(i));
    fprintf("x_sol %f hata oranı %f \n ",i,epsilon_a(i));
    if abs(epsilon_a(i)) < 1
        break;
    end
    i = i + 1;  
end
    
end

Answer 2

[Les Beckham]

Perhaps you meant to test the absolute value of epsilon_a?

%known veriables
syms x
f(x) = exp(-x) - x;
eqn = f(x) == 0;
mat_sol = solve(eqn,x);
x_var_1 = 1; 
x_var_2 = 2;
epsilon_c = 1;
[i, epsilon_a,x_sol] = secant_hyy(f,epsilon_c,x_var_1,x_var_2);

x_sol 3.000000 değeri: 0.487142
x_sol 3.000000 hata oranı -310.558199
x_sol 4.000000 değeri: 0.583780
x_sol 4.000000 hata oranı 16.553853
x_sol 5.000000 değeri: 0.567386
x_sol 5.000000 hata oranı -2.889254
x_sol 6.000000 değeri: 0.567143
x_sol 6.000000 hata oranı -0.043003

function [i, epsilon_a,x_sol] = secant_hyy(f,epsilon_c,x_var_1,x_var_2)
    syms x;
    i = 3;
    x_sol(1) = x_var_1;
    x_sol(2) = x_var_2;
    
    while 1
        x_sol(i) = x_sol(i-1) - subs(f,x_sol(i-1)) * (x_sol(i-2)-x_sol(i-1)) / (subs(f,x_sol(i-2))-subs(f,x_sol(i-1)));
        epsilon_a(i) = ((x_sol(i)-x_sol(i-1)) / x_sol(i)) * 100 ;
        fprintf("x_sol %f değeri: %f\n", i, x_sol(i));
        fprintf("x_sol %f hata oranı %f\n", i, epsilon_a(i));
        if abs(epsilon_a(i)) < 1
            break;
        end
        i = i + 1;  
    end
end