Vpasolve higher polynomials does not give a real solution

equation_clean = poly2sym(p,t) %the equation of the polynomial interpolation
yvalues = polyval(p,a,[],mu);     %yvalues of the linear interpolation
hold off
slope_graph = polyfit(a,yvalues,1);
    
    T = yvalues(1:14);
    
    stand_dev = std(T);
    
    while stand_dev < .03
        
        counter = counter + 1;
        T(counter) = yvalues(counter);
        stand_dev = std(T);
        
    end
    
    max_ind = find(a,1,'last');
    
    ts_ind = find(yvalues == T(counter),1,'last');
    
    ts = a(ts_ind);
    
    Temperature2 = yvalues(max_ind:-1:ts_ind);
    
    T_2 = Temperature2(1:14);
    
    stand_dev = 0;
    
    counter = 14;
    
    while stand_dev < .03
        
        counter = counter + 1;
        T_2(counter) = Temperature2(counter);
        stand_dev = std(T_2);
        
    end
    

    yH_ind = find( Temperature2 == T_2(counter),1,'last');

    
if slope_graph(1) > 0
    
    yL = mean(T)
    
    yH = Temperature2(yH_ind)
    
else
    
    yL = Temperature2(yH_ind)
    
    yH = mean(T)
    
end

y_tau = .632 * (yH - yL)

ts
     x_tau_t = vpasolve(equation_clean == y_tau,t,[0 Inf])
    
tau = x_tau_t(end) - ts;

Hello everyone, I need your help.

I am super beginner at Matlab, but have a challenging task in front of me. I want to find out tau value, I calculatd ts and y_tau. Now I just need to plug in value for y_tau and determine x_tau from it. However matlab tells me that the number does not exist, so there is no solution. but when I draw the graph it is obvious that there is a positive interger solution which is close to 1.7 seconds. Any help would be much appreciated. I have used polynomial interpolation or polyval to determine the polynomial equation.

[Walter Roberson]

We need to know what inputs to test with ?

[Rufat Imanov]

The inputs are given by the user

Answer 1

[Walter Roberson]

Q: "We need to know what inputs to test with ?"

A: "The inputs are given by the user"

Given that, then we can conclude that you are wrong about there being an error with the program. See attached implementation code.

[Rufat Imanov]

[p,~,mu] = polyfit(x,y,20);    %use polyfit to get the coefficiants of the polynomial
figure(1)      %figure 1
[a,b] = selection_data(x,y);
plot(a,b,'ko');   %plot the originaldata
grid on
xlabel("x")
ylabel("y")
hold on
t = sym('t');
equation_clean = poly2sym(p,t)      %the equation of th epolynomial interpolation
yvalues = polyval(p,a,[],mu);

This is the part that I get inputs and plot it and make a polynomial interpolation using polyval/

[Rufat Imanov]

Sorry for not displaying my code clearly

[Walter Roberson]

We do not have your x or your y, and we do not have your function selection_data