Fit data with a given equation for 3 variables

I want to fit my data to the following equation, but I dont know how to force the program to take the b values which i have, instead of calculating them automatically, I attached here my code which i wrote

fy = @(a,b,x) ((1-(x/a)).^(-a*b));

x = [0,0.1, 0.2, 0.3, 0.4, 0.46, 0.55, 0.6];
y = [0.001,	0.00111499,	0.0011926,	0.0013699,	0.00161633,	0.00192075,	0.00274991,	0.00357156]; 
b = [0,	1.1499,	0.963,	1.233,	1.540825,	2.001630435,	3.181654545,	4.285933333];

B = fmincon(@(c) norm(y - fy(c(1),c(2),x)), [1; 1], [],[],[],[], [0 0],[1 90]);
fprintf('PhiMax  = %.15f\nVisco = %.15f\n', B)
xv = linspace(min(x), max(x));
figure(1)
plot(x, y, 'pg')
hold on
plot(xv, fy(B(1),B(2),xv), '-r')
hold off
grid

[Torsten]

How should it be possible to have the value for b if you don't know the value for a ?

[Tesla]

Indeed i am looking for the value of a

Answer 1

[Torsten]

Your function is not suited to reflect your data.

x = [0,0.1, 0.2, 0.3, 0.4, 0.46, 0.55, 0.6];
y = [0.001,	0.00111499,	0.0011926,	0.0013699,	0.00161633,	0.00192075,	0.00274991,	0.00357156]; 
b = [0,	1.1499,	0.963,	1.233,	1.540825,	2.001630435,	3.181654545,	4.285933333];
p0 = 1;
B = lsqnonlin(@(a)fy(a,x,y,b),p0,max(x),Inf)
fprintf('PhiMax  = %.15f\nVisco = %.15f\n', B)
figure(1)
plot(x, y, 'pg')
hold on
plot(x, fy(B(1),x,y,b)+y, '-r')
hold off
grid

function res = fy(a,x,y,b)
  res = ((1-(x/a)).^a).^b - y;
end

[Tesla]

Thanks a lot, it works, I just need to multipy the function by 0.001.

function res = fy(a,x,y,b)
res = 0.001*((1-(x/a)).^a).^b - y;
end

Answer 2

[Hiro Yoshino]

How about this?

You only need to think about c as follows:

fy = @(a,b,x) ((1-(x/a)).^(-a*b));
x = [0,0.1, 0.2, 0.3, 0.4, 0.46, 0.55, 0.6];
y = [0.001,	0.00111499,	0.0011926,	0.0013699,	0.00161633,	0.00192075,	0.00274991,	0.00357156]; 
b = [0,	1.1499,	0.963,	1.233,	1.540825,	2.001630435,	3.181654545,	4.285933333];

B = fmincon(@(c) norm(y - fy(c,b,x)),1,[],[],0,1)

Converged to an infeasible point.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance but constraints are not
satisfied to within the value of the constraint tolerance.


Consider enabling the interior point method feasibility mode.

B = 6.6511e+03

[Tesla]

Thank you for the suggestion but the fitting plot is not working