Difference between predefined and custom exponential fit function

Hello all, I'm trying to define a custom function for fitting some data, of the shape a+b*exp(c*x). But to test whether Im' doing this correctly, I first tried to compare fitting a simple dataset with a predefined expoinential "exp1", and the one that I'd define myself.

x = 1:100;
y = 3*exp(0.2*x);  % some random exponential data
f1 = fit(x', y', 'exp1')

This gives the output of

General model Exp1:
     f1(x) = a*exp(b*x)
     Coefficients (with 95% confidence bounds):
       a =           3  (3, 3)
       b =         0.2  (0.2, 0.2)

which is correct.

Now, defining the same thing with fittype:

testexp = fittype('a*exp(b*x)', 'independent', 'x');
f2 = fit(x', y', testexp)

gives the output of

General model:
     f2(x) = a*exp(b*x)
     Coefficients (with 95% confidence bounds):
       a =  -3.317e-19  (-1.473e-17, 1.407e-17)
       b =      0.9402  (0.5052, 1.375)

which is slightly insane.

Can you please tell me what am I doing wrong?

Kind regards, Marko

Answer 1

[Steven Lord]

As described in the "Optimized Starting Points and Default Constraints" section of this documentation page, when you use the predefined exponential model it uses a heuristic to determine the starting point. When you use a custom nonlinear model, it uses a random starting point.

You can specify a starting point using the fitoptions function. Given that your model to fit includes exp(b*100) which for something as small as b = 0.5 is on the order of 5e21, I think the better a starting guess you can specify for the b coefficient the more likely it is that your fitting will succeed.

[Marko Filipovic]

Yes, you were right. When I introduced starting points closer to the actual values, the results were definitely better, but still pretty bad. But when I constrained x to go to 10 instead of to 100, even without starting values fit found the correct answer quickly. Thank you for your help!