I was wondering what the correct approach to fitting datapoints to a non-linear function should be in python.
I am trying to fit a series of data-points
t = [0., 0.5, 1., 1.5, ...., 4.] y = [6.3, 4.5,.................]
using the following model function
f(t, x) = x1*e^(x2*t)
I was mainly wondering which library routine is appropriate for this problem and how it should be setup. I tried using the following with unsuccessful results:
t_data = np.array([0.5, 1.0, 1.5, 2.0,........]) y_data = np.array([6.8, 3., 1.5, 0.75........]) def func_nl_lsq(x, t, y): return [x*np.exp(x*t)] - y popt, pcov = scipy.optimize.curve_fit(func_nl_lsq, t_data, y_data)
I know it's unsuccessful because I am able to solve the "equivalent" linear least squares problem (simply obtained by taking the log of the model function) and its answer doesn't even come close to the one I am getting by doing the above.