>>> import numpy as np >>> import matplotlib.pyplot as plt >>> from scipy.optimize import curve_fit
>>>
>>> def func(x, a, b, c): ... return a * np.exp(-b * x) + c
Define the data to be fit with some noise:
>>>
>>> xdata = np.linspace(0, 4, 50) >>> y = func(xdata, 2.5, 1.3, 0.5) >>> np.random.seed(1729) >>> y_noise = 0.2 * np.random.normal(size=xdata.size) >>> ydata = y + y_noise >>> plt.plot(xdata, ydata, 'b-', label='data')
Fit for the parameters a, b, c of the function func:
>>>
>>> popt, pcov = curve_fit(func, xdata, ydata) >>> popt array([ 2.55423706, 1.35190947, 0.47450618]) >>> plt.plot(xdata, func(xdata, *popt), 'r-', ... label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
Constrain the optimization to the region of 0 <= a <= 3, 0 <= b <= 1 and 0 <= c <= 0.5:
>>>
>>> popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 1., 0.5])) >>> popt array([ 2.43708906, 1. , 0.35015434]) >>> plt.plot(xdata, func(xdata, *popt), 'g--', ... label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
>>>
>>> plt.xlabel('x') >>> plt.ylabel('y') >>> plt.legend() >>> plt.show()