Fail to fit a normal distribution with Python. scipy package defects? - python-3.x

Question

import numpy as np
from astropy import modeling
import matplotlib.pyplot as plt
from scipy import optimize
def gaussian(x, amplitude, mean, stddev):
return amplitude * np.exp(-((x - mean)/4/stddev)**2)
# the data
m = modeling.models.Gaussian1D(amplitude=10, mean=100, stddev=10)
x = np.linspace(0, 400, 400)
data = m(x)
# fitting
popt, _ = optimize.curve_fit(gaussian, x, data)
plt.figure(0)
plt.plot(x, data)
plt.plot(x, gaussian(x, *popt))
plt.show()
I run this to do a normal distribution fitting. But it gave me a line. Can't figure out why.
However, if I decrease the mean under 45, it will give a good fitting. Is this a design defects of scipy package?

Answer 1

Initial estimates for the model parameters (in this case, amplitude, mean and standard deviation) make a big difference when you use scipy.optimize.curve_fit.
You did not provide any initial guess. Providing guess (with actual values), then then the fit is perfect (since the Gaussian is a perfect Gaussian with no noise added):
import numpy as np
from astropy import modeling
import matplotlib.pyplot as plt
from scipy import optimize
def gaussian(x, amplitude, mean, stddev):
return amplitude * np.exp(-((x - mean)/4/stddev)**2)
# the data
m = modeling.models.Gaussian1D(amplitude=10, mean=100, stddev=10)
x = np.linspace(0, 400, 400)
data = m(x)
# fitting
popt, _ = optimize.curve_fit(gaussian, x, data, p0 = [10, 100, 10])
plt.figure(0)
plt.plot(x, data)
plt.plot(x, gaussian(x, *popt))
plt.show()
and you get: gaussian fit
you can make sure the fit works by adding some noise to your data, e.g.:
from astropy import modeling
import matplotlib.pyplot as plt
from scipy import optimize
import numpy as np
def gaussian(x, amplitude, mean, stddev):
return amplitude * np.exp(-((x - mean)/4/stddev)**2)
# the data
m = modeling.models.Gaussian1D(amplitude=10, mean=100, stddev=10)
x = np.linspace(0, 400, 400)
data = m(x)
noise = np.random.normal(len(m))
data = data + noise
# fitting
popt, _ = optimize.curve_fit(gaussian, x, data, p0 = [10, 100, 10])
plt.figure(0)
plt.plot(x, data, 'o', label = 'data')
plt.plot(x, gaussian(x, *popt), label = 'fit')
plt.legend()
plt.show()
and you get: fit to noisy gaussian