问用scipy.curve_fit()拟合高斯直方图曲线的误差

EN

import matplotlib.pylab as plt 
from pylab import exp
import numpy as np 
from scipy import optimize
from math import sqrt

# Fit functions
def Gaussian(x,a,b,c):
    return a * exp(-(x - b)**2.0 / (2 * c**2))

# Generate data from random Guassian distribution
npix = 10200
nbins = int(sqrt(npix))
data = np.random.standard_normal(npix)
print('\n Length of y: %s' % len(data))
n,bins,patches = plt.hist(data,bins=nbins)

# Generate data from bins as a set of points 
bin_size = abs(bins[1]-bins[0])
x =np.linspace(start=bins[0]+bin_size/2.0,stop=bins[-2]+bin_size/2.0,\
num=nbins,endpoint=True)
print min(x),max(x),len(x), np.mean(x)
y = n
y[y==0]= 1e-8


popt, pcov = optimize.curve_fit(Gaussian,x,y) 

# Curve-fit error method
error = [] 
for i in range(len(popt)):
    try:
      error.append( np.absolute(pcov[i][i])**0.5)
    except:
      error.append( 0.00 )
pfit_curvefit = popt
perr_curvefit = np.array(error) 
print('\n Curve-fit Curve fit: %s' % pfit_curvefit)
print('\n Curve-fit Fit errors: %s' % perr_curvefit)

# Plot the fit
x_fit = np.linspace(x[0], x[-1], nbins)
y_gauss = Gaussian(x_fit, *popt)
# y_boot = Gaussian(x_fit, *pfit_bootstrap)
yerr=Gaussian(x_fit,*perr_curvefit)

plt.plot(x_fit, y_gauss,linestyle='--',linewidth=2,\
color='red',label='Gaussian')



plt.xlabel('Pixel Values')
plt.ylabel('Frequency')
plt.title('Npix = %s, Nbins = %s'% (npix,nbins))
plt.legend()
plt.show()