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# <examples/doc_fitting_emcee.py>
import numpy as np
import lmfit
try:
import matplotlib.pyplot as plt
HASPYLAB = True
except ImportError:
HASPYLAB = False
HASPYLAB = False
try:
import corner
HASCORNER = True
except ImportError:
HASCORNER = False
x = np.linspace(1, 10, 250)
np.random.seed(0)
y = (3.0*np.exp(-x/2) - 5.0*np.exp(-(x-0.1) / 10.) +
0.1*np.random.randn(x.size))
if HASPYLAB:
plt.plot(x, y, 'b')
plt.show()
p = lmfit.Parameters()
p.add_many(('a1', 4), ('a2', 4), ('t1', 3), ('t2', 3., True))
def residual(p):
v = p.valuesdict()
return v['a1']*np.exp(-x/v['t1']) + v['a2']*np.exp(-(x-0.1) / v['t2']) - y
mi = lmfit.minimize(residual, p, method='nelder', nan_policy='omit')
lmfit.printfuncs.report_fit(mi.params, min_correl=0.5)
if HASPYLAB:
plt.figure()
plt.plot(x, y, 'b')
plt.plot(x, residual(mi.params) + y, 'r', label='best fit')
plt.legend(loc='best')
plt.show()
# Place bounds on the ln(sigma) parameter that emcee will automatically add
# to estimate the true uncertainty in the data since is_weighted=False
mi.params.add('__lnsigma', value=np.log(0.1), min=np.log(0.001), max=np.log(2))
res = lmfit.minimize(residual, method='emcee', nan_policy='omit', burn=300,
steps=1000, thin=20, params=mi.params, is_weighted=False,
progress=False)
if HASPYLAB and HASCORNER:
emcee_corner = corner.corner(res.flatchain, labels=res.var_names,
truths=list(res.params.valuesdict().values()))
plt.show()
if HASPYLAB:
plt.plot(res.acceptance_fraction)
plt.xlabel('walker')
plt.ylabel('acceptance fraction')
plt.show()
if hasattr(res, "acor"):
print("Autocorrelation time for the parameters:")
print("----------------------------------------")
for i, par in enumerate(p):
print(par, res.acor[i])
print("\nmedian of posterior probability distribution")
print('--------------------------------------------')
lmfit.report_fit(res.params)
# find the maximum likelihood solution
highest_prob = np.argmax(res.lnprob)
hp_loc = np.unravel_index(highest_prob, res.lnprob.shape)
mle_soln = res.chain[hp_loc]
for i, par in enumerate(p):
p[par].value = mle_soln[i]
print('\nMaximum Likelihood Estimation from emcee ')
print('-------------------------------------------------')
print('Parameter MLE Value Median Value Uncertainty')
fmt = ' {:5s} {:11.5f} {:11.5f} {:11.5f}'.format
for name, param in p.items():
print(fmt(name, param.value, res.params[name].value,
res.params[name].stderr))
if HASPYLAB:
plt.figure()
plt.plot(x, y, 'b')
plt.plot(x, residual(mi.params) + y, 'r', label='Nelder-Mead')
plt.plot(x, residual(res.params) + y, 'k--', label='emcee')
plt.legend()
plt.show()
print('\nError Estimates from emcee ')
print('------------------------------------------------------')
print('Parameter -2sigma -1sigma median +1sigma +2sigma ')
for name in p.keys():
quantiles = np.percentile(res.flatchain[name],
[2.275, 15.865, 50, 84.135, 97.275])
median = quantiles[2]
err_m2 = quantiles[0] - median
err_m1 = quantiles[1] - median
err_p1 = quantiles[3] - median
err_p2 = quantiles[4] - median
fmt = ' {:5s} {:8.4f} {:8.4f} {:8.4f} {:8.4f} {:8.4f}'.format
print(fmt(name, err_m2, err_m1, median, err_p1, err_p2))
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