1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
#!/usr/bin/env python
# <examples/doc_fitting_emcee.py>
import numpy as np
import lmfit
try:
import matplotlib.pyplot as plt
HASPYLAB = True
except ImportError:
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(len(x)))
if HASPYLAB:
plt.plot(x, y, 'b')
# plt.savefig('../doc/_images/emcee_dbl_exp.png')
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')
# plt.savefig('../doc/_images/emcee_dbl_exp2.png')
plt.show()
# add a noise parameter
mi.params.add('noise', value=1, min=0.001, max=2)
def lnprob(p):
noise = p['noise']
return -0.5 * np.sum((residual(p) / noise)**2 + np.log(2 * np.pi * noise**2))
mini = lmfit.Minimizer(lnprob, mi.params)
res = mini.emcee(burn=300, steps=1000, thin=20, params=mi.params)
if HASPYLAB and HASCORNER:
emcee_corner = corner.corner(res.flatchain, labels=res.var_names,
truths=list(res.params.valuesdict().values()))
# emcee_corner.savefig('../doc/_images/emcee_corner.png')
plt.show()
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")
print('-----------------------------')
print(p)
if HASPYLAB:
plt.figure()
plt.plot(x, y)
plt.plot(x, residual(mi.params) + y, 'r', label='Nelder-Mead')
plt.plot(x, residual(res.params) + y, 'black', label='emcee')
plt.legend()
plt.show()
quantiles = np.percentile(res.flatchain['t1'], [2.28, 15.9, 50, 84.2, 97.7])
print("1 sigma spread", 0.5 * (quantiles[3] - quantiles[1]))
print("2 sigma spread", 0.5 * (quantiles[4] - quantiles[0]))
# <end of examples/doc_fitting_emcee.py>
|
