https://github.com/lmfit/lmfit-py
Tip revision: c06666c495d50f2abd12bfe7974adc553876e5c5 authored by Matthew Newville on 11 February 2018, 14:08:45 UTC
update doc for 5 digit-precision fit statistics
update doc for 5 digit-precision fit statistics
Tip revision: c06666c
lmfit_and_emcee.py
#!/usr/bin/env python
import emcee
import numpy as np
import lmfit
try:
import matplotlib.pyplot as plt
HASPYLAB = True
except ImportError:
HASPYLAB = False
def create_prior(params):
"""
emccee uses a uniform prior for every variable.
Here we create a functions which checks the bounds
and returns np.inf if a value is outside of its
allowed range. WARNING: A uniform prior may not be
what you want!
"""
none_to_inf = lambda x, sign=1: sign*np.inf if x is None else x
lower_bounds = np.array([none_to_inf(i.min, -1) for i in params.values() if i.vary])
upper_bounds = np.array([none_to_inf(i.max, 1) for i in params.values() if i.vary])
def bounds_prior(values):
values = np.asarray(values)
is_ok = np.all((lower_bounds < values) & (values < upper_bounds))
return 0 if is_ok else -np.inf
return bounds_prior
def create_lnliklihood(mini, sigma=None):
"""create a normal-likihood from the residuals"""
def lnprob(vals, sigma=sigma):
for v, p in zip(vals, [p for p in mini.params.values() if p.vary]):
p.value = v
residuals = mini.residual
if not sigma:
# sigma is either the error estimate or it will
# be part of the sampling.
sigma = vals[-1]
val = -0.5*np.sum(np.log(2*np.pi*sigma**2) + (residuals/sigma)**2)
return val
return lnprob
def starting_guess(mini, estimate_sigma=True):
"""
Use best a fit as a starting point for the samplers.
If no sigmas are given, it is assumed that
all points have the same uncertainty which will
be also part of the sampled parameters.
"""
vals = [i.value for i in mini.params.values() if i.vary]
if estimate_sigma:
vals.append(mini.residual.std())
return vals
def create_all(mini, sigma=None):
"""
creates the log-poposterior function from a minimizer.
sigma should is either None or an array with the
1-sigma uncertainties of each residual point. If None,
sigma will be assumed the same for all residuals and
is added to the sampled parameters.
"""
sigma_given = not sigma is None
lnprior = create_prior(mini.params)
lnprob = create_lnliklihood(mini, sigma=sigma)
guess = starting_guess(mini, not sigma_given)
if sigma_given:
func = lambda x: lnprior(x[:]) + lnprob(x)
else:
func = lambda x: lnprior(x[:-1]) + lnprob(x)
return func, guess
# setup example problem.
params = lmfit.Parameters()
params.add_many(('a', 5),
('b', -5),
('t1', 1, 1, 0),
('t2', 15, 1, 0))
x = np.linspace(0, 20, 350)
a, b, t1, t2 = 2, 3, 2, 10 # Real values
y_true = a * np.exp(-x/t1) + b * np.exp(-x/t2)
sigma = 0.02
y = y_true + np.random.randn(x.size)*sigma
def residuals(paras):
a = paras['a'].value
b = paras['b'].value
t1 = paras['t1'].value
t2 = paras['t2'].value
return a * np.exp(-x/t1) + b * np.exp(-x/t2) - y
# fit the data with lmfit.
mini = lmfit.Minimizer(residuals, params)
result = mini.leastsq()
lmfit.report_errors(result.params)
# create lnfunc and starting distribution.
lnfunc, guess = create_all(result)
nwalkers, ndim = 30, len(guess)
p0 = emcee.utils.sample_ball(guess, 0.1*np.array(guess), nwalkers)
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnfunc)
steps = 500
sampler.run_mcmc(p0, steps)
if HASPYLAB:
fig, axes = plt.subplots(5, 1, sharex=True, figsize=(8, 9))
for (i, name, rv) in zip(range(5), list(params.keys()) + ['sigma'], [a, b, t1, t2, sigma]):
axes[i].plot(sampler.chain[:, :, i].T, color="k", alpha=0.05)
axes[i].yaxis.set_major_locator(plt.MaxNLocator(5))
axes[i].axhline(rv, color="#888888", lw=2)
axes[i].set_ylabel("$%s$" % name)
axes[-1].set_xlabel("Steps")
plt.figure()
try:
import corner # use pip install corner
burnin = 100
samples = sampler.chain[:, burnin:, :].reshape((-1, ndim))
corner.corner(samples, labels=list(result.params.keys())+['sigma'],
truths=[a, b, t1, t2, sigma])
except ImportError:
print("Please install corner for a nice overview graphic")