#!/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>