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#!/usr/bin/env python
import numpy as np
from scipy.interpolate import interp1d
from lmfit import Minimizer, Parameters, conf_interval, conf_interval2d
try:
import matplotlib.pyplot as plt
HASPYLAB = True
except ImportError:
HASPYLAB = False
np.random.seed(1)
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('decay', value=0.010)
p_true.add('amp2', value=-10.0)
p_true.add('decay2', value=0.050)
def residual(pars, x, data=None):
model = pars['amp'] * np.exp(-x*pars['decay'])
model += pars['amp2'] * np.exp(-x*pars['decay2'])
if data is None:
return model
return model - data
n = 200
xmin = 0.
xmax = 250.0
noise = np.random.normal(scale=0.7215, size=n)
x = np.linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=14.0)
fit_params.add('decay', value=0.010)
fit_params.add('amp2', value=-10.0)
fit_params.add('decay2', value=0.050)
mini = Minimizer(residual, fit_params,
fcn_args=(x,), fcn_kws={'data': data})
out = mini.leastsq()
ci, trace = conf_interval(mini, out, trace=True)
names = list(out.params.keys())
if HASPYLAB:
plt.rcParams['font.size'] = 8
plt.plot(x, data)
plt.figure()
cm = plt.cm.coolwarm
for i in range(4):
for j in range(4):
plt.subplot(4, 4, 16-j*4-i)
if i != j:
x, y, m = conf_interval2d(mini, out, names[i], names[j], 20, 20)
plt.contourf(x, y, m, np.linspace(0, 1, 10), cmap=cm)
plt.xlabel(names[i])
plt.ylabel(names[j])
x = trace[names[i]][names[i]]
y = trace[names[i]][names[j]]
pr = trace[names[i]]['prob']
s = np.argsort(x)
plt.scatter(x[s], y[s], c=pr[s], s=30, lw=1, cmap=cm)
else:
x = trace[names[i]][names[i]]
y = trace[names[i]]['prob']
t, s = np.unique(x, True)
f = interp1d(t, y[s], 'slinear')
xn = np.linspace(x.min(), x.max(), 50)
plt.plot(xn, f(xn), 'g', lw=1)
plt.xlabel(names[i])
plt.ylabel('prob')
plt.show()
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