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#!/usr/bin/env python
from lmfit import Parameters, Minimizer, conf_interval, conf_interval2d, minimize
import numpy as np
from scipy.interpolate import interp1d
try:
import pylab
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):
amp = pars['amp'].value
decay = pars['decay'].value
amp2 = pars['amp2'].value
decay2 = pars['decay2'].value
model = amp*np.exp(-x*decay)+amp2*np.exp(-x*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)
out = minimize(residual, fit_params, args=(x,), kws={'data':data})
out.leastsq()
ci, trace = conf_interval(out, trace=True)
names=fit_params.keys()
if HASPYLAB:
pylab.rcParams['font.size']=8
pylab.plot(x,data)
pylab.figure()
cm=pylab.cm.coolwarm
for i in range(4):
for j in range(4):
pylab.subplot(4,4,16-j*4-i)
if i!=j:
x,y,m = conf_interval2d(out,names[i],names[j],20,20)
pylab.contourf(x,y,m,np.linspace(0,1,10),cmap=cm)
pylab.xlabel(names[i])
pylab.ylabel(names[j])
x=trace[names[i]][names[i]]
y=trace[names[i]][names[j]]
pr=trace[names[i]]['prob']
s=np.argsort(x)
pylab.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)
pylab.plot(xn,f(xn),'g',lw=1)
pylab.xlabel(names[i])
pylab.ylabel('prob')
pylab.show()
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