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#!/usr/bin/env python
from lmfit import Parameters, Minimizer
import numpy as np
try:
import pylab
HASPYLAB = True
except ImportError:
HASPYLAB = False
def func(pars, x, data=None):
a = pars['a'].value
b = pars['b'].value
c = pars['c'].value
model=a * np.exp(-b * x)+c
if data is None:
return model
return (model - data)
def dfunc(pars, x, data=None):
a = pars['a'].value
b = pars['b'].value
c = pars['c'].value
v = np.exp(-b*x)
return [v, -a*x*v, np.ones(len(x))]
def f(var, x):
return var[0]* np.exp(-var[1] * x)+var[2]
params1 = Parameters()
params1.add('a', value=10)
params1.add('b', value=10)
params1.add('c', value=10)
params2 = Parameters()
params2.add('a', value=10)
params2.add('b', value=10)
params2.add('c', value=10)
a, b, c = 2.5, 1.3, 0.8
x = np.linspace(0,4,50)
y = f([a, b, c], x)
data = y + 0.15*np.random.normal(size=len(x))
# fit without analytic derivative
min1 = Minimizer(func, params1, fcn_args=(x,), fcn_kws={'data':data})
min1.leastsq()
fit1 = func(params1, x)
# fit with analytic derivative
min2 = Minimizer(func, params2, fcn_args=(x,), fcn_kws={'data':data})
min2.leastsq(Dfun=dfunc, col_deriv=1)
fit2 = func(params2, x)
print '''Comparison of fit to exponential decay
with and without analytic derivatives, to
model = a*exp(-b*x) + c
for a = %.2f, b = %.2f, c = %.2f
==============================================
Statistic/Parameter| Without | With |
----------------------------------------------
N Function Calls | %3i | %3i |
Chi-square | %.4f | %.4f |
a | %.4f | %.4f |
b | %.4f | %.4f |
c | %.4f | %.4f |
----------------------------------------------
''' % (a, b, c,
min1.nfev, min2.nfev,
min1.chisqr, min2.chisqr,
params1['a'].value, params2['a'].value,
params1['b'].value, params2['b'].value,
params1['c'].value, params2['c'].value )
if HASPYLAB:
pylab.plot(x, data, 'ro')
pylab.plot(x, fit1, 'b')
pylab.plot(x, fit2, 'k')
pylab.show()
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