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#!/usr/bin/env python
from numpy import exp, linspace, pi, random, sign, sin
from lmfit import Parameters, minimize, report_fit
try:
import matplotlib.pyplot as plt
HASPYLAB = True
except ImportError:
HASPYLAB = False
p_true = Parameters()
p_true.add('amp', value=14.0)
p_true.add('period', value=5.33)
p_true.add('shift', value=0.123)
p_true.add('decay', value=0.010)
def residual(pars, x, data=None):
argu = (x * pars['decay'])**2
shift = pars['shift']
if abs(shift) > pi/2:
shift = shift - sign(shift)*pi
model = pars['amp'] * sin(shift + x/pars['period']) * exp(-argu)
if data is None:
return model
return model - data
n = 2500
xmin = 0.
xmax = 250.0
noise = random.normal(scale=0.7215, size=n)
x = linspace(xmin, xmax, n)
data = residual(p_true, x) + noise
fit_params = Parameters()
fit_params.add('amp', value=11.0, min=5, max=20)
fit_params.add('period', value=5., min=1., max=7)
fit_params.add('shift', value=.10, min=0.0, max=0.2)
fit_params.add('decay', value=6.e-3, min=0, max=0.1)
init = residual(fit_params, x)
out = minimize(residual, fit_params, method='lbfgsb', args=(x,),
kws={'data': data})
fit = residual(out.params, x)
for name, par in out.params.items():
nout = "%s:%s" % (name, ' '*(20-len(name)))
print("%s: %s (true=%s) " % (nout, par.value, p_true[name].value))
report_fit(fit_params)
if HASPYLAB:
plt.plot(x, data, 'r--')
plt.plot(x, init, 'k')
plt.plot(x, fit, 'b')
plt.show()
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