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from lmfit import Parameters, minimize, report_fit
from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign
from scipy.optimize import leastsq
try:
import pylab
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):
amp = pars['amp'].value
per = pars['period'].value
shift = pars['shift'].value
decay = pars['decay'].value
if abs(shift) > pi/2:
shift = shift - sign(shift)*pi
model = amp*sin(shift + x/per) * exp(-x*x*decay*decay)
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=13.0)
fit_params.add('period', value=2)
fit_params.add('shift', value=0.0)
fit_params.add('decay', value=0.02)
out = minimize(residual, fit_params, args=(x,), kws={'data':data})
fit = residual(fit_params, x)
print ' N fev = ', out.nfev
print out.chisqr, out.redchi, out.nfree
print '### Error Report:'
report_fit(fit_params)
if HASPYLAB:
pylab.plot(x, data, 'ro')
pylab.plot(x, fit, 'b')
pylab.show()
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