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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
from lmfit import Parameters, Minimizer, report_fit
from lmfit.lineshapes import gaussian
def residual(pars, x, data=None):
g1 = gaussian(x, pars['a1'].value, pars['c1'].value, pars['w1'].value)
g2 = gaussian(x, pars['a2'].value, pars['c2'].value, pars['w2'].value)
model = g1 + g2
if data is None:
return model
return (model - data)
n = 601
xmin = 0.
xmax = 15.0
noise = random.normal(scale=.65, size=n)
x = linspace(xmin, xmax, n)
fit_params = Parameters()
fit_params.add_many(('a1', 12.0, True, None, None, None),
('c1', 5.3, True, None, None, None),
('w1', 1.0, True, None, None, None),
('a2', 9.1, True, None, None, None),
('c2', 8.1, True, None, None, None),
('w2', 2.5, True, None, None, None))
data = residual(fit_params, x) + noise
if HASPYLAB:
pylab.plot(x, data, 'r+')
fit_params = Parameters()
fit_params.add_many(('a1', 8.0, True, None, 14., None),
('c1', 5.0, True, None, None, None),
('w1', 0.7, True, None, None, None),
('a2', 3.1, True, None, None, None),
('c2', 8.8, True, None, None, None))
fit_params.add('w2', expr='2.5*w1')
myfit = Minimizer(residual, fit_params,
fcn_args=(x,), fcn_kws={'data':data})
myfit.prepare_fit()
init = residual(fit_params, x)
if HASPYLAB:
pylab.plot(x, init, 'b--')
myfit.leastsq()
print ' N fev = ', myfit.nfev
print myfit.chisqr, myfit.redchi, myfit.nfree
report_fit(fit_params)
fit = residual(fit_params, x)
if HASPYLAB:
pylab.plot(x, fit, 'k-')
pylab.show()
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