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import sys
from numpy import linspace, zeros, sin, exp, random, sqrt, pi, sign
from lmfit import Parameters, Parameter, Minimizer, report_fit
from lmfit.lineshapes import gaussian, lorentzian, pvoigt
try:
import matplotlib
matplotlib.use('WXAGG')
import pylab
HASPYLAB = True
except ImportError:
HASPYLAB = False
def per_iteration(pars, i, resid, x, *args, **kws):
if i < 10 or i % 10 == 0:
print( '====== Iteration ', i)
for p in pars.values():
print( p.name , p.value)
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'].value,
pars['cen_g'].value, pars['wid_g'].value)
yl = lorentzian(x, pars['amp_l'].value,
pars['cen_l'].value, pars['wid_l'].value)
frac = pars['frac'].value
slope = pars['line_slope'].value
offset = pars['line_off'].value
model = (1-frac) * yg + frac * yl + offset + x * slope
if data is None:
return model
if sigma is None:
return (model - data)
return (model - data)/sigma
n = 601
xmin = 0.
xmax = 20.0
x = linspace(xmin, xmax, n)
p_true = Parameters()
p_true.add('amp_g', value=21.0)
p_true.add('cen_g', value=8.1)
p_true.add('wid_g', value=1.6)
p_true.add('frac', value=0.37)
p_true.add('line_off', value=-1.023)
p_true.add('line_slope', value=0.62)
data = (pvoigt(x, p_true['amp_g'].value, p_true['cen_g'].value,
p_true['wid_g'].value, p_true['frac'].value) +
random.normal(scale=0.23, size=n) +
x*p_true['line_slope'].value + p_true['line_off'].value )
if HASPYLAB:
pylab.plot(x, data, 'r+')
pfit = [Parameter(name='amp_g', value=10),
Parameter(name='amp_g', value=10.0),
Parameter(name='cen_g', value=9),
Parameter(name='wid_g', value=1),
Parameter(name='frac', value=0.50),
Parameter(name='amp_l', expr='amp_g'),
Parameter(name='cen_l', expr='cen_g'),
Parameter(name='wid_l', expr='wid_g'),
Parameter(name='line_slope', value=0.0),
Parameter(name='line_off', value=0.0)]
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit, # iter_cb=per_iteration,
fcn_args=(x,), fcn_kws={'sigma':sigma, 'data':data},
scale_covar=True)
myfit.prepare_fit()
init = residual(myfit.params, x)
if HASPYLAB:
pylab.plot(x, init, 'b--')
# fit with Nelder-Mead simplex method
supported_methods = ('BFGS', 'COBYLA', 'SLSQP', 'Powell', 'Nelder-Mead')
myfit.scalar_minimize(method='Nelder-Mead')
print(' Nfev = ', myfit.nfev)
# print( myfit.chisqr, myfit.redchi, myfit.nfree)
# report_fit(myfit.params, modelpars=p_true)
fit = residual(myfit.params, x)
if HASPYLAB:
pylab.plot(x, fit, 'k-')
pylab.show()
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