Note
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Fit with Algebraic ConstraintΒΆ

Out:
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 53
# data points = 601
# variables = 6
chi-square = 71878.3055
reduced chi-square = 120.803875
Akaike info crit = 2887.26503
Bayesian info crit = 2913.65660
[[Variables]]
amp_g: 21.1877707 +/- 0.32191819 (1.52%) (init = 10)
cen_g: 8.11125925 +/- 0.01162984 (0.14%) (init = 9)
wid_g: 1.20925847 +/- 0.01170853 (0.97%) (init = 1)
amp_tot: 30.6003727 +/- 0.36481395 (1.19%) (init = 20)
amp_l: 9.41260191 +/- 0.61672676 (6.55%) == 'amp_tot - amp_g'
cen_l: 9.61125925 +/- 0.01162984 (0.12%) == '1.5+cen_g'
wid_l: 2.41851694 +/- 0.02341706 (0.97%) == '2*wid_g'
line_slope: 0.49615727 +/- 0.00170178 (0.34%) (init = 0)
line_off: 0.04128604 +/- 0.02448064 (59.30%) (init = 0)
[[Correlations]] (unreported correlations are < 0.100)
C(amp_g, wid_g) = 0.866
C(amp_g, cen_g) = 0.750
C(line_slope, line_off) = -0.714
C(cen_g, amp_tot) = -0.695
C(cen_g, wid_g) = 0.623
C(amp_g, amp_tot) = -0.612
C(amp_tot, line_off) = -0.588
C(wid_g, amp_tot) = -0.412
C(cen_g, line_off) = 0.387
C(amp_g, line_off) = 0.183
C(amp_g, line_slope) = 0.183
C(wid_g, line_slope) = 0.174
import matplotlib.pyplot as plt
from numpy import linspace, random
from lmfit import Minimizer, Parameters
from lmfit.lineshapes import gaussian, lorentzian
from lmfit.printfuncs import report_fit
def residual(pars, x, sigma=None, data=None):
yg = gaussian(x, pars['amp_g'], pars['cen_g'], pars['wid_g'])
yl = lorentzian(x, pars['amp_l'], pars['cen_l'], pars['wid_l'])
slope = pars['line_slope']
offset = pars['line_off']
model = yg + yl + offset + x*slope
if data is None:
return model
if sigma is None:
return model - data
return (model - data) / sigma
random.seed(0)
x = linspace(0.0, 20.0, 601)
data = (gaussian(x, 21, 8.1, 1.2) +
lorentzian(x, 10, 9.6, 2.4) +
random.normal(scale=0.23, size=x.size) +
x*0.5)
pfit = Parameters()
pfit.add(name='amp_g', value=10)
pfit.add(name='cen_g', value=9)
pfit.add(name='wid_g', value=1)
pfit.add(name='amp_tot', value=20)
pfit.add(name='amp_l', expr='amp_tot - amp_g')
pfit.add(name='cen_l', expr='1.5+cen_g')
pfit.add(name='wid_l', expr='2*wid_g')
pfit.add(name='line_slope', value=0.0)
pfit.add(name='line_off', value=0.0)
sigma = 0.021 # estimate of data error (for all data points)
myfit = Minimizer(residual, pfit,
fcn_args=(x,), fcn_kws={'sigma': sigma, 'data': data},
scale_covar=True)
result = myfit.leastsq()
init = residual(pfit, x)
fit = residual(result.params, x)
report_fit(result)
plt.plot(x, data, 'r+')
plt.plot(x, init, 'b--', label='initial fit')
plt.plot(x, fit, 'k-', label='best fit')
plt.legend(loc='best')
plt.show()
Total running time of the script: ( 0 minutes 0.116 seconds)