doc_builtinmodels_nistgauss2.py

Out:

[[Model]]
    ((Model(gaussian, prefix='g1_') + Model(gaussian, prefix='g2_')) + Model(exponential, prefix='exp_'))
[[Fit Statistics]]
    # fitting method   = leastsq
    # function evals   = 37
    # data points      = 250
    # variables        = 8
    chi-square         = 1247.52821
    reduced chi-square = 5.15507524
    Akaike info crit   = 417.864631
    Bayesian info crit = 446.036318
[[Variables]]
    exp_amplitude:  99.0183270 +/- 0.53748905 (0.54%) (init = 94.53724)
    exp_decay:      90.9508890 +/- 1.10310483 (1.21%) (init = 111.1985)
    g1_amplitude:   4257.77343 +/- 42.3836427 (1.00%) (init = 3189.648)
    g1_center:      107.030956 +/- 0.15006873 (0.14%) (init = 106.5)
    g1_sigma:       16.6725765 +/- 0.16048227 (0.96%) (init = 14.5)
    g1_fwhm:        39.2609166 +/- 0.37790686 (0.96%) == '2.3548200*g1_sigma'
    g1_height:      101.880230 +/- 0.59217232 (0.58%) == '0.3989423*g1_amplitude/max(2.220446049250313e-16, g1_sigma)'
    g2_amplitude:   2493.41733 +/- 36.1696902 (1.45%) (init = 2818.337)
    g2_center:      153.270101 +/- 0.19466905 (0.13%) (init = 150)
    g2_sigma:       13.8069461 +/- 0.18679534 (1.35%) (init = 15)
    g2_fwhm:        32.5128728 +/- 0.43986939 (1.35%) == '2.3548200*g2_sigma'
    g2_height:      72.0455948 +/- 0.61722328 (0.86%) == '0.3989423*g2_amplitude/max(2.220446049250313e-16, g2_sigma)'
[[Correlations]] (unreported correlations are < 0.500)
    C(g1_amplitude, g1_sigma)   =  0.824
    C(g2_amplitude, g2_sigma)   =  0.815
    C(exp_amplitude, exp_decay) = -0.695
    C(g1_sigma, g2_center)      =  0.684
    C(g1_center, g2_amplitude)  = -0.669
    C(g1_center, g2_sigma)      = -0.652
    C(g1_amplitude, g2_center)  =  0.648
    C(g1_center, g2_center)     =  0.621
    C(g1_center, g1_sigma)      =  0.507
    C(exp_decay, g1_amplitude)  = -0.507

##
import warnings
warnings.filterwarnings("ignore")
##
# <examples/doc_nistgauss2.py>
import matplotlib.pyplot as plt
import numpy as np

from lmfit.models import ExponentialModel, GaussianModel

dat = np.loadtxt('NIST_Gauss2.dat')
x = dat[:, 1]
y = dat[:, 0]

exp_mod = ExponentialModel(prefix='exp_')
gauss1 = GaussianModel(prefix='g1_')
gauss2 = GaussianModel(prefix='g2_')


def index_of(arrval, value):
    """return index of array *at or below* value """
    if value < min(arrval):
        return 0
    return max(np.where(arrval <= value)[0])


ix1 = index_of(x, 75)
ix2 = index_of(x, 135)
ix3 = index_of(x, 175)

pars1 = exp_mod.guess(y[:ix1], x=x[:ix1])
pars2 = gauss1.guess(y[ix1:ix2], x=x[ix1:ix2])
pars3 = gauss2.guess(y[ix2:ix3], x=x[ix2:ix3])

pars = pars1 + pars2 + pars3
mod = gauss1 + gauss2 + exp_mod

out = mod.fit(y, pars, x=x)

print(out.fit_report(min_correl=0.5))

plt.plot(x, y, 'b')
plt.plot(x, out.init_fit, 'k--', label='initial fit')
plt.plot(x, out.best_fit, 'r-', label='best fit')
plt.legend(loc='best')
plt.show()
# <end examples/doc_nistgauss2.py>