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doc_uvars_params.pyΒΆ
[[Model]]
((Model(gaussian, prefix='g1_') + Model(gaussian, prefix='g2_')) + Model(exponential, prefix='exp_'))
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 46
# data points = 250
# variables = 8
chi-square = 1247.52821
reduced chi-square = 5.15507524
Akaike info crit = 417.864631
Bayesian info crit = 446.036318
R-squared = 0.99648654
[[Variables]]
g1_amplitude: 4257.77390 +/- 42.3837959 (1.00%) (init = 4000)
g1_center: 107.030957 +/- 0.15006877 (0.14%) (init = 105)
g1_sigma: 16.6725785 +/- 0.16048211 (0.96%) (init = 15)
g2_amplitude: 2493.41716 +/- 36.1697062 (1.45%) (init = 2000)
g2_center: 153.270104 +/- 0.19466774 (0.13%) (init = 155)
g2_sigma: 13.8069453 +/- 0.18680153 (1.35%) (init = 15)
exp_amplitude: 99.0183277 +/- 0.53748650 (0.54%) (init = 100)
exp_decay: 90.9508838 +/- 1.10310767 (1.21%) (init = 100)
g1_fwhm: 39.2609214 +/- 0.37790648 (0.96%) == '2.3548200*g1_sigma'
g1_height: 101.880229 +/- 0.59217051 (0.58%) == '0.3989423*g1_amplitude/max(1e-15, g1_sigma)'
g2_fwhm: 32.5128709 +/- 0.43988398 (1.35%) == '2.3548200*g2_sigma'
g2_height: 72.0455939 +/- 0.61721985 (0.86%) == '0.3989423*g2_amplitude/max(1e-15, g2_sigma)'
[[Correlations]] (unreported correlations are < 0.500)
C(g1_amplitude, g1_sigma) = +0.8243
C(g2_amplitude, g2_sigma) = +0.8154
C(exp_amplitude, exp_decay) = -0.6946
C(g1_sigma, g2_center) = +0.6842
C(g1_center, g2_amplitude) = -0.6689
C(g1_center, g2_sigma) = -0.6520
C(g1_amplitude, g2_center) = +0.6477
C(g1_center, g2_center) = +0.6205
C(g1_center, g1_sigma) = +0.5075
C(g1_amplitude, exp_decay) = -0.5074
### Peak Area:
Peak1: 4257.77390+/-42.38380
Peak2: 2493.41716+/-36.16971
Sum : 6751.19106+/-46.50802
Correlation of peak1 and peak2 areas: -0.30712
Stderr Quadrature sum for peak1 and peak2 area2: 55.71924
Stderr of peak1 + peak2 area, with correlation: 46.50802
### Peak Centroid:
Peak Centroid: 124.10846+/-0.14074
[[Model]]
((Model(gaussian, prefix='g1_') + Model(gaussian, prefix='g2_')) + Model(exponential, prefix='exp_'))
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 46
# data points = 250
# variables = 8
chi-square = 1247.52821
reduced chi-square = 5.15507524
Akaike info crit = 417.864631
Bayesian info crit = 446.036318
R-squared = 0.99648654
[[Variables]]
g1_amplitude: 4257.77390 +/- 42.3837959 (1.00%) (init = 4000)
g1_center: 107.030957 +/- 0.15006877 (0.14%) (init = 105)
g1_sigma: 16.6725785 +/- 0.16048211 (0.96%) (init = 15)
g2_amplitude: 2493.41716 +/- 36.1697062 (1.45%) (init = 2000)
g2_center: 153.270104 +/- 0.19466774 (0.13%) (init = 155)
g2_sigma: 13.8069453 +/- 0.18680153 (1.35%) (init = 15)
exp_amplitude: 99.0183277 +/- 0.53748650 (0.54%) (init = 100)
exp_decay: 90.9508838 +/- 1.10310767 (1.21%) (init = 100)
g1_fwhm: 39.2609214 +/- 0.37790648 (0.96%) == '2.3548200*g1_sigma'
g1_height: 101.880229 +/- 0.59217051 (0.58%) == '0.3989423*g1_amplitude/max(1e-15, g1_sigma)'
g2_fwhm: 32.5128709 +/- 0.43988398 (1.35%) == '2.3548200*g2_sigma'
g2_height: 72.0455939 +/- 0.61721985 (0.86%) == '0.3989423*g2_amplitude/max(1e-15, g2_sigma)'
post_area: 6751.19106 +/- 46.5080249 (0.69%) == 'g1_amplitude + g2_amplitude'
post_centroid: 124.108459 +/- 0.14074482 (0.11%) == '(g1_amplitude*g1_center+ g2_amplitude*g2_center)/(g1_amplitude + g2_amplitude)'
[[Correlations]] (unreported correlations are < 0.500)
C(g1_amplitude, g1_sigma) = +0.8243
C(g2_amplitude, g2_sigma) = +0.8154
C(exp_amplitude, exp_decay) = -0.6946
C(g1_sigma, g2_center) = +0.6842
C(g1_center, g2_amplitude) = -0.6689
C(g1_center, g2_sigma) = -0.6520
C(g1_amplitude, g2_center) = +0.6477
C(g1_center, g2_center) = +0.6205
C(g1_center, g1_sigma) = +0.5075
C(g1_amplitude, exp_decay) = -0.5074
[[Model]]
((Model(gaussian, prefix='g1_') + Model(gaussian, prefix='g2_')) + Model(exponential, prefix='exp_'))
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 46
# data points = 250
# variables = 8
chi-square = 1247.52821
reduced chi-square = 5.15507524
Akaike info crit = 417.864631
Bayesian info crit = 446.036318
R-squared = 0.99648654
[[Variables]]
g1_amplitude: 4257.77390 +/- 42.3837959 (1.00%) (init = 4000)
g1_center: 107.030957 +/- 0.15006877 (0.14%) (init = 105)
g1_sigma: 16.6725785 +/- 0.16048211 (0.96%) (init = 15)
g2_amplitude: 2493.41716 +/- 36.1697062 (1.45%) (init = 2000)
g2_center: 153.270104 +/- 0.19466774 (0.13%) (init = 155)
g2_sigma: 13.8069453 +/- 0.18680153 (1.35%) (init = 15)
exp_amplitude: 99.0183277 +/- 0.53748650 (0.54%) (init = 100)
exp_decay: 90.9508838 +/- 1.10310767 (1.21%) (init = 100)
g1_fwhm: 39.2609214 +/- 0.37790648 (0.96%) == '2.3548200*g1_sigma'
g1_height: 101.880229 +/- 0.59217051 (0.58%) == '0.3989423*g1_amplitude/max(1e-15, g1_sigma)'
g2_fwhm: 32.5128709 +/- 0.43988398 (1.35%) == '2.3548200*g2_sigma'
g2_height: 72.0455939 +/- 0.61721985 (0.86%) == '0.3989423*g2_amplitude/max(1e-15, g2_sigma)'
area: 6751.19106 +/- 46.5080249 (0.69%) == 'g1_amplitude + g2_amplitude'
centroid: 124.108459 +/- 0.14074482 (0.11%) == '(g1_amplitude*g1_center+ g2_amplitude*g2_center)/(g1_amplitude + g2_amplitude)'
post_area: 6751.19106 +/- 46.5080249 (0.69%) == 'g1_amplitude + g2_amplitude'
post_centroid: 124.108459 +/- 0.14074482 (0.11%) == '(g1_amplitude*g1_center+ g2_amplitude*g2_center)/(g1_amplitude + g2_amplitude)'
[[Correlations]] (unreported correlations are < 0.500)
C(g1_amplitude, g1_sigma) = +0.8243
C(g2_amplitude, g2_sigma) = +0.8154
C(exp_amplitude, exp_decay) = -0.6946
C(g1_sigma, g2_center) = +0.6842
C(g1_center, g2_amplitude) = -0.6689
C(g1_center, g2_sigma) = -0.6520
C(g1_amplitude, g2_center) = +0.6477
C(g1_center, g2_center) = +0.6205
C(g1_center, g1_sigma) = +0.5075
C(g1_amplitude, exp_decay) = -0.5074
# <examples/doc_uvars_params.py>
import numpy as np
from lmfit.models import ExponentialModel, GaussianModel
dat = np.loadtxt('NIST_Gauss2.dat')
x = dat[:, 1]
y = dat[:, 0]
bkg = ExponentialModel(prefix='exp_')
gauss1 = GaussianModel(prefix='g1_')
gauss2 = GaussianModel(prefix='g2_')
mod = gauss1 + gauss2 + bkg
pars = mod.make_params(g1_center=105, g1_amplitude=4000, g1_sigma={'value': 15, 'min': 0},
g2_center=155, g2_amplitude=2000, g2_sigma={'value': 15, 'min': 0},
exp_amplitude=100, exp_decay=100)
out = mod.fit(y, pars, x=x)
print(out.fit_report(min_correl=0.5))
# Area and Centroid of the combined peaks
# option 1: from output uncertainties values
uvar_g1amp = out.uvars['g1_amplitude']
uvar_g2amp = out.uvars['g2_amplitude']
uvar_g1cen = out.uvars['g1_center']
uvar_g2cen = out.uvars['g2_center']
print("### Peak Area: ")
print(f"Peak1: {out.params['g1_amplitude'].value:.5f}+/-{out.params['g1_amplitude'].stderr:.5f}")
print(f"Peak2: {out.params['g2_amplitude'].value:.5f}+/-{out.params['g2_amplitude'].stderr:.5f}")
print(f"Sum : {(uvar_g1amp + uvar_g2amp):.5f}")
area_quadrature = np.sqrt(out.params['g1_amplitude'].stderr**2 + out.params['g2_amplitude'].stderr**2)
print(f"Correlation of peak1 and peak2 areas: {out.params['g1_amplitude'].correl['g2_amplitude']:.5f}")
print(f"Stderr Quadrature sum for peak1 and peak2 area2: {area_quadrature:.5f}")
print(f"Stderr of peak1 + peak2 area, with correlation: {(uvar_g1amp+uvar_g2amp).std_dev:.5f}")
print("### Peak Centroid: ")
centroid = (uvar_g1amp * uvar_g1cen + uvar_g2amp * uvar_g2cen) / (uvar_g1amp + uvar_g2amp)
print(f"Peak Centroid: {centroid:.5f}")
# option 2: define corresponding variables after fit
def post_fit(result):
"example post fit function"
result.params.add('post_area', expr='g1_amplitude + g2_amplitude')
result.params.add('post_centroid', expr='(g1_amplitude*g1_center+ g2_amplitude*g2_center)/(g1_amplitude + g2_amplitude)')
mod.post_fit = post_fit
out = mod.fit(y, pars, x=x)
print(out.fit_report(min_correl=0.5))
# option 3: define corresponding variables before fit
pars.add('area', expr='g1_amplitude + g2_amplitude')
pars.add('centroid', expr='(g1_amplitude*g1_center+ g2_amplitude*g2_center)/(g1_amplitude + g2_amplitude)')
out = mod.fit(y, pars, x=x)
print(out.fit_report(min_correl=0.5))
# <end examples/doc_uvars_params.py>
Total running time of the script: (0 minutes 0.056 seconds)