Note
Click here to download the full example code
Using an ExpressionModelΒΆ
ExpressionModels allow a model to be built from a user-supplied expression. See: https://lmfit.github.io/lmfit-py/builtin_models.html#user-defined-models
import matplotlib.pyplot as plt
import numpy as np
from lmfit.models import ExpressionModel
Generate synthetic data for the user-supplied model:
x = np.linspace(-10, 10, 201)
amp, cen, wid = 3.4, 1.8, 0.5
y = amp * np.exp(-(x-cen)**2 / (2*wid**2)) / (np.sqrt(2*np.pi)*wid)
y = y + np.random.normal(size=x.size, scale=0.01)
Define the ExpressionModel and perform the fit:
gmod = ExpressionModel("amp * exp(-(x-cen)**2 /(2*wid**2))/(sqrt(2*pi)*wid)")
result = gmod.fit(y, x=x, amp=5, cen=5, wid=1)
this results in the following output:
print(result.fit_report())
plt.plot(x, y, 'bo')
plt.plot(x, result.init_fit, 'k--', label='initial fit')
plt.plot(x, result.best_fit, 'r-', label='best fit')
plt.legend(loc='best')
plt.show()

Out:
[[Model]]
Model(_eval)
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 52
# data points = 201
# variables = 3
chi-square = 0.01849367
reduced chi-square = 9.3402e-05
Akaike info crit = -1862.02001
Bayesian info crit = -1852.11010
[[Variables]]
amp: 3.40008409 +/- 0.00497993 (0.15%) (init = 5)
cen: 1.80137445 +/- 8.4449e-04 (0.05%) (init = 5)
wid: 0.49933503 +/- 8.4449e-04 (0.17%) (init = 1)
[[Correlations]] (unreported correlations are < 0.100)
C(amp, wid) = 0.577
/Users/Newville/Codes/lmfit-py/examples/example_expression_model.py:35: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
plt.show()
Total running time of the script: ( 0 minutes 0.144 seconds)