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"""
Fit Using differential_evolution Algorithm
==========================================
This example compares the ``leastsq`` and ``differential_evolution`` algorithms
on a fairly simple problem.
"""
import matplotlib.pyplot as plt
import numpy as np
import lmfit
def resid(params, x, ydata):
decay = params['decay'].value
offset = params['offset'].value
omega = params['omega'].value
amp = params['amp'].value
y_model = offset + amp * np.sin(x*omega) * np.exp(-x/decay)
return y_model - ydata
###############################################################################
# Generate synthetic data and set-up Parameters with initial values/boundaries:
decay = 5
offset = 1.0
amp = 2.0
omega = 4.0
np.random.seed(2)
x = np.linspace(0, 10, 101)
y = offset + amp*np.sin(omega*x) * np.exp(-x/decay)
yn = y + np.random.normal(size=y.size, scale=0.450)
params = lmfit.Parameters()
params.add('offset', 2.0, min=0, max=10.0)
params.add('omega', 3.3, min=0, max=10.0)
params.add('amp', 2.5, min=0, max=10.0)
params.add('decay', 1.0, min=0, max=10.0)
###############################################################################
# Perform the fits and show fitting results and plot:
o1 = lmfit.minimize(resid, params, args=(x, yn), method='leastsq')
print("# Fit using leastsq:")
lmfit.report_fit(o1)
###############################################################################
o2 = lmfit.minimize(resid, params, args=(x, yn), method='differential_evolution')
print("\n\n# Fit using differential_evolution:")
lmfit.report_fit(o2)
###############################################################################
plt.plot(x, yn, 'o', label='data')
plt.plot(x, yn+o1.residual, '-', label='leastsq')
plt.plot(x, yn+o2.residual, '--', label='diffev')
plt.legend()
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