Note
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Fit Using differential_evolution AlgorithmΒΆ
This example compares the leastsq
and differential_evolution
algorithms
on a fairly simple problem.
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:
Out:
# Fit using leastsq:
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 65
# data points = 101
# variables = 4
chi-square = 21.7961792
reduced chi-square = 0.22470288
Akaike info crit = -146.871969
Bayesian info crit = -136.411487
[[Variables]]
offset: 0.96333089 +/- 0.04735890 (4.92%) (init = 2)
omega: 3.98700839 +/- 0.02079709 (0.52%) (init = 3.3)
amp: 1.80253587 +/- 0.19401928 (10.76%) (init = 2.5)
decay: 5.76279753 +/- 1.04073348 (18.06%) (init = 1)
[[Correlations]] (unreported correlations are < 0.100)
C(amp, decay) = -0.7550
Out:
# Fit using differential_evolution:
[[Fit Statistics]]
# fitting method = differential_evolution
# function evals = 1425
# data points = 101
# variables = 4
chi-square = 21.7961792
reduced chi-square = 0.22470288
Akaike info crit = -146.871969
Bayesian info crit = -136.411487
## Warning: uncertainties could not be estimated:
this fitting method does not natively calculate uncertainties
and numdifftools is not installed for lmfit to do this. Use
`pip install numdifftools` for lmfit to estimate uncertainties
with this fitting method.
[[Variables]]
offset: 0.96333133 (init = 2)
omega: 3.98700854 (init = 3.3)
amp: 1.80252619 (init = 2.5)
decay: 5.76284507 (init = 1)
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()

Total running time of the script: ( 0 minutes 0.805 seconds)