Note
Click here to download the full example code
Fit Specifying Different Reduce Function¶
The reduce_fcn
specifies how to convert a residual array to a scalar value
for the scalar minimizers. The default value is None (i.e., “sum of squares of
residual”) - alternatives are: negentropy
, neglogcauchy
, or a
user-specified callable
. For more information please refer to:
https://lmfit.github.io/lmfit-py/fitting.html#using-the-minimizer-class
Here, we use as an example the Student’s t log-likelihood for robust fitting of data with outliers.
Generate synthetic data with noise/outliers and initialize fitting Parameters:
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=0.250)
outliers = np.random.randint(int(len(x)/3.0), len(x), int(len(x)/12))
yn[outliers] += 5*np.random.random(len(outliers))
params = lmfit.Parameters()
params.add('offset', 2.0)
params.add('omega', 3.3)
params.add('amp', 2.5)
params.add('decay', 1.0, min=0)
Perform fits using the L-BFGS-B
method with different reduce_fcn
:
Out:
# Fit using sum of squares:
[[Fit Statistics]]
# fitting method = L-BFGS-B
# function evals = 130
# data points = 101
# variables = 4
chi-square = 32.1674767
reduced chi-square = 0.33162347
Akaike info crit = -107.560626
Bayesian info crit = -97.1001440
## 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: 1.10392444 (init = 2)
omega: 3.97313428 (init = 3.3)
amp: 1.69977040 (init = 2.5)
decay: 7.65901653 (init = 1)
Out:
# Robust Fit, using log-likelihood with Cauchy PDF:
[[Fit Statistics]]
# fitting method = L-BFGS-B
# function evals = 135
# data points = 101
# variables = 4
chi-square = 33.5081340
reduced chi-square = 0.34544468
Akaike info crit = -103.436563
Bayesian info crit = -92.9760805
## 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: 1.02005973 (init = 2)
omega: 3.98224425 (init = 3.3)
amp: 1.83231462 (init = 2.5)
decay: 5.77327185 (init = 1)
plt.plot(x, y, 'o', label='true function')
plt.plot(x, yn, '--*', label='with noise+outliers')
plt.plot(x, yn+o1.residual, '-', label='sum of squares fit')
plt.plot(x, yn+o2.residual, '-', label='robust fit')
plt.legend()

Total running time of the script: ( 0 minutes 0.344 seconds)