Mixture fitting library

pymixfit is a Python mixture fitting library. This library tries to fit a variety of candidate functions to presented measurement data to extract the different components that make up the sampled data points. This may be used to identify different mechanisms that contribute to formation of data.

This library is based on fitting capabilities of lmfit.

The whole idea of mixture fitting and fitting sums using least squares is built on the ideas of

• Fitting mixtures of statistical distributions
• Bundle adjustment methods in engineering photogrammetry

Installation

pip install pymixfit-tspspi

Currently implemented model functions

• Constant (mixfitfunctions.constant.MixfitFunctionConstantFactory)
  • $f(x) = \text{offset}$
• Linear (mixfitfunctions.linear.MixfitFunctionLinearFactory)
  • $f(x) = \text{slope} * x + \text{intercept}$
• Gaussian (mixfitfunctions.gaussian.MixfitFunctionGaussianFactory)
  • $f(x) = \text{amp} * \frac{1}{\sqrt{2 \pi}} e^{- \frac{1}{2} \left(\frac{x-\mu}{\sigma}\right)^2} + \text{offset}$
• Differential Gaussian (mixfitfunctions.differentialgaussian.MixfitFunctionDifferentialGaussian)
• Cauchy / Lorentz (mixfitfunctions.cauchy.MixfitFunctionCauchyFactory)
• Differential Cauchy / Lorentz (mixfitfunctions.cauchy.MixfitFunctionDifferentialCauchyFactory)

By default all functions are used as candidate functions by the mixture fitter

Usage

To use the mixture fitter simply instantiate the Mixfit class and perform a fit function. It's a good idea to apply one of the abort conditions, else the fitter only aborts when it reaches the point of no further improvements. Possible abort conditions are:

• stopError is the improvement of the $\chi^2$. As soon as the fit quality of the fit goes below the threashold the process is aborted
• maxIterations limits the number of components that are fit

One may supply a list of allowed functions as well as their limits using the allowed argument:

Example

For more advanced examples take a look at the examples directory.

Fitting arbitrary models into our data

import numpy as np
import matplotlib.pyplot as plt

from mixfit.mixfit import Mixfit

data = np.load("examplefile.npz")

# Just a way to get the sample data
# This data includes different runs capturing
# in-phase and quadrature channels during
# frequency sweeps. The x axis is the frequencies,
# the fitted data is the mean of all runs
x = data["f_RF"]
I = data["sigI"].mean(1)

# Now create the mixture fitter for _all_
# models
mf = Mixfit(
	maxIterations = 4,
	stopError = 0.05
)

# And execute
resI = mf.fit(x, I)

# Plot
fig, ax = plt.subplots(1, 2, figsize=(6.4*2, 4.8))
ax[0].plot(x*2, I) # We plot raw data
ax[0].plot(x*2, resI(x)) # and our fit result
ax[0].grid()

ax[1].plot(resI._chis)
ax[1].grid()

plt.show()

Running this code yields the following decomposition:

DiffGaussian(amp=6.710041629819328+-4.470775516222519, mu=175.76446887225788+-0.1454700003529027, sigma=1.4076661399565236+-0.3343414565050647, offset=-23320382.44684337+-112828498842278.73)
DiffGaussian(amp=2.774258665757228+-1.4958867327164893, mu=179.76706853968935+-0.4050248108850253, sigma=1.2976513505933047+-0.3279503072202676, offset=17745816.52197658+-175430109563261.66)
Cauchy(amp=-2.7037880990536274+-3.5613251200337626, x0=179.17057600546437+-0.08406908277066111, gamma=0.6377217109551133+-0.3774710838448468, offset=5574563.378103231+-166637348925010.78)
DiffCauchy(amp=0.01760683178016082+-0.03633273296203317, x0=175.6555822822984+-0.028894691836587848, gamma=0.06706371066814047+-0.12080936119483864, offset=0.002912072266518264+-4552116.210404506)