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Curve fitting with global optimization routines

Project description


Most curve fitting algorithms rely on local optimization routines. These demand good estimates of the fit parameters.

Instead, this module allows to use global optimization routines of scipy.optimize_ to minimize the squared deviation function.


.. highlight:: none

This module can be installed from PyPI ::

pip3 install curve_fit.annealing


Let us fit a beat signal with two sinus functions, with a total of 6 free parameters.

By default, the curve_fit function of this module will use the scipy.optimize.dual_annealing_ method to find the global optimum of the curve fitting problem. The dual annealing algorithm requires bounds for the fitting parameters. Other global optimization methods like scipy.optimize.basinhopping_ require an initial guess of the parameters instead.

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import numpy as np from matplotlib import pyplot as plt from curve_fit import annealing

def f(x,p): # Sum of two sinus functions return p[0]*np.sin(p[1]*x + p[2]) + p[3]*np.sin(p[4]*x+p[5])

xdata = np.linspace(-100,100,1000) ydata = f(xdata, [1, 1, 0, 1, 0.9, 0])

plt.plot(xdata, ydata, label='data') bounds=[[0,2],[0,2],[0,2np.pi],[0,2],[0,2],[0,2np.pi]]

result = annealing.curve_fit(f, xdata, ydata, bounds=bounds)

p_opt = result.x # optimal fit parameters ydata_res = f(xdata, p_opt) plt.plot(xdata, ydata_res, label='fit') plt.legend() plt.grid()

Or use scipy.optimize.basinhopping_ ::

result = annealing.curve_fit(f, xdata, ydata, method='basinhopping', x0=np.zeros(6))


curve_fit(f, xdata, ydata, [method='dual_annealing', args, kwargs])

Fit function f to data with selectable optimization method from scipy.optimize.

Parameters: f: callable The model function, f(xdata, p). The second argument holds the fitting parameters. xdata : array_like or object The independent variable where the data is measured. Should usually be an M-length sequence or an (k,M)-shaped array for functions with k predictors, but can actually be any object. ydata : array_like The dependent data, a length M array - nominally f(xdata, ...). method : str scipy.optimize method to use for non-linear least squares minimization. Default is 'dual_annealing'. args, kwargs : tuple and dict, optional Additional arguments passed to the optimization method.

Returns: Return OptimizeResult object. The x attribute holds the fitting parameters.

.. _scipy.optimize: .. _scipy.optimize.dual_annealing: .. _scipy.optimize.basinhopping:

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