Fitting Data To A Custom Model In Python

Hi So I am fairly used to python but this is the first time I am using python for data analysis and I was wondering if you could shed some light on an issue I am having. I need to

Solution 1:

Here is code to restrict scipy's curve_fit parameters to within specified bounds. In this example, the first parameter's bounds are +/- infinity (unbounded), the second parameter's bounds are +/- 100 but the fitted parameter is within the bounds and fitted normally, and the third parameter is restricted by its bounds.

import numpy
import matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

xData = numpy.array([5.0, 6.1, 7.2, 8.3, 9.4])
yData = numpy.array([ 10.0,  18.4,  20.8,  23.2,  35.0])


def standardFunc(data, a, b, c):
    return a * data + b * data**2 + c


# some initial parameter values - must be within bounds
initialParameters = numpy.array([1.0, 1.0, 1.0])

# bounds on parameters - initial parameters must be within these
lowerBounds = (-numpy.Inf, -100.0, -5.0)
upperBounds = (numpy.Inf, 100.0, 5.0)
parameterBounds = [lowerBounds, upperBounds]

fittedParameters, pcov = curve_fit(standardFunc, xData, yData, initialParameters, bounds = parameterBounds)

# values for display of fitted function
a, b, c = fittedParameters

# for plotting the fitting results
xPlotData = numpy.linspace(min(xData), max(xData), 50)
y_plot = standardFunc(xPlotData, a, b, c)

plt.plot(xData, yData, 'D') # plot the raw data as a scatterplot
plt.plot(xPlotData, y_plot) # plot the equation using the fitted parameters
plt.show()

print('fitted parameters:', fittedParameters)