Tutorial

Simple Example

The example below shows how easy it is to define a model that we could fit to.

from symfit.api import Parameter, Variable

a = Parameter()
b = Parameter()
x = Variable()
model = a * x + b

Lets fit this model to some generated data.

from symfit.api import Fit
import numpy as np

xdata = np.linspace(0, 100, 100) # From 0 to 100 in 100 steps
a_vec = np.random.normal(15.0, scale=2.0, size=(100,))
b_vec = np.random.normal(100.0, scale=2.0, size=(100,))
ydata = a_vec * xdata + b_vec # Point scattered around the line 5 * x + 105

fit = Fit(model, xdata, ydata)
fit_result = fit.execute()
Linear Model Fit Data

Printing fit_result will give a full report on the values for every parameter, including the uncertainty, and quality of the fit.

Initial Guess

For fitting to work as desired you should always give a good initial guess for a parameter. The Parameter object can therefore be initiated with the following keywords:

  • value the initial guess value.
  • min Minimal value for the parameter.
  • max Maximal value for the parameter.
  • fixed Fix the value of the parameter during the fitting to value.

In the example above, we might change our Parameter‘s to the following after looking at a plot of the data:

a = Parameter(value=4, min=3, max=6)

Accessing the Results

A call to Fit.execute() returns a FitResults instance. This object holds all information about the fit. The fitting process does not modify the Parameter objects. In this example, a.value will still be 4.0 and not the value we obtain after fitting. To get the value of fit paramaters we can do:

>>> print(fit_result.params.a)
>>> 14.66946...
>>> print(fit_result.params.a_stdev)
>>> 0.3367571...
>>> print(fit_result.params.b)
>>> 104.6558...
>>> print(fit_result.params.b_stdev)
>>> 19.49172...
>>> print(fit_result.r_squared)
>>> 0.950890866472

For more FitResults, see the API docs. (Under construction.)

Evaluating the Model

With these parameters, we could now evaluate the model with these parameters so we can make a plot of it. In order to do this, we simply call the model with these values:

import matplotlib.pyplot as plt

y = model(x=xdata, a=fit_result.params.a, b=fit_result.params.b)
plt.plot(xdata, y)
plt.show()
Linear Model Fit

The model has to be called by keyword arguments to prevent any ambiguity. So the following does not work:

y = model(xdata, fit_result.params.a, fit_result.params.b)

To make life easier, there is a nice shorthand notation to immediately use a fit result:

y = model(x=xdata, **fit_result.params)

This unpacks the .params object as a dict. For more info view ParameterDict.