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Minimal fitting example

On this page you will find a small example of a script that needs to be created to run a fitting. The scattering from spherical nano particles in the Born approximation is used here as an example. Short explanations follow below.

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"""
Minimal working fit examples: finds radius of sphere in Born approximation.
"""
import bornagain as ba
from bornagain import deg, angstrom, nm


def get_simulation(params):
    """
    Returns GISAS simulation for given set of parameters.
    """
    radius = params["radius"]

    sphere = ba.Particle(ba.HomogeneousMaterial("Particle", 6e-4, 2e-8),
                         ba.FormFactorFullSphere(radius))

    layer = ba.Layer(ba.HomogeneousMaterial("Air", 0.0, 0.0))
    layer.addLayout(ba.ParticleLayout(sphere))
    multi_layer = ba.MultiLayer()
    multi_layer.addLayer(layer)

    simulation = ba.GISASSimulation()
    simulation.setDetectorParameters(100, -1.0*deg, 1.0*deg,
                                     100, 0.0*deg, 2.0*deg)
    simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg)
    simulation.setSample(multi_layer)

    return simulation


def real_data():
    """
    Generating "experimental" data by running simulation with default parameters.
    """
    simulation = get_simulation({'radius': 5.0*nm})
    simulation.runSimulation()
    return simulation.result().array()


def run_fitting():
    """
    Setups and runs fit.
    """
    fit_objective = ba.FitObjective()
    fit_objective.addSimulationAndData(get_simulation, real_data())
    fit_objective.initPrint(10)

    params = ba.Parameters()
    params.add("radius", 4.*nm, min=0.01)

    minimizer = ba.Minimizer()
    result = minimizer.minimize(fit_objective.evaluate, params)
    fit_objective.finalize(result)


if __name__ == '__main__':
    run_fitting()

Simulation builder

Simulation builder is represented by the get_simulation function. Its main task is to generate a new simulation object for the given values of the fit parameters. In the given case it returns a GISAS simulation object with a beam, detector and user sample defined. Here we are simulating the scattering from spherical nano particles in the Born approximation. The function has one free parameter: the radius of the spheres in nanometers. This is the value we will try to find in the course of the minimization.

The data

Experimental data is represented by the real_data function. It returns a 2D numpy array with intensity values obtained from the same simulation with the radius of the spheres equals to $5~nm$.

Fit objective

The method FitObjective.addSimulationAndData is used to put the model and the data in correspondence. Please pay attention on how get_simulation (no brackets) and real_data() (with brackets) are used. The absence of brackets in get_simulation means that we pass a callable object (aka function pointer) to FitObjective. During the fit it will be used on every iteration to generate a new simulation for every new set of fit parameter values.

Fit parameters and minimizers

The fit parameters collection contains a single fit parameter with the name radius and a starting value of $4~nm$. The method FitObjective.evaluate serves as the objective function. It is passed to the minimizer together with the fit parameters.