## External Minimizers: Plotting Fit Progress

In this example we are demonstrating how to run a typical fitting task in BornAgain using a third party minimizer while plotting the results. As in our previous example, we use lmfit for sake of illustration.

To plot the fit progress, it is needed to use the lmfit iteration callback function. It will come handy to define the plotting callback function as a specialized class:

class Plotter:
"""
Adapts standard plotter for lmfit minimizer.
"""
def __init__(self, fit_objective, every_nth = 10):
self.fit_objective = fit_objective
self.plotter_gisas = ba.PlotterGISAS()
self.every_nth = every_nth

def __call__(self, params, iter, resid):
if iter%self.every_nth == 0:
self.plotter_gisas.plot(self.fit_objective)


An instance of this class is then passed to the lmfit minimization function:

    plotter = Plotter(fit_objective)
result = lmfit.minimize(fit_objective.evaluate_residuals, params, iter_cb=plotter)


The complete script to plot the fitting progress and the image produced by it are shown below.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117  #!/usr/bin/env python3 """ External minimize: using lmfit minimizers for BornAgain fits. Fit progress is plotted using lmfit iteration calbback function. """ import numpy as np from matplotlib import pyplot as plt import bornagain as ba from bornagain import deg, angstrom, nm import lmfit def get_sample(params): """ Returns a sample with cylinders and pyramids on a substrate, forming a hexagonal lattice. """ radius = params['radius'] lattice_length = params['length'] m_vacuum = ba.HomogeneousMaterial("Vacuum", 0, 0) m_substrate = ba.HomogeneousMaterial("Substrate", 6e-6, 2e-8) m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8) sphere_ff = ba.FormFactorFullSphere(radius) sphere = ba.Particle(m_particle, sphere_ff) particle_layout = ba.ParticleLayout() particle_layout.addParticle(sphere) interference = ba.InterferenceFunction2DLattice( ba.HexagonalLattice2D(lattice_length, 0)) pdf = ba.FTDecayFunction2DCauchy(10*nm, 10*nm, 0) interference.setDecayFunction(pdf) particle_layout.setInterferenceFunction(interference) vacuum_layer = ba.Layer(m_vacuum) vacuum_layer.addLayout(particle_layout) substrate_layer = ba.Layer(m_substrate, 0) multi_layer = ba.MultiLayer() multi_layer.addLayer(vacuum_layer) multi_layer.addLayer(substrate_layer) return multi_layer def get_simulation(params): """ Create and return GISAXS simulation with beam and detector defined """ simulation = ba.GISASSimulation() simulation.setDetectorParameters(100, -1*deg, 1*deg, 100, 0, 2*deg) simulation.setBeamParameters(1*angstrom, 0.2*deg, 0) simulation.beam().setIntensity(1e+08) simulation.setSample(get_sample(params)) return simulation def create_real_data(): """ Generating "real" data by adding noise to the simulated data. """ params = {'radius': 6*nm, 'length': 12*nm} simulation = get_simulation(params) simulation.runSimulation() # retrieving simulated data in the form of numpy array real_data = simulation.result().array() # spoiling simulated data with noise to produce "real" data np.random.seed(0) noise_factor = 0.1 noisy = np.random.normal(real_data, noise_factor*np.sqrt(real_data)) noisy[noisy < 0.1] = 0.1 return noisy class LMFITPlotter: """ Adapts standard plotter for lmfit minimizer. """ def __init__(self, fit_objective, every_nth=10): self.fit_objective = fit_objective self.plotter_gisas = ba_fitmonitor.PlotterGISAS() self.every_nth = every_nth def __call__(self, params, iter, resid): if iter % self.every_nth == 0: self.plotter_gisas.plot(self.fit_objective) def run_fitting(): """ main function to run fitting """ real_data = create_real_data() fit_objective = ba.FitObjective() fit_objective.addSimulationAndData(get_simulation, real_data, 1) fit_objective.initPrint(10) params = lmfit.Parameters() params.add('radius', value=7*nm, min=5*nm, max=8*nm) params.add('length', value=10*nm, min=8*nm, max=14*nm) plotter = LMFITPlotter(fit_objective) result = lmfit.minimize(fit_objective.evaluate_residuals, params, iter_cb=plotter) fit_objective.finalize(result) result.params.pretty_print() print(lmfit.fit_report(result)) if __name__ == '__main__': run_fitting() plt.show() 
lmfit_with_plotting.py