# Random model¶

Generate a completely random film on Si to test fitting.

For example, the following generates a random film with three layers:

refl1d model.py 3 --preview


The model can also accept a noise level and a random number seed. Noise defaults to 3%. If no seed is given, a random seed is generated and printed so that the model can be regenerated.

To test the fitting engine, you will want to use –shake to set a random initial value before starting the fit:

refl1d model.py 3 –shake –fit=amoeba

You will find that the amoeba fitter does not work well for random models. Dream performs a bit better, able to recover models of 1-2 layers.

The –simrandom method is not very good for reflectometry models, where we would rather have layer thicknesses distributed as exponential values (occasional thick layers, lots of thinner layers), and with roughness small compared to the layer thickness. The –simrandom will still work, overriding the parameters we generate with uniformly distributed values.

There may be a more realistic choice for generated rho values than uniform in [-2, 10]; this may provide an unusual amount of contrast. Still, it is a good enough starting point, and does lead to some models with low contrast in neighbouring layers.

from refl1d.names import *


Process command line arguments to the model

n = int(sys.argv[1]) if len(sys.argv) > 1 else 2
noise = float(sys.argv[2]) if len(sys.argv) > 2 else 3.
seed = int(sys.argv[3]) if len(sys.argv) > 3 else np.random.randint(1, 9999)


Set the seed for the random number generator. Later we will print the seed, even if it was not set explicitly, so that interesting profiles can be regenerated.

np.random.seed(seed)


Set up a model with the desired number of layers. We will set the layer thickness and interfaces later.

materials = [SLD("L%d"%i, rho=1) for i in range(1, n+1)]
layers = [L(100, 5) for L in materials]
sample = silicon(0, 5) | layers | air


Set unlimited parameter ranges on those layers.

sample[0].interface.range(0, 200)
for L in layers:
L.material.rho.range(-2, 10)
L.thickness.range(0, 1000)
L.interface.range(0, 200)


Define the Q values at which to evaluate the model

T = numpy.linspace(0.1, 5, 100)
probe = NeutronProbe(T=T, dT=0.01, L=4.75, dL=0.0475)
M = Experiment(probe=probe, sample=sample)
problem = FitProblem(M)


Set random values for rho. This also sets thickness and interfaces, but these will be ignored.

problem.randomize()


Generate layer thicknesses, with film thickness of about 400, but lots of variability in layer sizes. Layers are limited to 950 so that the fit range can work. Exponential distribution isn’t suitable for single layer systems

for L in layers:
L.thickness.value = (min(np.random.exponential(400./np.sqrt(n)), 950)
if n > 1 else np.random.uniform(5, 950))


Set interface limits based on neighbouring layer thickness, with substrate and surface having infinite thickness. Choose an interface of at least 1 A

interfaces = [min(sample[i].thickness.value if i > 0 else np.inf,
sample[i+1].thickness.value if i < n else np.inf)
for i in range(n+1)]
for L, w in zip(sample[:n+1], interfaces):
L.interface.value = 1+np.random.exponential(w/7)
# Update the fit range if interface is excessively broad
if L.interface.value > 200:
L.interface.range(0, 2*L.interface.value)


Finally, generate some data with noise.

problem.simulate_data(noise=noise)
print("seed: %d"%seed)
print("target chisq: %s"%problem.chisq_str())
print(problem.summarize())