Define a function with a field output: the viscous free fall example

In this example, we define a function which has a vector input and a field output. This is why we use the PythonPointToFieldFunction class to create the associated function and propagate the uncertainties through it.

We consider a viscous free fall as explained here.

Define the model

import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
from openturns.usecases import viscous_free_fall

ot.Log.Show(ot.Log.NONE)

Load the viscous free fall example.

vff = viscous_free_fall.ViscousFreeFall()
distribution = vff.distribution
model = vff.model

Sample trajectories

In order to sample trajectories, we use the getSample method of the input distribution and apply the field function.

size = 10
inputSample = distribution.getSample(size)
outputSample = model(inputSample)

ot.ResourceMap.SetAsUnsignedInteger("Drawable-DefaultPalettePhase", size)

Draw some curves.

graph = outputSample.drawMarginal(0)
graph.setTitle("Viscous free fall: %d trajectories" % (size))
graph.setXTitle(r"$t$")
graph.setYTitle(r"$z$")
view = viewer.View(graph)
plt.show()

We see that the object first moves up and then falls down. Not all objects, however, achieve the same maximum altitude. We see that some trajectories reach a higher maximum altitude than others. Moreover, at the final time , one trajectory hits the ground: for this trajectory.

Reset default settings

ot.ResourceMap.Reload()