.. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_functional_modeling_field_functions_plot_viscous_fall_field_function.py: 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 :ref:`here `. Define the model ---------------- .. code-block:: default from __future__ import print_function import openturns as ot import openturns.viewer as viewer from matplotlib import pylab as plt import numpy as np ot.Log.Show(ot.Log.NONE) We first define the time grid associated with the model. .. code-block:: default tmin=0.0 # Minimum time tmax=12. # Maximum time gridsize=100 # Number of time steps mesh = ot.IntervalMesher([gridsize-1]).build(ot.Interval(tmin, tmax)) The `getVertices` method returns the time values in this mesh. .. code-block:: default vertices = mesh.getVertices() vertices[0:5] .. raw:: html
v0 0 0.1212121 0.2424242 0.3636364 0.4848485

Creation of the input distribution. .. code-block:: default distZ0 = ot.Uniform(100.0, 150.0) distV0 = ot.Normal(55.0, 10.0) distM = ot.Normal(80.0, 8.0) distC = ot.Uniform(0.0, 30.0) distribution = ot.ComposedDistribution([distZ0, distV0, distM, distC]) .. code-block:: default dimension = distribution.getDimension() dimension .. rst-class:: sphx-glr-script-out Out: .. code-block:: none 4 Then we define the Python function which computes the altitude at each time value. In order to compute all altitudes with a vectorized evaluation, we first convert the vertices into a `numpy` `array` and use the `numpy` function `exp` and `maximum`: this increases the evaluation performance of the script. .. code-block:: default def AltiFunc(X): g = 9.81 z0 = X v0 = X m = X c = X tau = m / c vinf = - m * g / c t = np.array(vertices) z = z0 + vinf * t + tau * (v0 - vinf) * (1 - np.exp( - t / tau)) z = np.maximum(z,0.) return [[zeta] for zeta in z] In order to create a `Function` from this Python function, we use the `PythonPointToFieldFunction` class. Since the altitude is the only output field, the third argument `outputDimension` is equal to `1`. If we had computed the speed as an extra output field, we would have set `2` instead. .. code-block:: default outputDimension = 1 alti = ot.PythonPointToFieldFunction(dimension, mesh, outputDimension, AltiFunc) Sample trajectories ------------------- In order to sample trajectories, we use the `getSample` method of the input distribution and apply the field function. .. code-block:: default size = 10 inputSample = distribution.getSample(size) outputSample = alti(inputSample) .. code-block:: default ot.ResourceMap.SetAsUnsignedInteger('Drawable-DefaultPalettePhase', size) Draw some curves. .. code-block:: default 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() .. image:: /auto_functional_modeling/field_functions/images/sphx_glr_plot_viscous_fall_field_function_001.png :alt: Viscous free fall: 10 trajectories :class: sphx-glr-single-img 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 :math:`t_{max}`, one trajectory hits the ground: :math:`z(t_{max})=0` for this trajectory. .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.093 seconds) .. _sphx_glr_download_auto_functional_modeling_field_functions_plot_viscous_fall_field_function.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_viscous_fall_field_function.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_viscous_fall_field_function.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_