"""
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 <use-case-viscous-fall>`.

# %%
# Define the model
# ----------------

# %%
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.

# %%
tmin = 0.0  # Minimum time
tmax = 12.0  # 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.

# %%
vertices = mesh.getVertices()
vertices[0:5]

# %%
# Creation of the input distribution.

# %%
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])

# %%
dimension = distribution.getDimension()
dimension


# %%
# 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.


# %%
def AltiFunc(X):
    g = 9.81
    z0 = X[0]
    v0 = X[1]
    m = X[2]
    c = X[3]
    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, 0.0)
    return [[zeta[0]] 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.

# %%
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.

# %%
size = 10
inputSample = distribution.getSample(size)
outputSample = alti(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 :math:`t_{max}`, one trajectory hits the ground: :math:`z(t_{max})=0` for this trajectory.

# %%
# Reset default settings
ot.ResourceMap.Reload()
