# Define a connection function with a field output¶

In this example, we define a function which has a vector input and a field output. The goal of this example is to show how to use the PointToFieldConnection to combine two functions. A detailed explanation of the model is presented here.

## 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))
```
```vertices = mesh.getVertices()
```

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
```
```4
```

Then we define the Python function which computes the altitude at each time value. This function has 5 inputs: z0, v0, m, c and zmin.

```def AltiFunc(X):
g = 9.81
z0 = X[0]
v0 = X[1]
m = X[2]
c = X[3]
zmin = X[4]
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, zmin)
return [[zeta[0]] for zeta in z]
```
```outputDimension = 1
altitudeWithFiveInputs = ot.PythonPointToFieldFunction(
5, mesh, outputDimension, AltiFunc
)
```

## Restrict the number of inputs¶

We define a function which has 4 inputs and 5 outputs: the 5th output zmin is set to zero.

```projectionFunction = ot.SymbolicFunction(
["z0", "v0", "m", "c"], ["z0", "v0", "m", "c", "0.0"]
)
```

Then we use the PointToFieldConnection to create a function which has 4 inputs and returns the output field.

```altitudeWithFourInputs = ot.PointToFieldConnection(
altitudeWithFiveInputs, projectionFunction
)
```

## 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 = altitudeWithFourInputs(inputSample)
```

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()
```