Create a parametric function

In this example, we show how to use the ParametricFunction class. This is a tool which is very convenient when we perform calibration, e.g. with NonLinearLeastSquaresCalibration or RandomWalkMetropolisHastings.

In this example we create a parametric function:

function from an existing “full” function:

import openturns as ot

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

Define the function

Create the function with all parameters d(E, F, L, I)

def d_func(X):
    E, F, L, II = X
    d = -F * L**3 / (3.0 * E * II)
    return [d]


beam = ot.PythonFunction(4, 1, d_func)
beam.setInputDescription(["E", "F", "L", "I"])

Evaluate d

x = [50.0, 1.0, 10.0, 5.0]
beam(x)

class=Point name=Unnamed dimension=1 values=[-1.33333]

In the physical model, the inputs and parameters are ordered as presented in the next table. Notice that there are no parameters in the physical model.

Index	Input variable
0	E
1	F
2	L
3	I

Index	Parameter
∅	∅

Table 1. Indices and names of the inputs and parameters of the physical model.

The next cell presents the description of the input variables and the description of the parameters of the physical model. We see that there is no parameter at this stage in this function.

print("Physical Model Inputs:", beam.getInputDescription())
print("Physical Model Parameters:", beam.getParameterDescription())

Physical Model Inputs: [E,F,L,I]
Physical Model Parameters: []

Define the parametric function

We create a ParametricFunction where the parameters are L and I which have the indices 2 and and 3 in the physical model.

Index	Input variable
0	E
1	F

Index	Parameter
0	L
1	I

Table 2. Indices and names of the inputs and parameters of the parametric model.

Create the indices of the frozen parameters (L,I) from the full parameter list

indices = [2, 3]

Create the values of the frozen parameters (L,I)

referencePoint = [10.0, 5.0]

Create the parametric function

beam_LI = ot.ParametricFunction(beam, indices, referencePoint)

The next cell presents the description of the input variables and the description of the parameters of the parametric function. We see that the parametric function has 2 parameters: L and I.

print("Physical Model Inputs:", beam_LI.getInputDescription())
print("Physical Model Parameters:", beam_LI.getParameterDescription())

Physical Model Inputs: [E,F]
Physical Model Parameters: [L,I]

Evaluate d on (E,F) with fixed parameters (L,I)

beam_LI([50.0, 1.0])

class=Point name=Unnamed dimension=1 values=[-1.33333]