Documentation / Manuel utilisateur en Python :

The idea is that when you want to consider your model as linear, you might have to transform it a bit to have a correct linear behaviour and to express and compute the needed regressors. For this peculiar behaviour, one will rely on our use-case discussed in Section XIV.12.2. In this case, one should linearise the flowrate function as done here by writing:

where the regressor can be expressed as . From there, it is clear that we will be calibrating a newly defined parameter , so we will have to transform that back into our parameter of interest at some point.

This is the the sole reason why the method setParameterTransformationFunction has been implemented: transform the parameters estimated given the linear regressor, the observation covariance matrix and prior distribution. As the transformations, it they do exist which is not compulsory, are expected to be done with simple operations using constant values, they should not affect the covariance matrix of the posterior multidimensional normal distribution, only the mean vector. The prototype of this function is as follows:

setParameterTransformationFunction(fTransfoParam)

Its only argument is a pointer to the transformation function in the usual C++ prototype. This function provided to get the proper values of the under-investigation parameters take two arguments: the input parameters which are the raw one estimated from the analytical formula detailed in [metho] and the output ones, which should be the ones one wants to have. Both parameters are double-array whose size must be the number of parameters.

The example provided in the use-case is really simple as there is only one parameter to be estimated, which implies that both argument are one-dimension double array which should look like this:

void transf(double *x, double *res)
{
    res[0] = 1050 - x[0];  // simply H_l = \theta - H_u
}

# Define all the needed material: dataservers, models...
cal=Calibration.TLinearBayesian(...) # Create the instance and distance function
# ...
# Load the file in which Transformation function
ROOT.gROOT.LoadMacro("myFunction.C")
# Provide this function to the TLinearBayesian instance
cal.setParameterTransformationFunction(ROOT.transf)

When the estimation is done, it is possible to access the results numerically by calling three methods detailed below. In all cases, the prototype is the same as these functions take no argument and return a TMatrixD instance filled with corresponding information. The functions are:

The parameters can be drawn with the newly-defined instance of drawParameters whose prototype is the same as the original one discussed in Section XI.2.3.6.

drawParameters(sTitre, variable = "*", select = "1>0", option = "")

It takes up to four arguments, three of which are optional:

The main difference with the usual instance of drawParameters defined in TCalibration is that the object drawn are analytical functions.

On top of the parameters, the residues can also be drawn by calling the drawResidue method and no modification has been done to it (for more details, see Section XI.2.3.7).