Documentation / User's manual in C++ :

The example script below uses the THSIC class to compute and display the indices. Note that HSIC indexes do not require a specific design of experiments, they can be computed on a given sample.

void sensitivityHSICFunctionFlowrate(){

gROOT->LoadMacro("UserFunctions.C");

// Define the DataServer
TDataServer *tds = new TDataServer("tdsflowreate", "DataBase flowreate");
tds->addAttribute( new TUniformDistribution("rw", 0.05, 0.15));
tds->addAttribute( new TUniformDistribution("r", 100.0, 50000.0));
tds->addAttribute( new TUniformDistribution("tu", 63070.0, 115600.0));
tds->addAttribute( new TUniformDistribution("tl", 63.1, 116.0));
tds->addAttribute( new TUniformDistribution("hu", 990.0, 1110.0));
tds->addAttribute( new TUniformDistribution("hl", 700.0, 820.0));
tds->addAttribute( new TUniformDistribution("l", 1120.0, 1680.0));
tds->addAttribute( new TUniformDistribution("kw", 9855.0, 12045.0));
  
// Generation of the sample (it can be a given sample).
Int_t nS = 500;
TSampling *sampling = new TSampling(tds, "lhs", nS);
sampling->generateSample();	
  
TLauncherFunction * tlf = new TLauncherFunction(tds, "flowrateModel");
tlf->setDrawProgressBar(kFALSE);
tlf->run();

// Create a THSIC object, compute indexes and print results
THSIC * thsic = new THSIC(tds, "rw:r:tu:tl:hu:hl:l:kw","flowrateModel");
thsic->computeIndexes("quiet");
thsic->getResultTuple()->SetScanField(60);
thsic->getResultTuple()->Scan("Out:Inp:Method:Order:Value:CILower:CIUpper");

// Print HSIC indexes
TCanvas  *can = new TCanvas("c1", "Graph for the Macro sensitivityHSICFunctionFlowrate",5,64,1270,667);
thsic->drawIndexes("Flowrate", "", "hist,first,nonewcanv");  
 
}

There is one kind of constructor to build a THSIC object based on provided data. The HSIC compute indices on given data, the TDataServer must be filled. The constructor does not require a model to run (this has to be done).

// Create a THSIC object data
THSIC(TDataServer *tds, const char *inp,  const char *out ,  const char *Option="")

This constructor takes up to four arguments:

Here is an example of how to use the constructor with provided data:

THSIC * thsic = new THSIC(tds, "rw:r:tu:tl:hu:hl:l:kw", "flowrateModel"); 

To compute the indices, run the method computeIndexes:

thsic->computeIndexes();

Note this method computes the 'V-stat' indices. If the "unbiased" option is provided, it computes the 'U-stat' indices. It computes three values for each variable:

thsic->setEstimatedVariance(URANIE::Sensitivity::THSIC::kStdEmpirical);

Two technics are available to compute the p-values to test the independence between inputs and outputs:

thsic->computeIndexes("nperm=100"); // specify the number of permutation

The measures, once computed, are stored in a TTree. To get this TTree, use the method TSensitivity::getResultTuple():

TTree * resultsHSIC = thsic->getResultTuple();

Several methods exist in ROOT to extract data from a TTree, it is advised to look for them into the ROOT documentation. We propose two ways of extracting the value of each coefficient from the TTree.

double hl_r2hsic_index = thsic->getValue("R2HSic","hl");
double hl_hsic_index = thsic->getValue("HSic","hl");
double hl_pvalues_index = thsic->getValue("pValues","hl");