13.3.3. Macro “samplingLHSCorrelation.C”

13.3.3.1. Objective

Generate a design-of-experiments, of 3000 patterns using the LHS method, with 3 random attributes and taking into account a correlation between the first two attributes. This correlation, equals to 0.99, is computed using the rank values (the Spearmann definition, c.f. Description of a correlation and in [Bla17] for more details).

1. Attribute x1 follows an uniform law on interval [3, 4];

2. Attribute x2 follows a normal law with a mean value equal to 0.5 and 1.5 as standard deviation;

3. Attribute x3 obeys a triangular law on interval [1, 5] with mode 4.

13.3.3.2. Macro Uranie

    // Create a TDataServer
    TDataServer * tds = new TDataServer();

    // Fill the DataServer with the three attributes of the study
    tds->addAttribute(new TUniformDistribution("x1", 3., 4.));
    tds->addAttribute(new TNormalDistribution("x2", 0.5, 1.5));
    tds->addAttribute(new TTriangularDistribution("x3", 1., 5., 4.));

    // Generate the sampling from the TDataServer
    TSampling *sampling = new TSampling(tds, "lhs", 3000);
    sampling->setUserCorrelation(0, 1, 0.99);
    sampling->generateSample();

    tds->exportData("toto.dat","x1:x3");
    tds->exportDataHeader("toto.h","x1:x2");

    // Graph
    TCanvas  *Canvas = new TCanvas("c1", "Graph for the Macro samplingCorrelation",5,64,1270,667);
    TPad *pad = new TPad("pad","pad",0, 0.03, 1, 1); pad->Draw();
    pad->Divide(2,2);

    pad->cd(1); tds->Draw("x1");
    pad->cd(2); tds->Draw("x2");
    pad->cd(3); tds->Draw("x3");
    pad->cd(4); tds->drawTufte("x1:x2");

Laws are set for each attribute and linked to a TDataServer:

    tds->addAttribute(new TUniformDistribution("x1", 3., 4.));
    tds->addAttribute(new TNormalDistribution("x2", 0.5, 1.5));
    tds->addAttribute(new TTriangularDistribution("x3", 1., 5., 4.));

The sampling is generated with the LHS method and a correlation is set between the two first attributes:

    TSampling *sampling = new TSampling(tds, "lhs", 3000);
    sampling->setUserCorrelation(0, 1, 0.99);
    sampling->generateSample();

Data are partially exported in an ASCII file and a header file:

    tds->exportData("toto.dat","x1:x3");
    tds->exportDataHeader("toto.h","x1:x2");

13.3.3.3. Graph

Figure 13.11 Graph de la macro “samplingLHSCorrelation.C”