added sampling function for NormalN and approximation of normalN using samples + testcases for both

tests/math/distribution/TestNormalN.cpp

@@ -0,0 +1,77 @@
+#ifdef WITH_TESTS
+
+#include "../../Tests.h"
+#include "../../../math/divergence/KullbackLeibler.h"
+#include "../../../math/Distributions.h"
+
+#include <random>
+
+#include <KLib/misc/gnuplot/Gnuplot.h>
+#include <KLib/misc/gnuplot/GnuplotPlot.h>
+#include <KLib/misc/gnuplot/GnuplotPlotElementLines.h>
+#include <KLib/misc/gnuplot/GnuplotPlotElementPoints.h>
+
+
+TEST(NormalN, multivariateGaussSampleData) {
+
+    Eigen::VectorXd mu(2);
+    mu[0] = 0.0;
+    mu[1] = 0.0;
+
+    Eigen::MatrixXd cov(2,2);
+    cov(0,0) = 1.0;
+    cov(0,1) = 0.0;
+    cov(1,0) = 0.0;
+    cov(1,1) = 1.0;
+
+    Distribution::NormalDistributionN normTest(mu, cov);
+
+    // draw
+    K::Gnuplot gp;
+    K::GnuplotPlot plot;
+    K::GnuplotPlotElementPoints pParticles;
+
+    gp << "set terminal qt size 1200,1200 \n";
+    gp << "set xrange [-5:5] \n set yrange [-5:5] \n";
+
+    // gen
+    std::vector<Eigen::VectorXd> vals;
+    for(int i = 0; i < 100000; ++i){
+        Eigen::VectorXd vec = normTest.draw();
+        vals.push_back(vec);
+
+        K::GnuplotPoint2 pos(vec[0], vec[1]);
+        pParticles.add(pos);
+    }
+
+    plot.add(&pParticles);
+
+    gp.draw(plot);
+    gp.flush();
+
+    sleep(5);
+
+    //create matrix out of the vector
+    Eigen::MatrixXd m(vals.size(), vals[0].rows());
+
+    for(int i = 0; i < vals.size(); ++i){
+        m(i,0) = vals[i][0];
+        m(i,1) = vals[i][1];
+    }
+
+    Distribution::NormalDistributionN norm =  Distribution::NormalDistributionN::getNormalNFromSamples(m);
+
+    //get distance between original and approximated mu and sigma
+    Eigen::MatrixXd diffM = cov - norm.getSigma();
+    double distM = diffM.norm();
+
+    Eigen::VectorXd diffV = mu - norm.getMu();
+    double distV = diffV.norm();
+
+    ASSERT_NEAR(0.0, distM, 0.01);
+    ASSERT_NEAR(0.0, distV, 0.01);
+
+}
+
+#endif
+