added kullback leibler for gaussian cases

math/Distributions.h

@@ -8,5 +8,6 @@
 #include "distribution/VonMises.h"
 #include "distribution/Region.h"
 #include "distribution/Triangle.h"
+#include "distribution/NormalN.h"
 
 #endif // DISTRIBUTIONS_H

math/distribution/Normal.h

@@ -44,6 +44,15 @@ namespace Distribution {
 			gen.seed(seed);
 		}
 
+        /** get the mean value */
+        const T getMu() {
+            return this->mu;
+        }
+
+        /** get the standard deviation */
+        const T getSigma() {
+            return this->sigma;
+        }
 
 		/** get the probability for the given value */
 		static T getProbability(const T mu, const T sigma, const T val) {

math/distribution/NormalN.h

@@ -0,0 +1,50 @@
+#ifndef NORMALN_H
+#define NORMALN_H
+
+#include <eigen3/Eigen/Dense>
+
+namespace Distribution {
+
+    class NormalDistributionN {
+
+    private:
+
+        const Eigen::VectorXd mu;
+        const Eigen::MatrixXd sigma;
+
+        const double _a;
+        const Eigen::MatrixXd _sigmaInv;
+
+    public:
+
+        /** ctor */
+        NormalDistributionN(const Eigen::VectorXd mu, const Eigen::MatrixXd sigma) :
+            mu(mu), sigma(sigma), _a( 1.0 / std::sqrt( (sigma * 2.0 * M_PI).determinant() ) ), _sigmaInv(sigma.inverse()) {
+
+        }
+
+
+        /** get probability for the given value */
+        double getProbability(const Eigen::VectorXd val) const {
+            const double b = ((val-mu).transpose() * _sigmaInv * (val-mu));
+            return _a * std::exp(-b/2.0);
+        }
+
+        /** get the mean vector */
+        const Eigen::VectorXd getMu(){
+            return this->mu;
+        }
+
+        /** get covariance matrix */
+        const Eigen::MatrixXd getSigma(){
+            return this->sigma;
+        }
+
+        const Eigen::MatrixXd getSigmaInv(){
+            return this->_sigmaInv;
+        }
+
+    };
+
+}
+#endif // NORMALN_H

math/divergence/KullbackLeibler.h

@@ -0,0 +1,90 @@
+#ifndef KULLBACKLEIBLER_H
+#define KULLBACKLEIBLER_H
+
+#include "../distribution/Normal.h"
+#include "../distribution/NormalN.h"
+
+#include "../../Assertions.h"
+#include <string>
+
+namespace Divergence {
+
+    template <typename Scalar> class KullbackLeibler {
+
+        public:
+
+            /** Calculate the Kullback Leibler Distance for a univariate Gaussian distribution
+            *   Info: https://tgmstat.wordpress.com/2013/07/10/kullback-leibler-divergence/
+            */
+            static inline Scalar getUnivariateGauss(Distribution::Normal<Scalar> norm1, Distribution::Normal<Scalar> norm2){
+
+                auto sigma1Quad = norm1.getSigma() * norm1.getSigma();
+                auto sigma2Quad = norm2.getSigma() * norm2.getSigma();
+                auto mu12Quad = (norm1.getMu() - norm2.getMu()) * (norm1.getMu() - norm2.getMu());
+                auto log1 = std::log(norm1.getSigma());
+                auto log2 = std::log(norm2.getSigma());
+
+                // kl = log(sigma_2 / sigma_1) + ((sigma_1^2 + (mu_1 - mu_2)^2) / 2 * sigma_2^2) - 0.5
+                double klb = (log2 - log1) + ((sigma1Quad + mu12Quad)/(2.0 * sigma2Quad)) - 0.5;
+
+                //klb is always greater 0
+                if(klb < 0.0){
+                    Assert::doThrow("The Kullback Leibler Distance is < 0! Thats not possible");
+                }
+                return klb;
+            }
+
+            /** Calculate the Kullback Leibler Distance for a univariate Gaussian distribution symmetric*/
+            static inline Scalar getUnivariateGaussSymmetric(Distribution::Normal<Scalar> norm1, Distribution::Normal<Scalar> norm2){
+                return getUnivariateGauss(norm1, norm2) + getUnivariateGauss(norm2, norm1);
+            }
+
+            /** Calculate the Kullback Leibler Distance for a multivariate Gaussian distribution */
+            static inline Scalar getMultivariateGauss(Distribution::NormalDistributionN norm1, Distribution::NormalDistributionN norm2){
+
+                //both gaussian have the same dimension.
+                Assert::equal(norm1.getMu().rows(), norm2.getMu().rows(), "mean vectors do not have the same dimension");
+                Assert::equal(norm1.getSigma().rows(), norm2.getSigma().rows(), "cov matrices do not have the same dimension");
+                Assert::equal(norm1.getSigma().cols(), norm2.getSigma().cols(), "cov matrices do not have the same dimension");
+
+                //log
+                auto det1 = norm1.getSigma().determinant();
+                auto det2 = norm2.getSigma().determinant();
+                auto log1 = std::log(det1);
+                auto log2 = std::log(det2);
+
+                //trace
+                Eigen::MatrixXd toTrace(norm1.getSigma().rows(),norm1.getSigma().cols());
+                toTrace = norm2.getSigmaInv() * norm1.getSigma();
+                auto trace = toTrace.trace();
+
+                //transpose
+                Eigen::VectorXd toTranspose(norm1.getMu().rows());
+                toTranspose = norm2.getMu() - norm1.getMu();
+                auto transpose = toTranspose.transpose();
+
+                //rawdensity
+                auto rawDensity = transpose * norm2.getSigmaInv() * toTranspose;
+                auto dimension = norm1.getMu().rows();
+
+                //0.5 * ((log(det(cov_2)/det(cov_1)) + tr(cov_2^-1 cov_1) + (mu_2 - mu_1)^T * cov_2^-1 * (mu_2 - mu_1) - dimension)
+                double klb = 0.5 * ((log2 - log1) + trace + rawDensity - dimension);
+
+                //klb is always greater 0
+                if(klb < 0.0){
+                    Assert::doThrow("The Kullback Leibler Distance is < 0! Thats not possible");
+                }
+                return klb;
+            }
+
+             /** Calculate the Kullback Leibler Distance for a multivariate Gaussian distribution symmetric*/
+            static inline Scalar getMultivariateGaussSymmetric(Distribution::NormalDistributionN norm1, Distribution::NormalDistributionN norm2){
+                return getMultivariateGauss(norm1, norm2) + getMultivariateGauss(norm2, norm1);
+            }
+
+
+    };
+
+}
+
+#endif // KULLBACKLEIBLER_H