Improved NormalCopula

Now the entropy is computed more efficiently

lib/src/Uncertainty/Distribution/Normal.cxx

@@ -414,6 +414,10 @@ Scalar Normal::computeComplementaryCDF(const Point & point) const
 /* Compute the entropy of the distribution */
 Scalar Normal::computeEntropy() const
 {
+  // The entropy is equal to (see https://statproofbook.github.io/P/mvn-dent):
+  // (dim/2)*(log(2pi))+(1/2)*log(det(Sigma))+(1/2)*dim
+  // We reuse the normalization factors to avoid the recomputation of
+  // the most costly parts:
   // EllipticalDistribution::normalizationFactor_ == 1/sqrt(det(Sigma))
   // logNormalizationFactor_ == log(1/sqrt(2*Pi)^dim)
   return 0.5 * getDimension() - std::log(EllipticalDistribution::normalizationFactor_) - logNormalizationFactor_;

lib/src/Uncertainty/Distribution/NormalCopula.cxx

@@ -363,7 +363,12 @@ CorrelationMatrix NormalCopula::getKendallTau() const
 /* Compute the entropy of the distribution */
 Scalar NormalCopula::computeEntropy() const
 {
-  return normal_.computeEntropy() - getDimension() * (SpecFunc::LOGSQRT2PI + 0.5);
+  // The entroy of the normal copula is the entropy of
+  // the associated standard normal distribution minus
+  // dim times the entropy of a standard univariate normal
+  // distribution, thus it is equal to (1/2)*log(|
+  //return normal_.computeEntropy() - getDimension() * (SpecFunc::LOGSQRT2PI + 0.5);
+  return -std::log(normal_.EllipticalDistribution::normalizationFactor_);
 }
 
 /* Get the Shape matrix of the copula */

lib/src/Uncertainty/Distribution/openturns/Normal.hxx

@@ -36,6 +36,10 @@ class OT_API Normal
 {
 
   CLASSNAME
+
+    /** The NormalCopula class is closely related with the Normal class */
+    friend class NormalCopula;
+
 public:
 
   /** Default constructor */