Add normalized version of MVN entropy estimator and fix floating point issue

entropy_estimators/continuous.py

@@ -71,8 +71,7 @@ def det(array_or_scalar):
 
 
 @convert_vectors_to_2d_arrays_if_any
-def get_h_mvn(x):
-
+def get_h_mvn(x, normalized=False):
     """
     Computes the entropy of a multivariate Gaussian distribution:
 
@@ -83,14 +82,44 @@ def get_h_mvn(x):
     x: (n, d) ndarray
         n samples from a d-dimensional multivariate normal distribution
 
+    normalized: bool
+        normalize distribution, if `True` each component is normalized such that
+        its standard deviation is `1` and the covariance matrix becomes equal to
+        the Pearson correlation coefficients and the entropy becomes invariant
+        under scalar multiplication
+
     Returns:
     --------
     h: float
         entropy H(X)
     """
 
     d = x.shape[1]
-    h  = 0.5 * log((2 * np.pi * np.e)**d * det(np.cov(x.T)))
+    if d == 1:
+        if normalized:
+            det_cov = 1
+        else:
+            det_cov = np.var(x, ddof=1)
+    else:
+        cov = np.cov(x.T)
+        # corrcoef calculation simplified from source code of np.corrcoef
+        stddev = np.sqrt(np.diagonal(cov))
+        corrcoef = cov / stddev[:, None] / stddev[None, :]
+        det_corrcoef = np.linalg.det(corrcoef)
+        # check if elements are exactly zero, then variables 100% correlated
+        if det_corrcoef == 0:
+            return -np.inf
+        # check if elements of corrcoef determinent is close to zero considering
+        # float precision
+        if np.isclose(det_corrcoef, 0, rtol=0,
+                      atol=100*np.finfo(det_corrcoef).resolution):
+            return np.nan
+        if normalized:
+            det_cov = det_corrcoef
+        else:
+            det_cov = np.linalg.det(cov)
+    h = 0.5 * np.log((2 * np.pi * np.e)**d * det_cov)
+
     return h