Merge remote-tracking branch 'origin/feature/v4_docs_review' into fea…

…ture/v4_docs_review

docs/source/utilities/distances/grassmann_distances.rst

@@ -1,6 +1,23 @@
 Grassmann Distances
 --------------------------------------
 
+The Grassmannian (or Riemannian) distance is a metric that assigns nonnegative values to each pair of subspaces
+:math:`Y_1, Y_2 \in \mathbb{R}^{n \times p}` on the Grassmann manifold :math:`\mathcal{G}(p, n)`. Formally,
+is defined as the length of the shortest geodesic connecting the two points on :math:`\mathcal{G}(p, n)`.
+:py:mod:`UQpy` introduces various Grassmann distances derived from the principal angles :cite:`Distances_1`.
+
+.. math:: 0 \leq \theta_1 \leq \theta_2 \leq \ldots \leq \theta_p \leq \pi/2,
+
+where the first principal angle :math:`\theta_1` is the smallest angle between all pairs of unit vectors in the
+first and the second subspaces. Practically, the principal angles can be calculated from the singular value
+decomposition (SVD) of :math:`\mathbf{Y}_1'\mathbf{Y}_2`,
+
+.. math:: \mathbf{Y}_1'\mathbf{Y}_2 = \mathbf{U}\cos(\Theta)\mathbf{V}'
+
+where :math:`\cos(\Theta)=\text{diag}(\cos\theta_1, \ldots,\cos\theta_p)`. This definition of distance can be extended
+to cases where :math:`\mathbf{Y}_1` and :math:`\mathbf{Y}_2` have different number of columns :math:`p`. More
+information can be found in :cite:`Distances_2`.
+
 GrassmannianDistance
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 

docs/source/utilities/distances/index.rst

@@ -1,26 +1,14 @@
 Distances
 --------------------------------------
 
-A collection of distances between points in the Euclidean space and between subspaces on the Grassmann manifold.
+A collection of distance measures between points in the Euclidean space and between subspaces on the Grassmann manifold.
 
-The Grassmannian (or Riemannian) distance is a metric that assigns nonnegative values to each pair of subspaces
-:math:`Y_1, Y_2 \in \mathbb{R}^{n \times p}` on the Grassmann manifold :math:`\mathcal{G}(p, n)`. Formally,
-is defined as the length of the shortest geodesic connecting the two points on :math:`\mathcal{G}(p, n)`.
-:py:mod:`UQpy` introduces various Grassmann distances derived from the principal angles :cite:`Distances_1`.
+Each distance function in :py:mod:`UQpy` is defined as a subclass of the :class:`.Distance` class. The
+:class:`.Distance` class has two further subclasses for Euclidean distances (:class:`.EuclideanDistance`) and
+Grassmann distances (:class:`.GrassmannianDistance`). Individual dsitances, depending on their type, are defined as
+subclasses of these.
 
-.. math:: 0 \leq \theta_1 \leq \theta_2 \leq \ldots \leq \theta_p \leq \pi/2,
-
-where the first principal angle :math:`\theta_1` is the smallest angle between all pairs of unit vectors in the
-first and the second subspaces. Practically, the principal angles can be calculated from the singular value
-decomposition (SVD) of :math:`\mathbf{Y}_1'\mathbf{Y}_2`,
-
-.. math:: \mathbf{Y}_1'\mathbf{Y}_2 = \mathbf{U}\cos(\Theta)\mathbf{V}'
-
-where :math:`\cos(\Theta)=\text{diag}(\cos\theta_1, \ldots,\cos\theta_p)`. This definition of distance can be extended
-to cases where :math:`\mathbf{Y}_1` and :math:`\mathbf{Y}_2` have different number of columns :math:`p`. More
-information can be found in :cite:`Distances_2`.
-
-Distance
+Distance Class
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
 The :class:`.Distances` class is imported using the following command:
@@ -30,9 +18,11 @@ The :class:`.Distances` class is imported using the following command:
 .. autoclass:: UQpy.utilities.distances.baseclass.Distance
     :members:
 
+Types of Distances
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
 .. toctree::
    :maxdepth: 1
 
-    Grassmannian Distances <grassmann_distances>
     Euclidean Distances <euclidean_distances>
+    Grassmannian Distances <grassmann_distances>

docs/source/utilities/kernels/index.rst

@@ -12,7 +12,7 @@ Each kernel function in :py:mod:`UQpy` is defined as a subclass of the :class:`.
 two further subclasses for Euclidean kernels (:class:`.EuclideanKernel`) and Grassmannian kernels
 (:class:`.GrassmannianKernel`). Individual kernels, depending on their type, are defined as subclasses of these.
 
-Kernel
+Kernel Class
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
 The :class:`UQpy.utilities.kernels.baseclass.Kernel` class is imported using the following command: