Documentation for v0.1 version (#199)

* Adding Equations, solving typos
* improve _code.rst
* the team rst and restuctore index.rst
* fixing errors

---------

Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>

pina/geometry/intersection_domain.py

@@ -1,48 +1,47 @@
-"""Module for Location class."""
+"""Module for Intersection class. """
+
 import torch
-from .exclusion_domain import Exclusion
 from ..label_tensor import LabelTensor
 from .operation_interface import OperationInterface
 import random
 
 
 class Intersection(OperationInterface):
-    """ PINA implementation of Intersection of Domains."""
 
     def __init__(self, geometries):
-        """
+        r"""
         PINA implementation of Intersection of Domains.
         Given two sets :math:`A` and :math:`B` then the
         domain difference is defined as:
 
-        ..:math:
-        A \cap B = \{x \mid x \in A \text{ and } x \in B\},
+        .. math::
+            A \cap B = \{x \mid x \in A \land x \in B\},
 
         with :math:`x` a point in :math:`\mathbb{R}^N` and :math:`N`
         the dimension of the geometry space.
 
-        :param list geometries: A list of geometries from 'pina.geometry' 
-            such as 'EllipsoidDomain' or 'CartesianDomain'. The intersection
+        :param list geometries: A list of geometries from ``pina.geometry`` 
+            such as ``EllipsoidDomain`` or ``CartesianDomain``. The intersection
             will be taken between all the geometries in the list. The resulting
             geometry will be the intersection of all the geometries in the list.
 
         :Example:
-            # Create two ellipsoid domains
+            >>> # Create two ellipsoid domains
             >>> ellipsoid1 = EllipsoidDomain({'x': [-1, 1], 'y': [-1, 1]})
             >>> ellipsoid2 = EllipsoidDomain({'x': [0, 2], 'y': [0, 2]})
-
-            # Create a Intersection of the ellipsoid domains
+            >>> # Create a Intersection of the ellipsoid domains
             >>> intersection = Intersection([ellipsoid1, ellipsoid2])
         """
         super().__init__(geometries)
 
     def is_inside(self, point, check_border=False):
-        """Check if a point is inside the Exclusion domain.
+        """
+        Check if a point is inside the ``Intersection`` domain.
 
         :param point: Point to be checked.
         :type point: torch.Tensor   
-        :param bool check_border: If True, the border is considered inside.
-        :return: True if the point is inside the Exclusion domain, False otherwise.
+        :param bool check_border: If ``True``, the border is considered inside.
+        :return: ``True`` if the point is inside the Intersection domain, ``False`` otherwise.
         :rtype: bool
         """
         flag = 0
@@ -52,31 +51,29 @@ class Intersection(OperationInterface):
         return flag == len(self.geometries)
 
     def sample(self, n, mode='random', variables='all'):
-        """Sample routine for intersection domain.
+        """
+        Sample routine for ``Intersection`` domain.
 
-        :param n: Number of points to sample in the shape.
-        :type n: int
-        :param mode: Mode for sampling, defaults to 'random'.
-            Available modes include: random sampling, 'random'.
-        :type mode: str, optional
-        :param variables: pinn variable to be sampled, defaults to 'all'.
-        :type variables: str or list[str], optional
+        :param int n: Number of points to sample in the shape.
+        :param str mode: Mode for sampling, defaults to ``random``. Available modes include: ``random``.
+        :param variables: Variables to be sampled, defaults to ``all``.
+        :type variables: str | list[str]
+        :return: Returns ``LabelTensor`` of n sampled points.
+        :rtype: LabelTensor
 
         :Example:
-            # Create two Cartesian domains
+            >>> # Create two Cartesian domains
             >>> cartesian1 = CartesianDomain({'x': [0, 2], 'y': [0, 2]})
             >>> cartesian2 = CartesianDomain({'x': [1, 3], 'y': [1, 3]})
-
-            # Create a Intersection of the ellipsoid domains
+            >>> # Create a Intersection of the ellipsoid domains
             >>> intersection = Intersection([cartesian1, cartesian2])
-
+            >>> # Sample
             >>> intersection.sample(n=5)
                 LabelTensor([[1.7697, 1.8654],
                             [1.2841, 1.1208],
                             [1.7289, 1.9843],
                             [1.3332, 1.2448],
                             [1.9902, 1.4458]])
-
             >>> len(intersection.sample(n=5)
                 5