Improved docstring for Basis class.

Basis_Function.py

 # -*- coding: utf-8 -*-
-"""
+"""Module for polynomial basis.
+
 @author: Laura C. Kühle
 
 """
+from functools import cache
 import numpy as np
 from sympy import Symbol, integrate
-from functools import cache
 
 from projection_utils import calculate_approximate_solution
 
@@ -26,7 +27,14 @@ class Basis:
         Array of wavelet.
     inv_mass : ndarray
         Inverse mass matrix.
-    basis_projection: ndarray
+    basis_projection : Tuple[ndarray, ndarray]
+        Two arrays containing integrals of all basis vector
+        combinations evaluated on the left and right cell boundary,
+        respectively.
+    wavelet_projection : Tuple[ndarray, ndarray]
+        Two arrays containing integrals of all basis vector/
+        wavelet vector combinations evaluated on the left and right cell
+        boundary, respectively.
 
 
     Methods
@@ -35,8 +43,9 @@ class Basis:
         Calculate cell averages for a given projection.
 
     """
+
     def __init__(self, polynomial_degree):
-        """Initializes Vector.
+        """Initialize Basis.
 
         Parameters
         ----------
@@ -58,7 +67,7 @@ class Basis:
         return self._build_basis_vector(x)
 
     def _build_basis_vector(self, eval_point):
-        """Constructs basis vector.
+        """Construct basis vector.
 
         Parameters
         ----------
@@ -76,11 +85,11 @@ class Basis:
     @property
     @cache
     def wavelet(self):
-        """Return basis vector."""
+        """Return wavelet vector."""
         return self._build_wavelet_vector(z)
 
     def _build_wavelet_vector(self, eval_point):
-        """Constructs wavelet vector.
+        """Construct wavelet vector.
 
         Parameters
         ----------
@@ -102,7 +111,7 @@ class Basis:
         return self._build_inverse_mass_matrix()
 
     def _build_inverse_mass_matrix(self):
-        """Constructs inverse mass matrix.
+        """Construct inverse mass matrix.
 
         Returns
         -------
@@ -192,8 +201,9 @@ class Basis:
 
 class Legendre(Basis):
     """Class for Legendre basis."""
+
     def _build_basis_vector(self, eval_point):
-        """Constructs basis vector.
+        """Construct basis vector.
 
         Parameters
         ----------
@@ -209,7 +219,7 @@ class Legendre(Basis):
         return self._calculate_legendre_vector(eval_point)
 
     def _calculate_legendre_vector(self, eval_point):
-        """Constructs Legendre vector.
+        """Construct Legendre vector.
 
         Parameters
         ----------
@@ -239,8 +249,9 @@ class Legendre(Basis):
 
 class OrthonormalLegendre(Legendre):
     """Class for orthonormal Legendre basis."""
+
     def _build_basis_vector(self, eval_point):
-        """Constructs basis vector.
+        """Construct basis vector.
 
         Parameters
         ----------
@@ -258,7 +269,7 @@ class OrthonormalLegendre(Legendre):
                 for degree in range(self._polynomial_degree+1)]
 
     def _build_wavelet_vector(self, eval_point):
-        """Constructs wavelet vector.
+        """Construct wavelet vector.
 
         Parameters
         ----------
@@ -323,6 +334,14 @@ class OrthonormalLegendre(Legendre):
                          up to degree 4 for this application')
 
     def _build_inverse_mass_matrix(self):
+        """Construct inverse mass matrix.
+
+        Returns
+        -------
+        ndarray
+            Inverse mass matrix.
+
+        """
         mass_matrix = []
         for i in range(self._polynomial_degree+1):
             new_row = []
@@ -337,21 +356,26 @@ class OrthonormalLegendre(Legendre):
     @property
     @cache
     def basis_projections(self):
-        """Returns basis projection.
+        """Return basis projection.
+
+        Construct matrices containing the integrals of the
+        product of two basis vectors for every degree combination evaluated
+        at the left and right cell boundary.
 
         Returns
         -------
-        ndarray
-            Array containing the basis projection based on the integrals of
-            the product of two basis vectors for each degree combination.
+        left_basis_projection : ndarray
+            Array containing the left basis projection.
+        right_basis_projection : ndarray
+            Array containing the right basis projection.
 
         """
-        basis_projection_left = self._build_basis_matrix(z, 0.5 * (z - 1))
-        basis_projection_right = self._build_basis_matrix(z, 0.5 * (z + 1))
-        return basis_projection_left, basis_projection_right
+        left_basis_projection = self._build_basis_matrix(z, 0.5 * (z - 1))
+        right_basis_projection = self._build_basis_matrix(z, 0.5 * (z + 1))
+        return left_basis_projection, right_basis_projection
 
     def _build_basis_matrix(self, first_param, second_param):
-        """Constructs a basis matrix.
+        """Construct a basis matrix.
 
         Parameters
         ----------
@@ -380,25 +404,29 @@ class OrthonormalLegendre(Legendre):
     @property
     @cache
     def multiwavelet_projections(self):
-        """Returns wavelet projection.
+        """Return wavelet projection.
+
+        Construct matrices containing the integrals of the
+        product of a basis vector and a wavelet vector  for every degree
+        combination evaluated at the left and right cell boundary.
 
         Returns
         -------
-        ndarray
-            Array containing the multiwavelet projection based on the integrals
-            of the product of a basis vector and a wavelet vector for each
-            degree combination.
+        left_wavelet_projection : ndarray
+            Array containing the left multiwavelet projection.
+        right_wavelet_projection : ndarray
+            Array containing the right multiwavelet projection.
 
         """
-        wavelet_projection_left = self._build_multiwavelet_matrix(
+        left_wavelet_projection = self._build_multiwavelet_matrix(
             z, -0.5*(z-1), True)
-        wavelet_projection_right = self._build_multiwavelet_matrix(
+        right_wavelet_projection = self._build_multiwavelet_matrix(
             z, 0.5*(z+1), False)
-        return wavelet_projection_left, wavelet_projection_right
+        return left_wavelet_projection, right_wavelet_projection
 
     def _build_multiwavelet_matrix(self, first_param, second_param,
                                    is_left_matrix):
-        """Constructs a multiwavelet matrix.
+        """Construct a multiwavelet matrix.
 
         Parameters
         ----------
@@ -439,7 +467,7 @@ class OrthonormalLegendre(Legendre):
 
         Notes
         -----
-            To increase speed. this function uses a simplified calculation
+            To increase speed, this function uses a simplified calculation
             specific to the orthonormal Legendre polynomial basis.
 
         Parameters
@@ -459,7 +487,6 @@ class OrthonormalLegendre(Legendre):
             projection.
 
         """
-
         cell_averages = np.array([projection[0] / np.sqrt(2)])
 
         if add_reconstructions:
@@ -478,11 +505,6 @@ class OrthonormalLegendre(Legendre):
     def _calculate_reconstructions(self, projection):
         """Calculate left and right reconstructions for a given projection.
 
-        Notes
-        -----
-            To increase speed. this function uses a simplified calculation
-            specific to the orthonormal Legendre polynomial basis.
-
         Parameters
         ----------
         projection : ndarray
@@ -495,8 +517,12 @@ class OrthonormalLegendre(Legendre):
         right_reconstruction : list
             List containing right reconstructions for given projection.
 
-        """
+        Notes
+        -----
+            To increase speed. this function uses a simplified calculation
+            specific to the orthonormal Legendre polynomial basis.
 
+        """
         left_reconstructions = [
             sum(projection[degree][cell] * (-1)**degree
                 * np.sqrt(degree + 0.5)