Added derivative basis to Basis class.

Snakefile

@@ -29,6 +29,7 @@ TODO: ASk whether cfl number should be absolute value
 Urgent:
 TODO: Add Burgers class completely
 TODO: Add 'update_time_step()' to Burgers -> Done
+TODO: Add derivative basis to Basis class -> Done
 TODO: Add 'solve_exactly()' to Burgers
 TODO: Add 'update_right_hand_side()' to Burgers
 TODO: Add initialization to Burgers

scripts/tcd/Basis_Function.py

@@ -28,6 +28,8 @@ class Basis(ABC):
         Array of basis.
     wavelet : ndarray
         Array of wavelet.
+    derivative: ndarray
+        Array of derivative basis.
     inv_mass : ndarray
         Inverse mass matrix.
     basis_projection : Tuple[ndarray, ndarray]
@@ -111,6 +113,29 @@ class Basis(ABC):
         """
         pass
 
+    @property
+    @cache
+    def derivative(self) -> ndarray:
+        """Return derivative basis vector."""
+        return self._build_derivative_vector(x)
+
+    @abstractmethod
+    def _build_derivative_vector(self, eval_point: float) -> ndarray:
+        """Construct derivative basis vector.
+
+        Parameters
+        ----------
+        eval_point : float
+            Evaluation point.
+
+        Returns
+        -------
+        ndarray
+            Vector containing derivative basis evaluated at evaluation point.
+
+        """
+        pass
+
     @property
     @cache
     def inverse_mass_matrix(self) -> ndarray:
@@ -261,6 +286,55 @@ class Legendre(Basis):
                     vector.append(poly)
         return np.array(vector)
 
+    def _build_derivative_vector(self, eval_point: float) -> ndarray:
+        """Construct derivative basis vector.
+
+        Parameters
+        ----------
+        eval_point : float
+            Evaluation point.
+
+        Returns
+        -------
+        ndarray
+            Vector containing derivative basis evaluated at evaluation point.
+
+        """
+        return self._calculate_derivative_legendre_vector(eval_point)
+
+    def _calculate_derivative_legendre_vector(self,
+                                              eval_point: float) -> ndarray:
+        """Construct derivative Legendre vector.
+
+        Parameters
+        ----------
+        eval_point : float
+            Evaluation point.
+
+        Returns
+        -------
+        ndarray
+            Vector containing derivative Legendre polynomial evaluated at
+            evaluation point.
+
+        """
+        derivative_vector = []
+        leg_vector = self._calculate_legendre_vector(eval_point)
+        for degree in range(self._polynomial_degree+1):
+            if degree == 0:
+                derivative_vector.append(0 * eval_point)
+            else:
+                if degree == 1:
+                    derivative_vector.append(1.0+0 * eval_point)
+                else:
+                    poly = ((2.0 * degree-1) / degree) * (
+                                leg_vector[degree-1]+(
+                                    eval_point * derivative_vector[-1]))-(
+                                       (degree-1) / degree) * \
+                           derivative_vector[-2]
+                    derivative_vector.append(poly)
+        return np.array(derivative_vector)
+
 
 class OrthonormalLegendre(Legendre):
     """Class for orthonormal Legendre basis."""
@@ -348,6 +422,26 @@ class OrthonormalLegendre(Legendre):
         raise ValueError('Invalid value: Alpert\'s wavelet is only available \
                          up to degree 4 for this application')
 
+    def _build_derivative_basis_vector(self, eval_point):
+        """Construct derivative basis vector.
+
+        Parameters
+        ----------
+        eval_point : float
+            Evaluation point.
+
+        Returns
+        -------
+        ndarray
+            Vector containing derivative Legendre polynomial evaluated at
+            evaluation point.
+
+        """
+        derivative_leg_vector = self._calculate_derivative_legendre_vector(
+            eval_point)
+        return np.array([derivative_leg_vector[degree] * np.sqrt(degree+0.5)
+                         for degree in range(self._polynomial_degree+1)])
+
     def _build_inverse_mass_matrix(self) -> ndarray:
         """Construct inverse mass matrix.