From 52ac10847f8501de2a52ff215a87ae474d92332c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?K=C3=BChle=2C=20Laura=20Christine=20=28lakue103=29?=
<laura.kuehle@uni-duesseldorf.de>
Date: Fri, 10 Mar 2023 15:25:25 +0100
Subject: [PATCH] Added derivative basis to Basis class.
---
Snakefile | 1 +
scripts/tcd/Basis_Function.py | 94 +++++++++++++++++++++++++++++++++++
2 files changed, 95 insertions(+)
diff --git a/Snakefile b/Snakefile
index d66ead6..b6035a9 100644
--- a/Snakefile
+++ b/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
diff --git a/scripts/tcd/Basis_Function.py b/scripts/tcd/Basis_Function.py
index 4144fb9..69b1347 100644
--- a/scripts/tcd/Basis_Function.py
+++ b/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.
--
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