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Commit 7b60bb58 authored by Laura Christine Kühle's avatar Laura Christine Kühle
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Improved docstring for Basis class.

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with 64 additions and 38 deletions
Basis_Function.py
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− 38
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# -*- 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)
......
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