diff --git a/Basis_Function.py b/Basis_Function.py
index 14315ad7341c96d5e5379955eaf542dc98972b76..5e69d31b0d896d1df9c6c612200b6b85fae3e363 100644
--- a/Basis_Function.py
+++ b/Basis_Function.py
@@ -5,7 +5,9 @@
"""
from functools import cache
+from typing import Tuple
import numpy as np
+from numpy import ndarray
from sympy import Symbol, integrate
from projection_utils import calculate_approximate_solution
@@ -44,7 +46,7 @@ class Basis:
"""
- def __init__(self, polynomial_degree):
+ def __init__(self, polynomial_degree: int) -> None:
"""Initialize Basis.
Parameters
@@ -56,17 +58,17 @@ class Basis:
self._polynomial_degree = polynomial_degree
@property
- def polynomial_degree(self):
+ def polynomial_degree(self) -> int:
"""Return polynomial degree."""
return self._polynomial_degree
@property
@cache
- def basis(self):
+ def basis(self) -> ndarray:
"""Return basis vector."""
return self._build_basis_vector(x)
- def _build_basis_vector(self, eval_point):
+ def _build_basis_vector(self, eval_point: float) -> ndarray:
"""Construct basis vector.
Parameters
@@ -80,15 +82,15 @@ class Basis:
Vector containing basis evaluated at evaluation point.
"""
- return []
+ pass
@property
@cache
- def wavelet(self):
+ def wavelet(self) -> ndarray:
"""Return wavelet vector."""
return self._build_wavelet_vector(z)
- def _build_wavelet_vector(self, eval_point):
+ def _build_wavelet_vector(self, eval_point: float) -> ndarray:
"""Construct wavelet vector.
Parameters
@@ -102,15 +104,15 @@ class Basis:
Vector containing wavelet evaluated at evaluation point.
"""
- return []
+ pass
@property
@cache
- def inverse_mass_matrix(self):
+ def inverse_mass_matrix(self) -> ndarray:
"""Return inverse mass matrix."""
return self._build_inverse_mass_matrix()
- def _build_inverse_mass_matrix(self):
+ def _build_inverse_mass_matrix(self) -> ndarray:
"""Construct inverse mass matrix.
Returns
@@ -123,18 +125,18 @@ class Basis:
@property
@cache
- def basis_projection(self):
+ def basis_projection(self) -> Tuple[ndarray, ndarray]:
"""Return basis projection."""
- return []
+ return np.array([]), np.array([])
@property
@cache
- def wavelet_projection(self):
+ def wavelet_projection(self) -> Tuple[ndarray, ndarray]:
"""Return wavelet projection."""
- return []
+ return np.array([]), np.array([])
- def calculate_cell_average(self, projection, stencil_length,
- add_reconstructions=True):
+ def calculate_cell_average(self, projection: ndarray, stencil_length: int,
+ add_reconstructions: bool = True) -> ndarray:
"""Calculate cell averages for a given projection.
Calculate the cell averages of all cells in a projection.
@@ -174,7 +176,8 @@ class Basis:
cell_averages[:, middle_idx+1:]))))
return np.array(list(map(np.float64, cell_averages)))
- def _calculate_reconstructions(self, projection):
+ def _calculate_reconstructions(self, projection: ndarray) \
+ -> Tuple[ndarray, ndarray]:
"""Calculate left and right reconstructions for a given projection.
Parameters
@@ -202,7 +205,7 @@ class Basis:
class Legendre(Basis):
"""Class for Legendre basis."""
- def _build_basis_vector(self, eval_point):
+ def _build_basis_vector(self, eval_point: float) -> ndarray:
"""Construct basis vector.
Parameters
@@ -218,7 +221,7 @@ class Legendre(Basis):
"""
return self._calculate_legendre_vector(eval_point)
- def _calculate_legendre_vector(self, eval_point):
+ def _calculate_legendre_vector(self, eval_point: float) -> ndarray:
"""Construct Legendre vector.
Parameters
@@ -244,13 +247,13 @@ class Legendre(Basis):
poly = (2.0*degree - 1)/degree * eval_point * vector[-1] \
- (degree-1)/degree * vector[-2]
vector.append(poly)
- return vector
+ return np.array(vector)
class OrthonormalLegendre(Legendre):
"""Class for orthonormal Legendre basis."""
- def _build_basis_vector(self, eval_point):
+ def _build_basis_vector(self, eval_point: float) -> ndarray:
"""Construct basis vector.
Parameters
@@ -265,10 +268,10 @@ class OrthonormalLegendre(Legendre):
"""
leg_vector = self._calculate_legendre_vector(eval_point)
- return [leg_vector[degree] * np.sqrt(degree+0.5)
- for degree in range(self._polynomial_degree+1)]
+ return np.array([leg_vector[degree] * np.sqrt(degree+0.5)
+ for degree in range(self._polynomial_degree+1)])
- def _build_wavelet_vector(self, eval_point):
+ def _build_wavelet_vector(self, eval_point: float) -> ndarray:
"""Construct wavelet vector.
Parameters
@@ -289,51 +292,51 @@ class OrthonormalLegendre(Legendre):
degree = self._polynomial_degree
if degree == 0:
- return [np.sqrt(0.5) + eval_point*0]
+ return np.array([np.sqrt(0.5) + eval_point*0])
if degree == 1:
- return [np.sqrt(1.5) * (-1 + 2*eval_point),
- np.sqrt(0.5) * (-2 + 3*eval_point)]
+ return np.array([np.sqrt(1.5) * (-1 + 2*eval_point),
+ np.sqrt(0.5) * (-2 + 3*eval_point)])
if degree == 2:
- return [1/3 * np.sqrt(0.5) *
- (1 - 24*eval_point + 30*(eval_point**2)),
- 1/2 * np.sqrt(1.5) *
- (3 - 16*eval_point + 15*(eval_point**2)),
- 1/3 * np.sqrt(2.5) *
- (4 - 15*eval_point + 12*(eval_point**2))]
+ return np.array([1/3 * np.sqrt(0.5) *
+ (1 - 24*eval_point + 30*(eval_point**2)),
+ 1/2 * np.sqrt(1.5) *
+ (3 - 16*eval_point + 15*(eval_point**2)),
+ 1/3 * np.sqrt(2.5) *
+ (4 - 15*eval_point + 12*(eval_point**2))])
if degree == 3:
- return [np.sqrt(15/34) *
- (1 + 4*eval_point - 30*(eval_point**2)
- + 28*(eval_point**3)),
- np.sqrt(1/42) *
- (-4 + 105*eval_point - 300*(eval_point**2)
- + 210*(eval_point**3)),
- 1/2 * np.sqrt(35/34) *
- (-5 + 48*eval_point - 105*(eval_point**2)
- + 64*(eval_point**3)),
- 1/2 * np.sqrt(5/42) *
- (-16 + 105*eval_point - 192*(eval_point**2)
- + 105*(eval_point**3))]
+ return np.array([np.sqrt(15/34) *
+ (1 + 4*eval_point - 30*(eval_point**2)
+ + 28*(eval_point**3)),
+ np.sqrt(1/42) *
+ (-4 + 105*eval_point - 300*(eval_point**2)
+ + 210*(eval_point**3)),
+ 1/2 * np.sqrt(35/34) *
+ (-5 + 48*eval_point - 105*(eval_point**2)
+ + 64*(eval_point**3)),
+ 1/2 * np.sqrt(5/42) *
+ (-16 + 105*eval_point - 192*(eval_point**2)
+ + 105*(eval_point**3))])
if degree == 4:
- return [np.sqrt(1/186) *
- (1 + 30*eval_point + 210*(eval_point**2)
- - 840*(eval_point**3) + 630*(eval_point**4)),
- 0.5 * np.sqrt(1/38) *
- (-5 - 144*eval_point + 1155*(eval_point**2)
- - 2240*(eval_point**3) + 1260*(eval_point**4)),
- np.sqrt(35/14694) *
- (22 - 735*eval_point + 3504*(eval_point**2)
- - 5460*(eval_point**3) + 2700*(eval_point**4)),
- 1/8 * np.sqrt(21/38) *
- (35 - 512*eval_point + 1890*(eval_point**2)
- - 2560*(eval_point**3) + 1155*(eval_point**4)),
- 0.5 * np.sqrt(7/158) *
- (32 - 315*eval_point + 960*(eval_point**2)
- - 1155*(eval_point**3) + 480*(eval_point**4))]
+ return np.array([np.sqrt(1/186) *
+ (1 + 30*eval_point + 210*(eval_point**2)
+ - 840*(eval_point**3) + 630*(eval_point**4)),
+ 0.5 * np.sqrt(1/38) *
+ (-5 - 144*eval_point + 1155*(eval_point**2)
+ - 2240*(eval_point**3) + 1260*(eval_point**4)),
+ np.sqrt(35/14694) *
+ (22 - 735*eval_point + 3504*(eval_point**2)
+ - 5460*(eval_point**3) + 2700*(eval_point**4)),
+ 1/8 * np.sqrt(21/38) *
+ (35 - 512*eval_point + 1890*(eval_point**2)
+ - 2560*(eval_point**3) + 1155*(eval_point**4)),
+ 0.5 * np.sqrt(7/158) *
+ (32 - 315*eval_point + 960*(eval_point**2)
+ - 1155*(eval_point**3) + 480*(eval_point**4))])
raise ValueError('Invalid value: Alpert\'s wavelet is only available \
up to degree 4 for this application')
- def _build_inverse_mass_matrix(self):
+ def _build_inverse_mass_matrix(self) -> ndarray:
"""Construct inverse mass matrix.
Returns
@@ -355,7 +358,7 @@ class OrthonormalLegendre(Legendre):
@property
@cache
- def basis_projections(self):
+ def basis_projections(self) -> Tuple[ndarray, ndarray]:
"""Return basis projection.
Construct matrices containing the integrals of the
@@ -374,7 +377,8 @@ class OrthonormalLegendre(Legendre):
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):
+ def _build_basis_matrix(self, first_param: float, second_param: float) \
+ -> ndarray:
"""Construct a basis matrix.
Parameters
@@ -399,11 +403,11 @@ class OrthonormalLegendre(Legendre):
(z, -1, 1))
row.append(np.float64(entry))
matrix.append(row)
- return matrix
+ return np.array(matrix)
@property
@cache
- def multiwavelet_projections(self):
+ def multiwavelet_projections(self) -> Tuple[ndarray, ndarray]:
"""Return wavelet projection.
Construct matrices containing the integrals of the
@@ -424,8 +428,9 @@ class OrthonormalLegendre(Legendre):
z, 0.5*(z+1), False)
return left_wavelet_projection, right_wavelet_projection
- def _build_multiwavelet_matrix(self, first_param, second_param,
- is_left_matrix):
+ def _build_multiwavelet_matrix(self, first_param: float,
+ second_param: float, is_left_matrix: bool) \
+ -> ndarray:
"""Construct a multiwavelet matrix.
Parameters
@@ -455,10 +460,10 @@ class OrthonormalLegendre(Legendre):
entry = entry * (-1)**(j + self._polynomial_degree + 1)
row.append(np.float64(entry))
matrix.append(row)
- return matrix
+ return np.array(matrix)
- def calculate_cell_average(self, projection, stencil_length,
- add_reconstructions=True):
+ def calculate_cell_average(self, projection: ndarray, stencil_length: int,
+ add_reconstructions: bool = True) -> ndarray:
"""Calculate cell averages for a given projection.
Calculate the cell averages of all cells in a projection.
@@ -502,7 +507,8 @@ class OrthonormalLegendre(Legendre):
cell_averages[:, middle_idx+1:]))))
return np.array(list(map(np.float64, cell_averages)))
- def _calculate_reconstructions(self, projection):
+ def _calculate_reconstructions(self, projection: ndarray) \
+ -> Tuple[list, list]:
"""Calculate left and right reconstructions for a given projection.
Parameters