diff --git a/Basis_Function.py b/Basis_Function.py
index d4eb15c7eb2f8f10d6dd2ce405cf8c0e42234b60..4fb2628980f535d30c2421ba621fdb075462e1a0 100644
--- a/Basis_Function.py
+++ b/Basis_Function.py
@@ -7,14 +7,14 @@ import numpy as np
from sympy import Symbol, integrate
x = Symbol('x')
-xi = Symbol('z')
+z = Symbol('z')
class Vector(object):
def __init__(self, polynomial_degree):
self._polynomial_degree = polynomial_degree
self._basis = self._build_basis_vector(x)
- self._wavelet = self._build_wavelet_vector(xi)
+ self._wavelet = self._build_wavelet_vector(z)
def get_basis_vector(self):
return self._basis
@@ -90,8 +90,8 @@ class OrthonormalLegendre(Legendre):
up to degree 4 for this application')
def get_basis_projections(self):
- basis_projection_left = self._build_basis_matrix(xi, 0.5 * (xi - 1))
- basis_projection_right = self._build_basis_matrix(xi, 0.5 * (xi + 1))
+ 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
def _build_basis_matrix(self, first_param, second_param):
@@ -101,14 +101,14 @@ class OrthonormalLegendre(Legendre):
for j in range(self._polynomial_degree + 1):
entry = integrate(self._basis[i].subs(x, first_param)
* self._basis[j].subs(x, second_param),
- (xi, -1, 1))
+ (z, -1, 1))
row.append(np.float64(entry))
matrix.append(row)
return matrix
def get_multiwavelet_projections(self):
- wavelet_projection_left = self._build_multiwavelet_matrix(xi, -0.5*(xi-1), True)
- wavelet_projection_right = self._build_multiwavelet_matrix(xi, 0.5*(xi+1), False)
+ wavelet_projection_left = self._build_multiwavelet_matrix(z, -0.5*(z-1), True)
+ wavelet_projection_right = self._build_multiwavelet_matrix(z, 0.5*(z+1), False)
return wavelet_projection_left, wavelet_projection_right
def _build_multiwavelet_matrix(self, first_param, second_param, is_left_matrix):
@@ -116,8 +116,8 @@ class OrthonormalLegendre(Legendre):
for i in range(self._polynomial_degree+1):
row = []
for j in range(self._polynomial_degree+1):
- entry = integrate(self._basis[i].subs(x, first_param) * self._wavelet[j].subs(xi, second_param),
- (xi, -1, 1))
+ entry = integrate(self._basis[i].subs(x, first_param) * self._wavelet[j].subs(z, second_param),
+ (z, -1, 1))
if is_left_matrix:
entry = entry * (-1)**(j + self._polynomial_degree + 1)
row.append(np.float64(entry))
diff --git a/DG_Approximation.py b/DG_Approximation.py
index c7c892abac9d86f98a8592c7a977e08362ed76cf..8c9e8cda152bf1b7c27c7d4d8a8c72ad97ba41ab 100644
--- a/DG_Approximation.py
+++ b/DG_Approximation.py
@@ -14,10 +14,11 @@ TODO: Restructure Vectors_of_Polynomials -> Done
TODO: Rename Vectors_of_Polynomials -> Done (Basis_Function)
TODO: Contemplate how to make shock tubes comparable
TODO: Implement type check for all kwargs and configs -> Done (not recommended for Python)
+TODO: Create a Conda environment with dependencies -> Done
"""
import numpy as np
-from sympy import Symbol, integrate
+from sympy import Symbol
import math
import matplotlib.pyplot as plt
@@ -29,7 +30,6 @@ import Update_Scheme
from Basis_Function import OrthonormalLegendre
x = Symbol('x')
-xi = Symbol('z')
class DGScheme(object):
diff --git a/Main.py b/Main.py
index 112e3fdcf3bb592366a98a1d02f1b1ffd074f4b1..3a48775b40214014e06bbc14fb2e6f6cb1b080b7 100644
--- a/Main.py
+++ b/Main.py
@@ -20,21 +20,22 @@ xL = -1
xR = 1
detector_config = {}
+init_config = {}
+limiter_config = {}
+quadrature_config = {}
+
fold_len = 16
whisker_len = 3
detector_config['fold_len'] = fold_len
detector_config['whisker_len'] = whisker_len
-init_config = {}
init_config['factor'] = 4
init_config['left_factor'] = 3
-limiter_config = {}
limiter_config['mod_factor'] = 0
limiter_config['erase_degree'] = 0
-quadrature_config = {}
quadrature_config['num_eval_points'] = 12 # 12
detector = 'Theoretical'
diff --git a/Troubled_Cell_Detector.py b/Troubled_Cell_Detector.py
index ee2fca4fecedba1abdcacbae4c525160d7bf28a5..182b8f214e0a633a923119c7c56da192453e0ce6 100644
--- a/Troubled_Cell_Detector.py
+++ b/Troubled_Cell_Detector.py
@@ -7,10 +7,10 @@ import os
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
-from sympy import Symbol, integrate
+from sympy import Symbol
x = Symbol('x')
-xi = Symbol('z')
+z = Symbol('z')
class TroubledCellDetector(object):
@@ -232,9 +232,9 @@ class WaveletDetector(TroubledCellDetector):
# for degree in range(self._polynomial_degree + 1):
# leftMesh = coarse_projection[degree] * basis[degree].subs(x, -1 / 2)
# rightMesh = coarse_projection[degree] * basis[degree].subs(x, 1 / 2)
- # leftTest = multiwavelet_coeffs[degree] * wavelet[degree].subs(xi, 1 / 2) \
+ # leftTest = multiwavelet_coeffs[degree] * wavelet[degree].subs(z, 1 / 2) \
# * (-1)**(self._polynomial_degree + 1 + degree)
- # rightTest = multiwavelet_coeffs[degree] * wavelet[degree].subs(xi, 1 / 2)
+ # rightTest = multiwavelet_coeffs[degree] * wavelet[degree].subs(z, 1 / 2)
# newRowMesh = []
# newRowTest = []
# for i in range(len(coarse_projection[0])):
@@ -254,7 +254,7 @@ class WaveletDetector(TroubledCellDetector):
for value in [-0.5, 0.5]]
for degree in range(self._polynomial_degree + 1)]
- wavelet_projection = [[multiwavelet_coeffs[degree][cell] * wavelet[degree].subs(xi, 0.5) * value
+ wavelet_projection = [[multiwavelet_coeffs[degree][cell] * wavelet[degree].subs(z, 0.5) * value
for cell in range(self._num_coarse_grid_cells)
for value in [(-1) ** (self._polynomial_degree + degree + 1), 1]]
for degree in range(self._polynomial_degree + 1)]