Replaced symbol 'x' with 'z' for Alpert's wavelet.

DG_Approximation.py

@@ -8,7 +8,8 @@ TODO: Contemplate using Seaborn instead of matplotlib
 TODO: Double-check everything!
 TODO: Replace loops with list comprehension if feasible
 TODO: Combine initial projection and approx solution somehow
-TODO: Contemplate erasing inv_mass-matrix as it is identity -> Discuss
+TODO: Contemplate erasing inv_mass-matrix as it is identity
+    -> Done (No, because could be problematic for other functions)
 TODO: Investigate why we need inverse mass matrix for initial projection, \
     but not A and B
 TODO: Investigate why there are no weights in approx calc
@@ -28,6 +29,8 @@ TODO: Make sure instance variables are only set in __init__()
 TODO: Contemplate moving plots to pertaining files
 TODO: Discuss details plot!
 TODO: Fix typo in Vectors_of_Polynomials -> Done
+TODO: Replace symbol 'x' with 'z' for Alpert's wavelet -> Done
+TODO: Check time efficiency of details plot
 
 """
 import numpy as np
@@ -379,9 +382,9 @@ class DGScheme(object):
                                for degree in range(self.polynom_degree+1)]
 
         multiwavelet_coeffs = self.detector._calculate_wavelet_coeffs(projection)
-        wavelet = AlpertsWavelet(self.polynom_degree).get_vector(x)
+        wavelet = AlpertsWavelet(self.polynom_degree).get_vector(xi)
 
-        wavelet_projection = [[multiwavelet_coeffs[degree][cell]*wavelet[degree].subs(x, 0.5) * value
+        wavelet_projection = [[multiwavelet_coeffs[degree][cell]*wavelet[degree].subs(xi, 0.5) * value
                                for cell in range(len(coarse_projection[0]))
                                for value in [(-1)**(self.polynom_degree+degree+1), 1]]
                               for degree in range(self.polynom_degree+1)]
@@ -391,8 +394,8 @@ class DGScheme(object):
         for degree in range(self.polynom_degree + 1):
             leftMesh = coarse_projection[degree] * self.basis[degree].subs(x, -1 / 2)
             rightMesh = coarse_projection[degree] * self.basis[degree].subs(x, 1 / 2)
-            leftTest = multiwavelet_coeffs[degree] * wavelet[degree].subs(x, 1 / 2) * (-1) ** (self.polynom_degree + 1 + degree)
-            rightTest = multiwavelet_coeffs[degree] * wavelet[degree].subs(x, 1 / 2)
+            leftTest = multiwavelet_coeffs[degree] * wavelet[degree].subs(xi, 1 / 2) * (-1) ** (self.polynom_degree + 1 + degree)
+            rightTest = multiwavelet_coeffs[degree] * wavelet[degree].subs(xi, 1 / 2)
             newRowMesh = []
             newRowTest = []
             for i in range(len(coarse_projection[0])):
@@ -431,6 +434,7 @@ class DGScheme(object):
         plt.xlabel('X')
         plt.ylabel('Detail Coefficients')
         plt.title('Wavelet Coefficients')
+        plt.show()
 
     def _plot_shock_tube(self):
         time_history = self.update_scheme.get_time_history()