Merge branch 'master' into lax_friedrichs_flux

.github/CODEOWNERS

@@ -0,0 +1,3 @@
+@amanabt
+@Balavarun5
+@mchandra

code/app/global_variables.py

@@ -43,7 +43,6 @@ def LGL_points(N):
 
     return lgl_points
 
-
 def lobatto_weight_function(n, x):
     '''
     Calculates and returns the weight function for an index :math:`n`
@@ -64,9 +63,10 @@ def lobatto_weight_function(n, x):
     
     Returns
     -------
+
     gauss_lobatto_weights : arrayfire.Array
-                          An array of lobatto weight functions for
-                          the given :math: `x` points and index.
+                            An array of lobatto weight functions for
+                            the given :math: `x` points and index.
     Reference
     ---------
     Gauss-Lobatto weights Wikipedia link-

code/app/lagrange.py

@@ -118,6 +118,4 @@ def dLp_xi_LGL(lagrange_coeff_array):
 
     dLp_xi = af.blas.matmul(differentiation_coeffs, nodes_power_tile)
 
-    return dLp_xi
-
-
+    return dLp_xi

code/app/wave_equation.py

@@ -38,7 +38,6 @@
 plt.rcParams['ytick.direction'] = 'in'
 
 
-
 def mapping_xi_to_x(x_nodes, xi):
     '''
     Maps points in :math: `\\xi` space to :math:`x` space using the formula
@@ -63,15 +62,15 @@ def mapping_xi_to_x(x_nodes, xi):
     N_0 = (1 - xi) / 2
     N_1 = (1 + xi) / 2
 
+
     N0_x0 = af.broadcast(utils.multiply, N_0, x_nodes[0])
     N1_x1 = af.broadcast(utils.multiply, N_1, x_nodes[1])
 
     x = N0_x0 + N1_x1
 
     return x
 
-
-
+
 def dx_dxi_numerical(x_nodes, xi):
     '''
     Differential :math: `\\frac{dx}{d \\xi}` calculated by central differential
@@ -92,6 +91,7 @@ def dx_dxi_numerical(x_nodes, xi):
              :math:`\\frac{dx}{d \\xi}`. 
     '''
     dxi = 1e-7
+
     x2  = mapping_xi_to_x(x_nodes, xi + dxi)
     x1  = mapping_xi_to_x(x_nodes, xi - dxi)
 
@@ -120,7 +120,6 @@ def dx_dxi_analytical(x_nodes, xi):
 
     return analytical_dx_dxi
 
-
 def A_matrix():
     '''
     Calculates A matrix whose elements :math:`A_{p i}` are given by
@@ -153,13 +152,13 @@ def A_matrix():
 
 def flux_x(u):
     '''
-    A function which returns the value of flux for a given wave function u.
-    :math:`f(u) = c u^k`
+    A function which calcultes and returns the value of flux for a given
+    wave function u. :math:`f(u) = c u^k`
     
     Parameters
     ----------
-    u    : arrayfire.Array
-           A 1-D array which contains the value of wave function.
+    u : arrayfire.Array [N 1 1 1]
+        A 1-D array which contains the value of wave function.
     
     Returns
     -------
@@ -181,6 +180,7 @@ def volume_integral_flux(u):
     
     Parameters
     ----------
+
     u             : arrayfire.Array [N_LGL N_Elements 1 1]
                     A 1-D array containing the value of the wave function at
                     the mapped LGL nodes in the element.
@@ -192,6 +192,7 @@ def volume_integral_flux(u):
                     for various lagrange basis functions.
     '''
 
+
     dLp_xi        = gvar.dLp_xi
     weight_tile   = af.transpose(af.tile(gvar.lobatto_weights, 1, gvar.N_LGL))
     dLp_xi       *= weight_tile
@@ -323,5 +324,4 @@ def time_evolution():
             fig.savefig('results/1D_Wave_images/%04d' %(t_n / 100) + '.png')
             plt.close('all')
 
-    return
-
+    return

code/main.py

@@ -11,4 +11,5 @@
 
 if __name__ == '__main__':
 
-    wave_equation.time_evolution()
+
+    wave_equation.time_evolution()

code/unit_test/test_waveEqn.py

@@ -9,6 +9,7 @@
 af.set_backend('opencl')
 
 
+
 def test_mapping_xi_to_x():
     '''
     A test function to check the mapping_xi_to_x function in wave_equation module,
@@ -21,18 +22,20 @@ def test_mapping_xi_to_x():
     test_element_nodes = af.interop.np_to_af_array(np.array([7, 11]))
     test_xi            = 0
     analytical_x_value = 9
+
     numerical_x_value  = wave_equation.mapping_xi_to_x(test_element_nodes, test_xi)
 
     assert af.abs(analytical_x_value - numerical_x_value) <= threshold
 
-
 def test_dx_dxi():
     '''
     A Test function to check the dx_xi function in wave_equation module by
     passing nodes of an element and using the LGL points. Analytically, the
     differential would be a constant. The check has a tolerance 1e-7.
     '''
+
     threshold = 1e-14
+
     nodes = np.array([7, 10], dtype = np.float64)
     test_nodes = af.interop.np_to_af_array(nodes)
     analytical_dx_dxi = 1.5
@@ -56,6 +59,7 @@ def test_dx_dxi_analytical():
     assert check_analytical_dx_dxi
 
 
+
 def test_lagrange_coeffs():
     '''
     Function to test the lagrange_coeffs in global_variables module by
@@ -69,6 +73,7 @@ def test_lagrange_coeffs():
     https://cocalc.com/projects/1b7f404c-87ba-40d0-816c-2eba17466aa8/files
     /PM_2_5/wave_equation/worksheets/l_basis_array.sagews
     '''
+
     threshold = 6e-10 
     basis_array_analytical = np.zeros([8, 8])
 
@@ -142,6 +147,7 @@ def test_lagrange_coeffs():
 
     basis_array_analytical = af.interop.np_to_af_array(basis_array_analytical)
 
+
     assert af.sum(af.abs(basis_array_analytical - gvar.lagrange_coeffs)) < threshold
 
 
@@ -153,6 +159,7 @@ def test_integral_Li_Lp():
     all elements above a certain threshold to be 1 and plotting it.
     '''
     threshold = 1e-5
+
     A_matrix_structure = np.zeros([gvar.N_LGL, gvar.N_LGL])
     non_zero_indices  = np.where(np.array(wave_equation.A_matrix()) > threshold)
 
@@ -178,6 +185,7 @@ def test_A_matrix():
     The A matrix calculated analytically gives a different matrix.
     
     '''
+
     threshold = 3e-10
 
     reference_A_matrix = af.tile(gvar.lobatto_weights, 1, gvar.N_LGL)\
@@ -188,6 +196,7 @@ def test_A_matrix():
     test_A_matrix = wave_equation.A_matrix()
     error_array   = af.abs(reference_A_matrix - test_A_matrix)
 
+
     print(af.max(error_array))
 
     assert af.algorithm.max(error_array) < threshold
@@ -235,7 +244,6 @@ def test_dLp_xi():
 
     assert af.max(reference_d_Lp_xi - gvar.dLp_xi) < threshold
 
-
 def test_volume_integral_flux():
     '''
     A test function to check the volume_integral_flux function in wave_equation
@@ -245,6 +253,7 @@ def test_volume_integral_flux():
     ---------
     The link to the sage worksheet where the calculations were caried out is
     given below.
+
     https://cocalc.com/projects/1b7f404c-87ba-40d0-816c-2eba17466aa8/files
     /PM_2_5/wave_equation/worksheets/volume_integral_flux.sagews
     
@@ -273,6 +282,7 @@ def test_volume_integral_flux():
         [-0.102576031756, 0.0154359890788, 0.0209837936827, 0.019612124119, \
         0.0144355176966, 0.00882630935977, 0.00431252844519, 0.018969769374],\
         [-0.0176615086879, 0.00344551201015 ,0.00432019709409, 0.00362050204766,\
+
         0.00236838757932, 0.00130167737191, 0.000588597708116, 0.00201663487667\
             ]])))
 
@@ -335,4 +345,4 @@ def test_b_vector():
                                     (surface_term)) * gvar.delta_t
     b_vector_array       = wave_equation.b_vector(gvar.u[:, :, 0])
 
-    assert (b_vector_analytical - b_vector_array) < threshold
+    assert (b_vector_analytical - b_vector_array) < threshold

code/utils/utils.py

@@ -5,19 +5,25 @@
 def add(a, b):
     '''
     '''
-    return a + b
+    sum = a + b
+
+    return sum
 
 
 def divide(a, b):
     '''
     '''
-    return a / b
+    quotient = a / b
+
+    return quotient
 
 
 def multiply(a, b):
     '''
     '''
-    return a * b
+    product = a* b
+
+    return product
 
 
 def linspace(start, end, number_of_points):