Fix linting errors

Author: Amund211

numdiff/conditions.py

@@ -1,4 +1,3 @@
-from collections.abc import Callable
 from dataclasses import dataclass
 from typing import Any
 

numdiff/examples.py

@@ -2,7 +2,7 @@
 import numpy as np
 
 from .conditions import Dirichlet, Neumann
-from .equations import HeatEquation, InviscidBurgers, InviscidBurgers2, PeriodicKdV
+from .equations import HeatEquation, InviscidBurgers, PeriodicKdV
 from .plotting import solve_and_plot
 from .poisson import amr, poisson
 from .refine import refine_mesh

numdiff/helpers.py

@@ -21,8 +21,8 @@ def central_difference(N, power=2, format="lil"):
 
 def l2(v, axis=None):
     """Calculate the discrete l2 norm of the vector v"""
-    l = v.shape[0]
-    return np.sqrt(np.sum(np.square(v), axis=axis) / l)
+    length = v.shape[0]
+    return np.sqrt(np.sum(np.square(v), axis=axis) / length)
 
 
 def relative_l2_error(u, U):

numdiff/laplace.py

@@ -1,6 +1,9 @@
 """
-This module considers the following 2D Laplace equation on the unit square (x,y) ∈ [0,1]^2 = Ω
-u_xx + u_yy = 0
+This module considers an instance of the 2D Laplace equation
+
+Specifically it solves
+u_xx + u_yy = 0, on the unit square (x,y) ∈ [0,1]^2 = Ω
+with boundary conditions:
 u(0,y) = 0, 0≤y≤1
 u(x,0) = 0, 0≤x≤1
 u(1,y) = 0, 0≤y≤1

tasks/advection_diffusion.py

@@ -61,7 +61,8 @@ class Scheme(ThetaMethod, PeriodicAdvectionDiffusion2ndOrder):
         f"Periodic advection diffusion - numerical solution with $M={M}, N={N}$"
     )
     plt.title(
-        r"$u_t = c u_x + d u_{xx}, u(x, 0) = \sin{\left( 4 \pi x\right)}, u(x, t) = u(x+1, t)$"
+        r"$u_t = c u_x + d u_{xx}, u(x, 0) = \sin{\left( 4 \pi x\right)}, "
+        "u(x, t) = u(x+1, t)$"
     )
     plt.xlabel("$x$")
     plt.ylabel("Time $t$")
@@ -223,7 +224,8 @@ def u(x, t):
     )
 
     plt.suptitle(
-        fr"Periodic advection diffusion - refinement with constant $r=\frac{{k}}{{h^2}}={r}$"
+        "Periodic advection diffusion - refinement "
+        fr"with constant $r=\frac{{k}}{{h^2}}={r}$"
     )
 
     plt.subplot(121)

tasks/burgers.py

@@ -2,7 +2,7 @@
 import numpy as np
 
 from numdiff.conditions import Dirichlet
-from numdiff.equations import InviscidBurgers, InviscidBurgers2
+from numdiff.equations import InviscidBurgers
 from numdiff.schemes import RK4
 from numdiff.settings import FINE_PARAMETERS
 

tasks/heat_eqn.py

@@ -67,7 +67,8 @@ def f(x):
 
     plt.suptitle(f"The heat equation - numerical solution with $M={M}, N={N}$")
     plt.title(
-        r"$u_t = u_{xx}, u(x, 0) = 2 \pi x + \sin{\left( 2 \pi x\right)}, u_x(0, t) = u_x(1, t) = 0$"
+        r"$u_t = u_{xx}, u(x, 0) = 2 \pi x + \sin{\left( 2 \pi x\right)}, "
+        "u_x(0, t) = u_x(1, t) = 0$"
     )
     plt.xlabel("$x$")
     plt.ylabel("Time $t$")
@@ -157,7 +158,8 @@ def f(x):
 
     plt.suptitle("The heat equation - discretization of the boundary conditions")
     plt.title(
-        f"Comparison with reference solution with $M^* = {M_star}$ at $t = {T}$. $N = {N}$"
+        "Comparison with reference solution with "
+        f"$M^* = {M_star}$ at $t = {T}$. $N = {N}$"
     )
     plt.xlabel("Internal nodes $M$")
     plt.ylabel(r"Relative $l_2$ error $\frac{\|U-u\|}{\|u\|}$")
@@ -275,7 +277,8 @@ def task_2bh():
 
     plt.suptitle("The heat equation - $h$-refinement")
     plt.title(
-        f"Backwards Euler vs Crank Nicholson with $N={TASK_2B_PARAMS['N']}$ at $t = {TASK_2B_PARAMS['T']}$"
+        "Backwards Euler vs Crank Nicholson with "
+        f"$N={TASK_2B_PARAMS['N']}$ at $t = {TASK_2B_PARAMS['T']}$"
     )
     plt.xlabel("Internal nodes $M$")
     plt.ylabel(r"Relative error $\frac{\|U-u\|}{\|u\|}$")
@@ -315,7 +318,8 @@ def task_2bk():
 
     plt.suptitle("The heat equation - $k$-refinement")
     plt.title(
-        f"Backwards Euler vs Crank Nicholson with $M={TASK_2B_PARAMS['M']}$ at $t = {TASK_2B_PARAMS['T']}$"
+        "Backwards Euler vs Crank Nicholson with "
+        f"$M={TASK_2B_PARAMS['M']}$ at $t = {TASK_2B_PARAMS['T']}$"
     )
     plt.xlabel("Time steps $N$")
     plt.ylabel(r"Relative error $\frac{\|U-u\|}{\|u\|}$")

tasks/kdv.py

@@ -58,7 +58,8 @@ def task_4_solution():
         f"Linearized Korteweg-deVries - numerical solution with $M={M}, N={N}$"
     )
     plt.title(
-        r"$u_t + \left(1 + \pi^2\right) u_x + u_{xxx} = 0, u(x, 0) = \sin{\left( \pi x\right)}, u(x, t) = u(x+2, t)$"
+        r"$u_t + \left(1 + \pi^2\right) u_x + u_{xxx} = 0, "
+        r"u(x, 0) = \sin{\left( \pi x\right)}, u(x, t) = u(x+2, t)$"
     )
     plt.xlabel("$x$")
     plt.ylabel("Time $t$")

tasks/laplace_2D.py

@@ -21,7 +21,8 @@ def task_3_solution():
     c = plt.pcolormesh(x, y, U, cmap="hot", shading="nearest")
     plt.colorbar(c, ax=plt.gca())
     plt.title(
-        r"$u_{xx} + u_{yy} = 0, \> u(x, 1) = \sin{\left( 2 \pi x\right)}, u(0, y) = u(x, 0) = u(1, y) = 0$"
+        r"$u_{xx} + u_{yy} = 0, \> u(x, 1) = \sin{\left( 2 \pi x\right)}, "
+        "u(0, y) = u(x, 0) = u(1, y) = 0$"
     )
     plt.xlabel("$x$")
     plt.ylabel("$y$")

tasks/poisson_1D.py

@@ -77,7 +77,8 @@ def u(x):
 
     plt.suptitle(f"Poisson's equation - Analytical vs numerical with $M={M}$")
     plt.title(
-        fr"$u_{{xx}} = f(x) = \cos{{\left( 2 \pi x \right)}} + x, u(0, t) = {alpha}, u_x(1, t) = {sigma}$"
+        r"$u_{xx} = f(x) = \cos{\left( 2 \pi x \right)} + x, "
+        f"u(0, t) = {alpha}, u_x(1, t) = {sigma}$"
     )
     plt.xlabel("$x$")
     plt.ylabel("$y$")
@@ -169,7 +170,8 @@ def u(x):
 
     plt.suptitle(f"Poisson's equation - Analytical vs numerical with $M={M}$")
     plt.title(
-        fr"$u_{{xx}} = f(x) = \cos{{\left( 2 \pi x \right)}} + x, u(0, t) = {alpha}, u(1, t) = {beta}$"
+        r"$u_{xx} = f(x) = \cos{\left( 2 \pi x \right)} + x, "
+        f"u(0, t) = {alpha}, u(1, t) = {beta}$"
     )
     plt.xlabel("$x$")
     plt.ylabel("$y$")
@@ -268,7 +270,8 @@ def u(x):
 
     plt.suptitle(f"Poisson's equation - ill posed problem with $M={M}$")
     plt.title(
-        fr"$u_{{xx}} = f(x) = \cos{{\left( 2 \pi x \right)}} + x, u_x(0) = {sigma1}, u_x(1) = {sigma2}$"
+        r"$u_{xx} = f(x) = \cos{\left( 2 \pi x \right)} + x, "
+        f"u_x(0) = {sigma1}, u_x(1) = {sigma2}$"
     )
     plt.xlabel("$x$")
     plt.ylabel("$y$")