def plot_error_comparison(solvers, time_steps, final_errors, **kwargs):
fig = plt.figure(figsize = (7, 7 * 2 / 3), dpi = 600)
fig.set_tight_layout(True)
axis = plt.subplot(111)
for solver in solvers:
plt.plot(time_steps, final_errors[solver], label = solver.method)
axis.set_yscale('log')
axis.set_xscale('log')
title = axis.set_title(r'Error in $y_{\mathrm{numeric}}(t=1)$ vs. time step', fontsize = 15)
title.set_y(1.05)
axis.set_xlabel(r'$\Delta t$', fontsize = 15)
axis.set_ylabel(r'$\left| y_{\mathrm{analytic}}(t=1) - y_{\mathrm{numeric}}(t=1) \right|$', fontsize = 15)
axis.set_xlim(time_steps[0], time_steps[-1])
axis.grid(True, color = 'black', linestyle = '--')
axis.tick_params(axis = 'both', which = 'major', labelsize = 10)
axis.legend(loc = 'best', fontsize = 12)
utils.save_current_figure(name = 'error_comparison', img_format = 'pdf', **kwargs)
plt.close()
def plot_solution_comparison(solutions, analytic, **kwargs):
fig = plt.figure(figsize = (7, 7 * 2 / 3), dpi = 600)
fig.set_tight_layout(True)
axis = plt.subplot(111)
for sol in solutions:
sol.attach_y_vs_t_to_axis(axis)
dense_t = np.linspace(sol.t[0], sol.t[-1], 10 * len(sol.t))
line, = plt.plot(dense_t, analytic(dense_t), label = 'Analytic', linestyle = '--', color = 'orange')
title = axis.set_title(r'$y$ vs. $t$, with $\Delta t = {}$'.format(sol.delta_t), fontsize = 15)
title.set_y(1.05)
axis.set_xlabel(r'$t$', fontsize = 15)
axis.set_ylabel(r'$y$', fontsize = 15)
axis.set_xlim(sol.t[0], sol.t[-1])
axis.grid(True, color = 'black', linestyle = ':')
axis.tick_params(axis = 'both', which = 'major', labelsize = 10)
axis.legend(loc = 'best', fontsize = 12)
utils.save_current_figure(name = 'solution_comparison_dt{}'.format(sol.delta_t), img_format = 'pdf', **kwargs)
plt.close()
def plot(self, **kwargs):
plt.figure(figsize = (7, 7), dpi = 600)
con = plt.contour(self.x_mesh, self.y_mesh, self.u,
levels = [1]
)
plt.title(r'$u(x,y)$ at $t = {}$'.format(np.around(self.t, 7)), fontsize = 20)
plt.xlabel(r'$x$', fontsize = 16)
plt.ylabel(r'$y$', fontsize = 16)
plt.grid(True)
utils.save_current_figure(name = 'u_{}'.format(self.t_counter), **kwargs)
plt.close()
def plot_uv_vs_t(self, time_index=0, **kwargs):
fig = plt.figure(figsize=(7, 7 * 2 / 3), dpi=600)
fig.set_tight_layout(True)
axis = plt.subplot(111)
t = self.time(time_index)
plt.plot(self.x,
self.u[time_index],
color='blue',
label='$u_{\mathrm{numeric}}$')
plt.plot(self.x,
self.u_analytic(self.x, t),
color='teal',
label='$u_{\mathrm{analytic}}$')
plt.plot(self.x,
self.v[time_index],
color='red',
label='$v_{\mathrm{numeric}}$')
plt.plot(self.x,
self.v_analytic(self.x, t),
color='orange',
label='$v_{\mathrm{analytic}}$')
axis.set_xlim(self.x[0], self.x[-1])
axis.set_ylim(-2, 2)
axis.set_xlabel(r'$x$', fontsize=15)
axis.set_ylabel(r'$u(x, t), \, v(x, t)$', fontsize=15)
title = axis.set_title(r'Solution at $t = {}$'.format(round(t, 3)),
fontsize=15)
title.set_y(1.05)
axis.grid(True, color='gray', linestyle=':', alpha=0.9)
axis.tick_params(axis='both', which='major', labelsize=10)
axis.legend(loc='best', fontsize=12)
utils.save_current_figure(name='{}_i={}_t={}'.format(
self.method, time_index, round(t, 3)),
**kwargs)
plt.close()
def plot_y_vs_t(self, **kwargs):
fig = plt.figure(figsize = (7, 7 * 2 / 3), dpi = 600)
fig.set_tight_layout(True)
axis = plt.subplot(111)
self.attach_y_vs_t_to_axis(axis)
title = axis.set_title(r'y vs. t, using {} with $\Delta t = {}$'.format(self.method, self.delta_t), fontsize = 15)
title.set_y(1.05)
axis.set_xlabel(r't', fontsize = 15)
axis.set_ylabel(r'y', fontsize = 15)
axis.set_xlim(self.t[0], self.t[-1])
axis.grid(True, color = 'black', linestyle = ':')
axis.tick_params(axis = 'both', which = 'major', labelsize = 10)
# axis.legend(loc = 'best', fontsize = 12)
utils.save_current_figure(**kwargs)
plt.close()
def plot_u_vs_x_vs_t(self, t_indices = (0, 20, 40, 60, 80, 100), **kwargs):
fig = plt.figure(figsize = (7, 7 * 2 / 3), dpi = 600)
fig.set_tight_layout(True)
axis = plt.subplot(111)
for t_index in t_indices:
self.attach_u_vs_x_to_axis(axis, t_index = t_index)
title = axis.set_title(r'$u(x, t)$ vs. $x$, using {} with $\Delta t = {}$'.format(self.method, self.delta_t), fontsize = 15)
title.set_y(1.05)
axis.set_xlabel(r'$x$', fontsize = 15)
axis.set_ylabel(r'$u(x)$', fontsize = 15)
axis.set_xlim(self.t[0], self.t[-1])
axis.grid(True, color = 'black', linestyle = ':')
axis.tick_params(axis = 'both', which = 'major', labelsize = 10)
plt.legend(loc = 'best', fontsize = 10)
utils.save_current_figure(**kwargs)
plt.close()
def plot_u(self, colormesh=False, postfix='', **kwargs):
fig = plt.figure(figsize=(7, 7 * .75), dpi=600)
fig.set_tight_layout(True)
axis = plt.subplot(111)
contour = axis.contour(self.x_mesh,
self.y_mesh,
self.u,
levels=[0],
colors='green')
plt.clabel(contour, inline=1, fontsize=10)
if colormesh:
vmin = min(np.min(self.u), -1)
vmax = max(np.max(self.u), 1)
color = axis.pcolormesh(self.x_mesh,
self.y_mesh,
self.u,
cmap=plt.get_cmap('gray'),
shading='gouraud',
vmin=vmin,
vmax=vmax)
cbar = plt.colorbar(color)
postfix += '_colormesh'
axis.set_xlabel(r'$x$', fontsize=15)
axis.set_ylabel(r'$y$', fontsize=15)
title = axis.set_title(r'$u(x,y, t = {})$'.format(
np.around(self.t[self.time_index], 4)),
fontsize=15)
title.set_y(1.05)
utils.save_current_figure('RDSO_u' + postfix, **kwargs)
plt.close()
def plot_u_vs_x(self, t_index = 0, overlay_analytic = True, **kwargs):
fig = plt.figure(figsize = (7, 7 * 2 / 3), dpi = 600)
fig.set_tight_layout(True)
axis = plt.subplot(111)
self.attach_u_vs_x_to_axis(axis, t_index = t_index)
if overlay_analytic:
axis.plot(self.x_dense, self.u_analytic(self.x_dense, self.t[t_index]), linestyle = '--', label = r'$u_{\mathrm{analytic}}$')
title = axis.set_title(r'$u(t={})$ vs. $x$, using {} with $\Delta t = {}$'.format(np.around(self.t[t_index], 3), self.method, self.delta_t), fontsize = 15)
title.set_y(1.05)
axis.set_xlabel(r'$x$', fontsize = 15)
axis.set_ylabel(r'$u(t={})$'.format(np.around(self.t[t_index], 3)), fontsize = 15)
axis.set_xlim(self.t[0], self.t[-1])
axis.grid(True, color = 'black', linestyle = ':')
axis.tick_params(axis = 'both', which = 'major', labelsize = 10)
if overlay_analytic:
plt.legend(loc = 'best')
utils.save_current_figure(**kwargs)
plt.close()