def plot_function_xt_phase(plot_1_chars=False, plot_2_chars=False):
plt.figure(figsize=(7, 2))
ax = plt.subplot(121)
riemann_tools.plot_waves(states,
speeds,
reval,
wave_types,
t=0,
ax=ax,
color='multi')
if plot_1_chars:
riemann_tools.plot_characteristics(reval,
shallow_water.lambda_1,
axes=ax,
extra_lines=extra_lines)
if plot_2_chars:
riemann_tools.plot_characteristics(reval,
shallow_water.lambda_2,
axes=ax,
extra_lines=extra_lines)
ax = plt.subplot(122)
shallow_water.phase_plane_plot(q_l,
q_r,
g,
ax=ax,
force_waves=force_waves,
y_axis='u')
plt.title('Phase plane')
plt.show()
def plot_waves(f,q_left, q_right, xi_left, xi_right, n=1000, axes=None, t=0.2):
qtilde = nonconvex.osher_solution(f, q_left, q_right, 1000)
xi = np.linspace(xi_left, xi_right, n)
qvals = qtilde(xi)
fvals = f(qvals)
dxi = xi[1]-xi[0]
smoothness = riemann_tools.detect_smoothness(qvals,dxi,dmax=10)
values, ranges = riemann_tools.intervals(smoothness)
# filter out extraneous constant states between rarefactions:
# For complicated nonconvex fluxes,
# values tend to contain sequences [1,0,1] indicating a constant
# state between two rarefaction waves, which shouldn't happen,
# so merge such ranges into a single rarefaction wave.
jd = []
for j in range(len(values)):
try:
if values[j]==0 and values[j+1]==1 and values[j-1]==1:
jd.append(j)
except:
pass
jd.reverse()
for j in jd:
ranges[j-1] = (ranges[j-1][0], ranges[j+1][1]) # merge
values.pop(j+1)
values.pop(j)
ranges.pop(j+1)
ranges.pop(j)
wave_types, speeds = riemann_tools.make_waves(values, ranges, xi)
riemann_tools.plot_waves(None,speeds,None,wave_types,ax=axes,
t_pointer=False,t=t)
#plt.xlim(xi_left, xi_right)
plt.xlabel('x')
def plot_function_xt_phase(plot_1_chars=False,plot_2_chars=False,plot_tracer_chars=False):
plt.figure(figsize=(7,2))
ax = plt.subplot(121)
riemann_tools.plot_waves(states, speeds, reval, wave_types, t=0,
ax=ax, color='multi')
if plot_1_chars:
riemann_tools.plot_characteristics(reval,lambda_1,
axes=ax,extra_lines=extra_lines)
if plot_2_chars:
riemann_tools.plot_characteristics(reval,lambda_2,
axes=ax,extra_lines=extra_lines)
if plot_tracer_chars:
riemann_tools.plot_characteristics(reval,lambda_tracer,
axes=ax,extra_lines=extra_lines)
ax = plt.subplot(122)
phase_plane_plot(q_l,q_r,g,ax=ax,
force_waves=force_waves,y_axis='u')
plt.title('Phase plane')
plt.show()