def main(tend=10.0, N=25, nt=30, nstencil=3, linterpol=False,
rinterpol=False, num_jacobian=False, plot=False,
savefig='None', verbose=False):
x = np.linspace(0.1, 1.0, N+1)
def f(x):
return 2*x**2/(x**4+1) # f(0)=0, f(1)=1, f'(0)=0, f'(1)=0
y0 = f(x[1:])+x[0] # (x[0]/2+x[1:])**2
t0 = 1e-10
tout = np.linspace(t0, tend, nt)
res, systems = [], []
for g in 'fcs':
rd = ReactionDiffusion(1, [], [], [], N=N, D=[0.02], x=x,
geom=g, nstencil=nstencil, lrefl=not linterpol,
rrefl=not rinterpol)
integr = run(rd, y0, tout, with_jacobian=(not num_jacobian))
res.append(integr.yout)
systems.append(rd)
if plot:
# matplotlib
from mpl_toolkits.mplot3d import Axes3D
assert Axes3D # silence pyflakes
from matplotlib import cm
from matplotlib import pyplot as plt
fig = plt.figure()
# Plot spatio-temporal conc. evolution
for i, g in enumerate('fcs'):
yout = res[i]
ax = fig.add_subplot(2, 3, 'fcs'.index(g)+1, projection='3d')
plot_C_vs_t_and_x(rd, tout, yout, 0, ax,
rstride=1, cstride=1, cmap=cm.gist_earth)
ax.set_title(Geom_names[g])
# Plot mass conservation
ax = fig.add_subplot(2, 3, 4)
for j in range(3):
ax.plot(tout, np.apply_along_axis(
systems[j].integrated_conc, 1, res[j][:, :, 0]), label=str(j))
ax.legend(loc='best')
ax.set_title('Mass conservation')
# Plot difference from flat evolution (not too informative..)
for i, g in enumerate('fcs'):
yout = res[i] # only one specie
if i != 0:
yout = yout - res[0] # difference (1 specie)
ax = fig.add_subplot(2, 3, 3+'fcs'.index(g)+1, projection='3d')
plot_C_vs_t_and_x(rd, tout, yout, 0, ax,
rstride=1, cstride=1, cmap=cm.gist_earth)
ax.set_title(Geom_names[g] + ' minus ' + Geom_names[0])
save_and_or_show_plot(savefig)
def test_plot_C_vs_t_and_x():
import mpl_toolkits
N = 3
rd = _get_decay_rd(N)
tout = np.linspace(0, 3.0, 7)
y0 = [3.0, 1.0]*N
integr = run(rd, y0, tout)
ax = plot_C_vs_t_and_x(rd, tout, integr.yout, 0)
assert isinstance(ax, mpl_toolkits.mplot3d.Axes3D)
