def test_plot_C_vs_t_in_bin():
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_in_bin(rd, tout, integr.yout, 0)
assert isinstance(ax, matplotlib.axes.Axes)
def integrate_rd(tend=1.0, k1=7e-1, k2=3e2, k3=7.0,
A0=1.0, B0=0.0, C0=0.0, nt=512,
plot=False, savefig='None'):
"""
Runs integration and (optionally) generates plots.
Examples
--------
::
$ python steady_state_approx.py --plot --savefig steady_state_approx.png
.. image:: ../_generated/steady_state_approx.png
::
$ python steady_state_approx.py --plot --savefig \
steady_state_approx.html
:download:`steady_state_approx.html\
<../_generated/steady_state_approx.html>`
"""
def f(t):
return A0/(k3/k2*A0 + 1)*np.exp(-k1*t)
y = [A0, B0, C0]
k = [k1, k2, k3]
rd = ReactionDiffusion(
3, [[0], [1], [0, 1]], [[1], [2], [1, 2]], k)
t = np.linspace(0, tend, nt)
integr = run(rd, y, t)
A_ssB = 1/(1/f(t) - k3/k2)
A_ssB_2fast = f(t)
if plot:
import matplotlib.pyplot as plt
plt.figure(figsize=(6, 10))
ax = plt.subplot(3, 1, 1)
plot_C_vs_t_in_bin(rd, t, integr.Cout, ax=ax)
plt.subplot(3, 1, 2)
plt.plot(t, integr.Cout[:, 0, 0] - A_ssB,
label="Abs. err. in A assuming steady state of B")
plt.legend(loc='best', prop={'size': 11})
plt.subplot(3, 1, 3)
plt.plot(t, integr.Cout[:, 0, 0] - A_ssB_2fast,
label="Abs. err. in A when also assuming k2 >> k3")
plt.legend(loc='best', prop={'size': 11})
plt.tight_layout()
save_and_or_show_plot(savefig=savefig)
def ydot(x, y):
return (-k1*y[0] - k3*y[0]*y[1], k1*y[0] - k2*y[1],
k2*y[1] + k3*y[0]*y[1])
return t, integr.Cout, A_ssB, A_ssB_2fast, ydot
