def check_rd_integration_run(cb, forgiveness=10, **kwargs):
"""
Tests whether numerical solution is within error-bounds
of reference solution. User provided callback "cb" needs
to return a tuple of (yout, linCref, rd, info).
"""
yout, linCref, rd, info = cb(**kwargs)
assert info['success']
for i in range(rd.n):
try:
atol = info['atol'][i]
except:
atol = info['atol']
try:
rtol = info['rtol'][i]
except:
rtol = info['rtol']
lb, ub = solver_linear_error(yout[..., i], rtol, atol, rd.logy,
scale_err=forgiveness, expb=rd.expb)
assert np.all(lb < linCref[..., i])
assert np.all(ub > linCref[..., i])
def integrate_rd(tend=2.0, A0=1.0, nt=67, t0=0.0,
rates='3.40715,4.0', logy=False, logt=False,
plot=False, savefig='None', method='bdf',
atol='1e-7,1e-6,1e-5', rtol='1e-6', sigm_damp=False,
num_jac=False, scale_err=1.0, small='None', use_log2=False,
plotlogy=False, plotlogt=False, verbose=False):
"""
Analytic solution through Bateman equation =>
ensure :math:`|k_i - k_j| \gg eps`
"""
k = list(map(float, rates.split(',')))
n = len(k)+1
if n > 4:
raise ValueError("Max 3 consequtive decays supported at the moment.")
atol = list(map(float, atol.split(',')))
if len(atol) == 1:
atol = atol[0]
rtol = float(rtol)
rd = ReactionDiffusion(
n, [[i] for i in range(n-1)], [[i] for i in range(1, n)],
k, logy=logy, logt=logt, use_log2=use_log2)
y0 = np.zeros(n)
y0[0] = A0
if small == 'None':
tiny = None
else:
tiny = 0
y0 += float(small)
tout = np.linspace(t0, tend, nt)
integr = run(rd, y0, tout, atol=atol, rtol=rtol, method=method,
with_jacobian=not num_jac, sigm_damp=sigm_damp, tiny=tiny)
Cout, yout, info = integr.Cout, integr.yout, integr.info
Cref = get_Cref(k, y0, tout - tout[0]).reshape((nt, 1, n))
if verbose:
print('rate: ', k)
print(info)
if plot:
nshow = min(n, 3)
try:
min_atol = min(info['atol'])
except:
min_atol = info['atol']
import matplotlib.pyplot as plt
plt.figure(figsize=(6, 10))
c = 'rgb'
for i, l in enumerate('ABC'[:nshow]):
ax = plt.subplot(nshow+1, 1, 1)
if plotlogy:
ax.set_yscale('log')
if plotlogt:
ax.set_xscale('log')
ax.plot(tout, Cout[:, 0, i], label=l, color=c[i])
ax = plt.subplot(nshow+1, 1, 2+i)
if plotlogy:
ax.set_yscale('symlog') # abs error might be < 0
if plotlogt:
ax.set_xscale('log')
ax.plot(tout, (Cout[:, 0, i]-Cref[:, 0, i])/min_atol,
label=l, color=c[i])
try:
atol = info['atol'][i]
except:
atol = info['atol']
try:
rtol = info['rtol'][i]
except:
rtol = info['rtol']
le_l, le_u = solver_linear_error(
yout[:, 0, i], rtol, atol, rd.logy, scale_err=scale_err, expb=rd.expb)
plt.fill_between(tout, (le_l - Cout[:, 0, i])/min_atol,
(le_u - Cout[:, 0, i])/min_atol,
color=c[i], alpha=0.2)
# Print indices and values of violations of (scaled) error bounds
def _print(violation):
print(violation)
print(le_l[violation],
Cref[violation, 0, i],
le_u[violation])
l_viols = np.where(le_l > Cref[:, 0, i])[0]
u_viols = np.where(le_u < Cref[:, 0, i])[0]
if verbose and (len(l_viols) > 0 or len(u_viols) > 0):
print("Outside error bounds for rtol, atol:", rtol, atol)
# for violation in chain(l_viols, u_viols):
# _print(violation)
plt.subplot(nshow+1, 1, 1)
plt.title('Concentration vs. time')
plt.legend(loc='best', prop={'size': 11})
plt.xlabel('t')
plt.ylabel('[X]')
for i in range(nshow):
plt.subplot(nshow+1, 1, 2+i)
plt.title('Absolute error in [{}](t) / min(atol)'.format('ABC'[i]))
plt.legend(loc='best')
plt.xlabel('t')
plt.ylabel('|E[{0}]| / {1:7.0g}'.format('ABC'[i], min_atol))
plt.tight_layout()
save_and_or_show_plot(savefig=savefig)
return integr.yout, Cref, rd, info
def test_solver_linear_error():
assert np.allclose(solver_linear_error(1.0, 1.0, 1.0), [-1, 3])