def test_integrate_nondimensionalisation__g_values(from_rsys):
from chempy import Reaction, ReactionSystem
from chempy.units import allclose, default_units as u
rstr = "-> H + OH; Radiolytic({'radiolytic_yield': 2.1e-7*mol/J})"
if from_rsys:
rxn = Reaction.from_string(rstr, None)
rsys = ReactionSystem([rxn], 'H OH')
rd = ReactionDiffusion.from_ReactionSystem(
rsys, unit_registry=SI_base_registry,
variables=dict(doserate=0.15*u.Gy/u.s, density=0.998*u.kg/u.dm3))
assert rd.g_value_parents == [-1]
assert rd.g_values == [[2.1e-7]*2]
assert abs(rd.fields[0][0] - 0.15*998) < 1e-14
else:
rd = ReactionDiffusion.nondimensionalisation(
2, [[]], [[0, 1]], [2.1e-7*0.15*0.998*u.molar/u.second],
unit_registry=SI_base_registry)
C0 = [3*molar, 4*molar]
tout = np.linspace(0, 1)*day
integr = Integration(rd, C0, tout, integrator='scipy')
k_m3_p_mol_p_sec = 0.15*998*2.1e-7
t_sec = np.linspace(0, 24*3600)
C0_mol_p_m3 = [3000, 4000]
Cref_mol_p_m3 = np.empty(integr.Cout.squeeze().shape)
Cref_mol_p_m3[:, 0] = C0_mol_p_m3[0] + k_m3_p_mol_p_sec*t_sec
Cref_mol_p_m3[:, 1] = C0_mol_p_m3[1] + k_m3_p_mol_p_sec*t_sec
print(integr.with_units('Cout').squeeze())
print(integr.with_units('Cout').squeeze() - Cref_mol_p_m3*u.mole/u.metre**3)
assert allclose(integr.with_units('tout'), t_sec*u.s)
assert allclose(integr.with_units('Cout').squeeze(),
Cref_mol_p_m3*u.mole/u.metre**3)
def test_integrate_nondimensionalisation(from_rsys):
from chempy import Reaction, ReactionSystem
from chempy.units import allclose, default_units as u
# 2A -> B
if from_rsys:
rxn = Reaction.from_string('2 A -> B; 2e-3*metre**3/mol/hour', None)
rsys = ReactionSystem([rxn], 'A B')
rd = ReactionDiffusion.from_ReactionSystem(rsys, unit_registry=SI_base_registry)
else:
rd = ReactionDiffusion.nondimensionalisation(
2, [[0, 0]], [[1]], [2e-9/(umol/metre**3)/hour],
unit_registry=SI_base_registry)
C0 = [3*molar, 4*molar]
tout = np.linspace(0, 1)*day
integr = Integration(rd, C0, tout, integrator='scipy')
k_m3_p_mol_p_sec = 2e-3/3600
t_sec = np.linspace(0, 24*3600)
C0_mol_p_m3 = [3000, 4000]
Cref_mol_p_m3 = np.empty(integr.Cout.squeeze().shape)
Cref_mol_p_m3[:, 0] = 1/(C0_mol_p_m3[0]**-1 + 2*k_m3_p_mol_p_sec*t_sec)
missing_A = (C0_mol_p_m3[0] - Cref_mol_p_m3[:, 0])
Cref_mol_p_m3[:, 1] = C0_mol_p_m3[1] + missing_A/2
assert allclose(integr.with_units('tout'), t_sec*u.s)
assert allclose(integr.with_units('Cout').squeeze(),
Cref_mol_p_m3*u.mol/u.metre**3, rtol=1e-6)
def integrate_rd(
tend=1.9, A0=4.2, B0=3.1, C0=1.4, nt=100, t0=0.0, kf=0.9, kb=0.23,
atol='1e-7,1e-6,1e-5', rtol='1e-6', integrator='scipy', method='bdf',
logy=False, logt=False, num_jac=False, plot=False, savefig='None',
splitplots=False, plotlogy=False, plotsymlogy=False, plotlogt=False,
scale_err=1.0, scaling=1.0, verbose=False):
"""
Runs the integration and (optionally) plots:
- Individual concentrations as function of time
- Reaction Quotient vs. time (with equilibrium constant as reference)
- Numerical error commited (with tolerance span plotted)
- Excess error committed (deviation outside tolerance span)
Concentrations (A0, B0, C0) are taken to be in "M" (molar),
kf in "M**-1 s**-1" and kb in "s**-1", t0 and tend in "s"
"""
rtol = float(rtol)
atol = list(map(float, atol.split(',')))
if len(atol) == 1:
atol = atol[0]
registry = SI_base_registry.copy()
registry['amount'] = 1.0/scaling*registry['amount']
registry['length'] = registry['length']/10 # decimetre
kf = kf/molar/second
kb = kb/second
rd = ReactionDiffusion.nondimensionalisation(
3, [[0, 1], [2]], [[2], [0, 1]], [kf, kb], logy=logy, logt=logt,
unit_registry=registry)
C0 = np.array([A0, B0, C0])*molar
if plotlogt:
eps = 1e-16
tout = np.logspace(np.log10(t0+eps), np.log10(tend+eps), nt)*second
else:
tout = np.linspace(t0, tend, nt)*second
integr = Integration(
rd, C0, tout, integrator=integrator, atol=atol, rtol=rtol,
with_jacobian=not num_jac, method=method)
Cout = integr.with_units('Cout')
yout, info = integr.yout, integr.info
try:
import mpmath
assert mpmath # silence pyflakes
except ImportError:
use_mpmath = False
else:
use_mpmath = True
time_unit = get_derived_unit(registry, 'time')
conc_unit = get_derived_unit(registry, 'concentration')
Cref = _get_Cref(
to_unitless(tout - tout[0], time_unit),
to_unitless(C0, conc_unit),
[to_unitless(kf, 1/time_unit/conc_unit),
to_unitless(kb, 1/time_unit)],
use_mpmath
).reshape((nt, 1, 3))*conc_unit
if verbose:
print(info)
if plot:
npltcols = 3 if splitplots else 1
import matplotlib.pyplot as plt
plt.figure(figsize=(18 if splitplots else 6, 10))
def subplot(row=0, idx=0, adapt_yscale=True, adapt_xscale=True,
span_all_x=False):
offset = idx if splitplots else 0
ax = plt.subplot(4, 1 if span_all_x else npltcols,
1 + row*npltcols + offset)
if adapt_yscale:
if plotlogy:
ax.set_yscale('log')
elif plotsymlogy:
ax.set_yscale('symlog')
if adapt_xscale and plotlogt:
ax.set_xscale('log')
return ax
tout_unitless = to_unitless(tout, second)
c = 'rgb'
for i, l in enumerate('ABC'):
# Plot solution trajectory for i:th species
ax_sol = subplot(0, i)
ax_sol.plot(tout_unitless, to_unitless(Cout[:, 0, i], molar),
label=l, color=c[i])
if splitplots:
# Plot relative error
ax_relerr = subplot(1, 1)
ax_relerr.plot(
tout_unitless, Cout[:, 0, i]/Cref[:, 0, i] - 1.0,
label=l, color=c[i])
ax_relerr.set_title("Relative error")
ax_relerr.legend(loc='best', prop={'size': 11})
# Plot absolute error
ax_abserr = subplot(1, 2)
ax_abserr.plot(tout_unitless, Cout[:, 0, i]-Cref[:, 0, i],
label=l, color=c[i])
ax_abserr.set_title("Absolute error")
ax_abserr.legend(loc='best', prop={'size': 11})
# Plot absolute error
linE = Cout[:, 0, i] - Cref[:, 0, i]
try:
atol_i = atol[i]
except:
atol_i = atol
wtol_i = (atol_i + rtol*yout[:, 0, i])*get_derived_unit(
rd.unit_registry, 'concentration')
if np.any(np.abs(linE/wtol_i) > 1000):
# Plot true curve in first plot when deviation is large enough
# to be seen visually
ax_sol.plot(tout_unitless, to_unitless(Cref[:, 0, i], molar),
label='true '+l, color=c[i], ls='--')
ax_err = subplot(2, i)
plot_solver_linear_error(integr, Cref, ax_err, si=i,
scale_err=1/wtol_i, color=c[i], label=l)
ax_excess = subplot(3, i, adapt_yscale=False)
plot_solver_linear_excess_error(integr, Cref, ax_excess,
si=i, color=c[i], label=l)
# Plot Reaction Quotient vs time
ax_q = subplot(1, span_all_x=False, adapt_yscale=False,
adapt_xscale=False)
Qnum = Cout[:, 0, 2]/(Cout[:, 0, 0]*Cout[:, 0, 1])
Qref = Cref[:, 0, 2]/(Cref[:, 0, 0]*Cref[:, 0, 1])
ax_q.plot(tout_unitless, to_unitless(Qnum, molar**-1),
label='Q', color=c[i])
if np.any(np.abs(Qnum/Qref-1) > 0.01):
# If more than 1% error in Q, plot the reference curve too
ax_q.plot(tout_unitless, to_unitless(Qref, molar**-1),
'--', label='Qref', color=c[i])
# Plot the
ax_q.plot((tout_unitless[0], tout_unitless[-1]),
[to_unitless(kf/kb, molar**-1)]*2,
'--k', label='K')
ax_q.set_xlabel('t')
ax_q.set_ylabel('[C]/([A][B]) / M**-1')
ax_q.set_title("Transient towards equilibrium")
ax_q.legend(loc='best', prop={'size': 11})
for i in range(npltcols):
subplot(0, i, adapt_yscale=False)
plt.title('Concentration vs. time')
plt.legend(loc='best', prop={'size': 11})
plt.xlabel('t')
plt.ylabel('[X]')
subplot(2, i, adapt_yscale=False)
plt.title('Absolute error in [{}](t) / wtol'.format('ABC'[i]))
plt.legend(loc='best')
plt.xlabel('t')
ttl = '|E_i[{0}]|/(atol_i + rtol*(y0_i+yf_i)/2'
plt.ylabel(ttl.format('ABC'[i]))
plt.tight_layout()
subplot(3, i, adapt_yscale=False)
ttl = 'Excess error in [{}](t) / integrator linear error span'
plt.title(ttl.format(
'ABC'[i]))
plt.legend(loc='best')
plt.xlabel('t')
plt.ylabel('|E_excess[{0}]| / e_span'.format('ABC'[i]))
plt.tight_layout()
save_and_or_show_plot(savefig=savefig)
return yout, to_unitless(Cref, conc_unit), rd, info
def integrate_rd(D=2e-3, t0=1., tend=13., x0=1e-10, xend=1.0, N=256,
nt=42, logt=False, logy=False, logx=False,
random=False, k=1.0, nstencil=3, linterpol=False,
rinterpol=False, num_jacobian=False, method='bdf',
integrator='scipy', iter_type='default',
linear_solver='default', atol=1e-8, rtol=1e-10, factor=1e5,
random_seed=42, plot=False, savefig='None', verbose=False,
scaling=1.0, ilu_limit=1000.0, first_step=0.0, n_jac_diags=0, use_log2=False):
"""
Solves the time evolution of diffusion from a constant (undepletable)
source term. Optionally plots the results. In the plots time is represented
by color scaling from black (:math:`t_0`) to red (:math:`t_{end}`)
"""
if t0 == 0.0:
raise ValueError("t0==0 => Dirac delta function C0 profile.")
if random_seed:
np.random.seed(random_seed)
tout = np.linspace(t0, tend, nt)
units = defaultdict(lambda: 1)
units['amount'] = 1.0/scaling
# Setup the grid
x = generate_grid(x0, xend, N, logx, random=random)
modulation = [1 if (i == 0) else 0 for i in range(N)]
rd = ReactionDiffusion.nondimensionalisation(
2,
[[0], [1]],
[[1], [0]],
[k, factor*k],
N=N,
D=[0, D],
x=x,
logy=logy,
logt=logt,
logx=logx,
nstencil=nstencil,
lrefl=not linterpol,
rrefl=not rinterpol,
modulated_rxns=[0, 1],
modulation=[modulation, modulation],
unit_registry=units,
ilu_limit=ilu_limit,
n_jac_diags=n_jac_diags,
faraday_const=1,
vacuum_permittivity=1,
use_log2=use_log2
)
# Calc initial conditions / analytic reference values
Cref = analytic(rd.xcenters, tout, D, x0, xend, logx, use_log2=use_log2).reshape(
nt, N, 1)
source = np.zeros_like(Cref[0, ...])
source[0, 0] = factor
y0 = np.concatenate((source, Cref[0, ...]), axis=1)
# Run the integration
integr = Integration(
rd, y0, tout, integrator=integrator, atol=atol, rtol=rtol,
with_jacobian=(not num_jacobian), method=method,
iter_type=iter_type,
linear_solver=linear_solver, first_step=first_step)
Cout = integr.with_units('Cout')
if verbose:
import pprint
pprint.pprint(integr.info)
spat_ave_rmsd_over_atol = spat_ave_rmsd_vs_time(
Cout[:, :, 1], Cref[:, :, 0]) / atol
tot_ave_rmsd_over_atol = np.average(spat_ave_rmsd_over_atol)
if plot:
# Plot results
import matplotlib.pyplot as plt
plt.figure(figsize=(6, 10))
def _plot(C, c, ttl=None, vlines=False,
smooth=True):
if vlines:
plt.vlines(rd.x, 0, np.ones_like(rd.x)*max(C),
linewidth=1, colors='gray')
if smooth:
plt.plot(rd.xcenters, C, c=c)
else:
for i, _C in enumerate(C):
plt.plot([rd.x[i], rd.x[i+1]], [_C, _C], c=c)
plt.xlabel('x / m')
plt.ylabel('C / M')
if ttl:
plt.title(ttl)
for i in range(nt):
kwargs = dict(smooth=(N >= 20),
vlines=(i == 0 and N < 20))
c = 1-tout[i]/tend
c = (1.0-c, .5-c/2, .5-c/2)
plt.subplot(4, 1, 1)
_plot(Cout[i, :, 1], c, 'Simulation (N={})'.format(rd.N),
**kwargs)
plt.subplot(4, 1, 2)
_plot(Cref[i, :, 0], c, 'Analytic', **kwargs)
plt.subplot(4, 1, 3)
_plot((Cout[i, :, 1]-Cref[i, :, 0]), c,
"Error".format(atol),
**kwargs)
plt.subplot(4, 1, 4)
plt.plot(integr.tout, spat_ave_rmsd_over_atol)
plt.plot([integr.tout[0], integr.tout[-1]],
[tot_ave_rmsd_over_atol]*2, '--')
plt.title("RMSD / atol")
plt.tight_layout()
save_and_or_show_plot(savefig=savefig)
return tout, Cout, integr.info, rd, tot_ave_rmsd_over_atol