def with_units(self, attr):
if attr == "tout":
return self.tout * get_derived_unit(self.rd.unit_registry, "time")
if attr == "Cout":
return self.Cout * get_derived_unit(self.rd.unit_registry, "concentration")
else:
raise ValueError("Unknown attr: %s" % attr)
def with_units(self, attr):
if attr == 'tout':
return self.tout * get_derived_unit(self.rd.unit_registry, 'time')
elif attr == 'Cout':
return self.Cout * get_derived_unit(self.rd.unit_registry,
'concentration')
elif attr == 'x':
return self.rd.x * get_derived_unit(self.rd.unit_registry, 'length')
else:
raise ValueError("Unknown attr: %s" % attr)
def _dedim(arg, key, unit_registry):
return to_unitless(arg, get_derived_unit(unit_registry, key))
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 plot_solver_linear_excess_error(integration, Cref, ax=None, x=None, ti=slice(None), bi=0, si=0, **kwargs):
"""
Plots the excess error commited by the intergrator, divided by the span
of the tolerances (atol + rtol*|y_i|).
Parameters
----------
integration: chemreac.integrate.Integration
result from integration.
Cref: array or float
analytic solution to compare with
ax: Axes instance or dict
if ax is a dict it is used as \*\*kwargs passed to
matplotlib.pyplot.axes (default: None)
x: array
(optional) x-values, when None it is deduced to be
either t or x (when ti or bi are slices repecitvely)
(default: None)
ti: slice
time indices
bi: slice
bin indices
si: integer
specie index
plot_kwargs: dict
keyword arguments passed to matplotlib.pyplot.plot (default: None)
fill_between_kwargs: dict
keyword arguments passed to matplotlib.pyplot.fill_between
(default: None)
scale_err: float
value with which errors are scaled. (default: 1.0)
fill: bool
whether or not to fill error span
\*\*kwargs:
common keyword arguments of plot_kwargs and fill_between_kwargs,
e.g. 'color', (default: None).
See Also
--------
plot_solver_linear_error
"""
if x is None:
if isinstance(ti, slice):
x = integration.tout[ti]
elif isinstance(bi, slice):
x = integration.rd.xcenters[bi]
else:
raise NotImplementedError("Failed to deduce x-axis.")
ax = _init_axes(ax)
le_l, le_u = solver_linear_error_from_integration(integration, ti, bi, si)
Eexcess_l = Cref[ti, bi, si] - le_l # Excessive if negative
Eexcess_u = Cref[ti, bi, si] - le_u # Excessive if positive
u_conc = get_derived_unit(integration.rd.unit_registry, "concentration")
Eexcess_l[np.argwhere(Eexcess_l >= 0)] = 0 * u_conc
Eexcess_u[np.argwhere(Eexcess_u <= 0)] = 0 * u_conc
fused = np.concatenate((Eexcess_l[..., np.newaxis], Eexcess_u[..., np.newaxis]), axis=-1)
indices = np.argmax(abs(fused), axis=-1)
Eexcess = fused[np.indices(indices.shape), indices][0, ...]
le_span = le_u - le_l
ax.plot(np.asarray(integration.tout), np.asarray(Eexcess / le_span), **kwargs)
return ax
def plot_solver_linear_error(
integration,
Cref=0,
ax=None,
x=None,
ti=slice(None),
bi=0,
si=0,
plot_kwargs=None,
fill_between_kwargs=None,
scale_err=1.0,
fill=True,
**kwargs
):
"""
Parameters
----------
integration: chemreac.integrate.Integration
result from integration.
Cref: array or float
analytic solution to compare with
ax: Axes instance or dict
if ax is a dict it is used as key word arguments passed to
matplotlib.pyplot.axes (default: None)
x: array
(optional) x-values, when None it is deduced to be
either t or x (when ti or bi are slices repecitvely)
(default: None)
ti: slice
time indices
bi: slice
bin indices
si: integer
specie index
plot_kwargs: dict
keyword arguments passed to matplotlib.pyplot.plot (default: None)
fill_between_kwargs: dict
keyword arguments passed to matplotlib.pyplot.fill_between
(default: None)
scale_err: float
value with which errors are scaled. (default: 1.0)
fill: bool
whether or not to fill error span
\*\*kwargs
common keyword arguments of plot_kwargs and fill_between_kwargs,
e.g. 'color', (default: None).
See Also
--------
plot_solver_linear_excess_error
"""
ax = _init_axes(ax)
Cerr = integration.Cout - to_unitless(Cref, get_derived_unit(integration.rd.unit_registry, "concentration"))
if x is None:
if isinstance(ti, slice):
x = integration.tout[ti]
elif isinstance(bi, slice):
x = integration.rd.xcenters[bi]
else:
raise NotImplementedError("Failed to deduce x-axis.")
plot_kwargs = plot_kwargs or {}
set_dict_defaults_inplace(plot_kwargs, kwargs)
plt.plot(np.asarray(x), np.asarray(scale_err * Cerr[ti, bi, si]), **plot_kwargs)
if fill:
le_l, le_u = solver_linear_error_from_integration(integration, ti=ti, bi=bi, si=si)
Cerr_u = le_u - Cref[ti, bi, si]
Cerr_l = le_l - Cref[ti, bi, si]
fill_between_kwargs = fill_between_kwargs or {}
set_dict_defaults_inplace(fill_between_kwargs, {"alpha": 0.2}, kwargs)
plt.fill_between(
np.asarray(x), np.asarray(scale_err * Cerr_l), np.asarray(scale_err * Cerr_u), **fill_between_kwargs
)
return ax