def _integrate(self):
"""
Performs the integration by calling the callback chosen by
:attr:`integrator`. If rd.logy == True, a transformation of self.C0 to
log_b(C0) will be performed before running the integration (the same
is done for self.tout / rd.logt == True).
After the integration is done the attributes `Cout`, `info` and `yout`
are set. Cout is guaranteed to be linear concentrations (transformed
from yout by calling exp if rd.logy==True) and yout is the unprocessed
output from the integrator.
"""
# Pre-processing
# --------------
C0 = self.C0
# Transform initial concentrations
if self.rd.logy:
if not self.C0_is_log:
C0 = self.rd.logb(C0 + self.tiny)
if self.sigm_damp is True:
y0 = sigm(C0)
elif isinstance(self.sigm_damp, tuple):
y0 = sigm(C0, *self.sigm_damp)
else:
y0 = C0
else:
if self.C0_is_log:
if self.sigm_damp is True:
y0 = self.rd.expb(sigm(C0))
elif isinstance(self.sigm_damp, tuple):
y0 = self.rd.expb(sigm(C0, *self.sigm_damp))
else:
y0 = self.rd.expb(C0)
else:
y0 = C0
# Transform time
tout = self.tout
if tout[0] == 0.0 and self.rd.logt:
t0_set = True
t0 = suggest_t0(self.rd, y0)
t = self.rd.logb(tout + t0) # conserve total time
else:
t0_set = False
t = self.rd.logb(tout) if self.rd.logt else tout
# Run the integration
# -------------------
self.yout, self.internal_t, self.info = self._callbacks[self.integrator](self.rd, y0, t, **self.kwargs)
self.info['t0_set'] = t0 if t0_set else False
# Post processing
# ---------------
# Back-transform independent variable into linear time
if self.rd.logt:
self.tout = (self.rd.expb(self.internal_t) - (t0 if t0_set else 0))
else:
self.tout = self.internal_t
# Back-transform integration output into linear concentration
self.Cout = self.rd.expb(self.yout) if self.rd.logy else self.yout
def integrate_rd(tend=1e2, A0=1.0, B0=0.0, C0=0.0, k1=0.04, k2=1e4, k3=3e7,
t0=1e2, nt=100, N=1, nstencil=3, logt=False, logy=False,
plot=False, savefig='None', verbose=False, dump_expr='False',
use_chempy=False, D=2e-3):
if N == 1:
init_conc = (A0, B0, C0)
else:
init_conc = np.tile((A0, B0, C0), (N, 1))
init_conc /= np.linspace(1, 2, N).reshape((N, 1))**.5
rsys = ReactionSystem(get_reactions((k1, k2, k3)), 'ABC')
if verbose:
print([str(_) for _ in rsys.rxns])
if use_chempy:
from chempy.kinetics.ode import get_odesys
odesys = get_odesys(rsys, include_params=True)
if N != 1:
raise ValueError("ChemPy does not support diffusion")
odesys.integrate(np.logspace(log10(t0), log10(tend)), init_conc)
if plot:
odesys.plot_result(xscale='log', yscale='log')
result = None
else:
rd = ReactionDiffusion.from_ReactionSystem(
rsys, N=N, nstencil=1 if N == 1 else nstencil, logt=logt,
logy=logy, D=[D/2, D/3, D/5])
if dump_expr.lower() not in ('false', '0'):
from chemreac.symbolic import SymRD
import sympy as sp
cb = {'latex': sp.latex,
'ccode': sp.ccode}.get(dump_expr.lower(), str)
srd = SymRD.from_rd(rd, k=sp.symbols('k:3'))
print('dydx:')
print('\n'.join(map(cb, srd._f)))
print('jac:')
for ri, row in enumerate(srd.jacobian.tolist()):
for ci, expr in enumerate(row):
if expr == 0:
continue
print(ri, ci, cb(expr))
return None
if t0 == 0 and logt:
t0 = 1e-3*suggest_t0(rd, init_conc)
if verbose:
print("Using t0 = %12.5g" % t0)
t = np.logspace(np.log10(t0), np.log10(tend), nt)
print(t[0], t[-1])
integr = run(rd, init_conc, t)
if verbose:
import pprint
pprint.pprint(integr.info)
if plot:
if N == 1:
plot_C_vs_t(integr, xscale='log', yscale='log')
else:
import matplotlib.pyplot as plt
for idx, name in enumerate('ABC', 1):
plt.subplot(1, 3, idx)
rgb = [.5, .5, .5]
rgb[idx-1] = 1
plot_faded_time(integr, name, rgb=rgb, log_color=True)
result = integr
if plot:
save_and_or_show_plot(savefig=savefig)
return result