def test_get_odesys_3():
M = u.molar
s = u.second
mol = u.mol
m = u.metre
substances = list(map(Substance, 'H2O H+ OH-'.split()))
dissociation = Reaction({'H2O': 1}, {'H+': 1, 'OH-': 1}, 2.47e-5 / s)
recombination = Reaction({'H+': 1, 'OH-': 1}, {'H2O': 1}, 1.37e11 / M / s)
rsys = ReactionSystem([dissociation, recombination], substances)
odesys = get_odesys(rsys,
include_params=True,
unit_registry=SI_base_registry,
output_conc_unit=M)[0]
c0 = {'H2O': 55.4 * M, 'H+': 1e-7 * M, 'OH-': 1e-4 * mol / m**3}
x, y, p = odesys.pre_process(-42 * u.second,
rsys.as_per_substance_array(c0, unit=M))
fout = odesys.f_cb(x, y, p)
time_unit = get_derived_unit(SI_base_registry, 'time')
conc_unit = get_derived_unit(SI_base_registry, 'concentration')
r1 = to_unitless(55.4 * 2.47e-5 * M / s, conc_unit / time_unit)
r2 = to_unitless(1e-14 * 1.37e11 * M / s, conc_unit / time_unit)
assert abs(fout[0] - r2 + r1) < 1e-10
assert abs(fout[1] - r1 + r2) < 1e-10
assert abs(fout[2] - r1 + r2) < 1e-10
def test_get_odesys__with_units():
a = Substance('A')
b = Substance('B')
molar = u.molar
second = u.second
r = Reaction({'A': 2}, {'B': 1}, param=1e-3 / molar / second)
rsys = ReactionSystem([r], [a, b])
odesys = get_odesys(rsys,
include_params=True,
unit_registry=SI_base_registry)[0]
c0 = {'A': 13 * u.mol / u.metre**3, 'B': .2 * u.molar}
conc_unit = get_derived_unit(SI_base_registry, 'concentration')
t = np.linspace(0, 10) * u.hour
xout, yout, info = odesys.integrate(t,
rsys.as_per_substance_array(
c0, unit=conc_unit),
atol=1e-10,
rtol=1e-12)
t_unitless = to_unitless(xout, u.second)
Aref = dimerization_irrev(t_unitless, 1e-6, 13.0)
# Aref = 1/(1/13 + 2*1e-6*t_unitless)
yref = np.zeros((xout.size, 2))
yref[:, 0] = Aref
yref[:, 1] = 200 + (13 - Aref) / 2
print((yout - yref * conc_unit) / yout)
assert allclose(yout, yref * conc_unit)
def test_get_odesys__with_units():
a = Substance('A')
b = Substance('B')
molar = u.molar
second = u.second
r = Reaction({'A': 2}, {'B': 1}, param=1e-3/molar/second)
rsys = ReactionSystem([r], [a, b])
odesys = get_odesys(rsys, include_params=True,
unit_registry=SI_base_registry)[0]
c0 = {
'A': 13*u.mol / u.metre**3,
'B': .2 * u.molar
}
conc_unit = get_derived_unit(SI_base_registry, 'concentration')
t = np.linspace(0, 10)*u.hour
xout, yout, info = odesys.integrate(
t, rsys.as_per_substance_array(c0, unit=conc_unit),
atol=1e-10, rtol=1e-12)
t_unitless = to_unitless(xout, u.second)
Aref = dimerization_irrev(t_unitless, 1e-6, 13.0)
# Aref = 1/(1/13 + 2*1e-6*t_unitless)
yref = np.zeros((xout.size, 2))
yref[:, 0] = Aref
yref[:, 1] = 200 + (13-Aref)/2
print((yout - yref*conc_unit)/yout)
assert allclose(yout, yref*conc_unit)
def test_get_odesys_3():
M = u.molar
s = u.second
mol = u.mol
m = u.metre
substances = list(map(Substance, 'H2O H+ OH-'.split()))
dissociation = Reaction({'H2O': 1}, {'H+': 1, 'OH-': 1}, 2.47e-5/s)
recombination = Reaction({'H+': 1, 'OH-': 1}, {'H2O': 1}, 1.37e11/M/s)
rsys = ReactionSystem([dissociation, recombination], substances)
odesys = get_odesys(
rsys, include_params=True, unit_registry=SI_base_registry,
output_conc_unit=M)[0]
c0 = {'H2O': 55.4*M, 'H+': 1e-7*M, 'OH-': 1e-4*mol/m**3}
x, y, p = odesys.pre_process(-42*u.second,
rsys.as_per_substance_array(c0, unit=M))
fout = odesys.f_cb(x, y, p)
time_unit = get_derived_unit(SI_base_registry, 'time')
conc_unit = get_derived_unit(SI_base_registry, 'concentration')
r1 = to_unitless(55.4*2.47e-5*M/s, conc_unit/time_unit)
r2 = to_unitless(1e-14*1.37e11*M/s, conc_unit/time_unit)
assert abs(fout[0] - r2 + r1) < 1e-10
assert abs(fout[1] - r1 + r2) < 1e-10
assert abs(fout[2] - r1 + r2) < 1e-10
def test_get_odesys_1():
k = .2
a = Substance('A')
b = Substance('B')
r = Reaction({'A': 1}, {'B': 1}, param=k)
rsys = ReactionSystem([r], [a, b])
odesys = get_odesys(rsys, include_params=True)[0]
c0 = {
'A': 1.0,
'B': 3.0,
}
t = np.linspace(0.0, 10.0)
xout, yout, info = odesys.integrate(t, rsys.as_per_substance_array(c0))
yref = np.zeros((t.size, 2))
yref[:, 0] = np.exp(-k * t)
yref[:, 1] = 4 - np.exp(-k * t)
assert np.allclose(yout, yref)
def test_get_odesys_1():
k = .2
a = Substance('A')
b = Substance('B')
r = Reaction({'A': 1}, {'B': 1}, param=k)
rsys = ReactionSystem([r], [a, b])
odesys = get_odesys(rsys, include_params=True)[0]
c0 = {
'A': 1.0,
'B': 3.0,
}
t = np.linspace(0.0, 10.0)
xout, yout, info = odesys.integrate(t, rsys.as_per_substance_array(c0))
yref = np.zeros((t.size, 2))
yref[:, 0] = np.exp(-k*t)
yref[:, 1] = 4 - np.exp(-k*t)
assert np.allclose(yout, yref)
def test_get_odesys_2():
g = Radiolytic([3.14])
a = Substance('A')
b = Substance('B')
r = Reaction({'A': 1}, {'B': 1}, param=g)
rsys = ReactionSystem([r], [a, b])
odesys = get_odesys(rsys, include_params=True)[0]
c0 = {
'A': 1.0,
'B': 3.0,
}
t = np.linspace(0.0, .1)
xout, yout, info = odesys.integrate(t, rsys.as_per_substance_array(c0), {'doserate': 2.72, 'density': .998})
yref = np.zeros((t.size, 2))
k = 3.14*2.72*.998
yref[:, 0] = 1 - k*t
yref[:, 1] = 3 + k*t
assert np.allclose(yout, yref)
def test_get_odesys__time_dep_temperature():
import sympy as sp
def refA(t, A0, A, Ea_over_R, T0, dTdt):
T = (T0 + dTdt * t)
d_Ei = sp.Ei(-Ea_over_R / T0).n(100).round(90) - sp.Ei(
-Ea_over_R / T).n(100).round(90)
d_Texp = T0 * sp.exp(-Ea_over_R / T0) - T * sp.exp(-Ea_over_R / T)
return A0 * sp.exp(A / dTdt * (Ea_over_R * d_Ei + d_Texp)).n(30)
params = A0, A, Ea_over_R, T0, dTdt = [13, 1e10, 56e3 / 8, 273, 2]
B0 = 11
rate = ArrheniusMassAction([A, Ea_over_R])
rxn = Reaction({'A': 1}, {'B': 3}, rate)
rsys = ReactionSystem([rxn], 'A B')
rt = RampedTemp([T0, dTdt], ('init_temp', 'ramp_rate'))
odesys = get_odesys(rsys, False, substitutions={'temperature': rt})[0]
conc = {'A': A0, 'B': B0}
x, y, p = odesys.pre_process([2, 5, 10], conc)
fout = odesys.f_cb(x, y, p)
def r(t):
return A * np.exp(-Ea_over_R /
(T0 + dTdt * t)) * A0 # refA(t, *params)
ref = np.array([[-r(2), -r(5), -r(10)], [3 * r(2), 3 * r(5), 3 * r(10)]]).T
assert np.allclose(fout, ref)
for ramp_rate in [2, 3, 4]:
xout, yout, info = odesys.integrate(10,
rsys.as_per_substance_array(conc),
{'ramp_rate': ramp_rate},
atol=1e-10,
rtol=1e-12)
params[-1] = ramp_rate
Aref = np.array([float(refA(t, *params)) for t in xout])
# Aref = 1/(1/13 + 2*1e-6*t_unitless)
yref = np.zeros((xout.size, 2))
yref[:, 0] = Aref
yref[:, 1] = B0 + 3 * (A0 - Aref)
assert allclose(yout, yref)
def test_get_odesys_2():
g = Radiolytic([3.14])
a = Substance('A')
b = Substance('B')
r = Reaction({'A': 1}, {'B': 1}, param=g)
rsys = ReactionSystem([r], [a, b])
odesys = get_odesys(rsys, include_params=True)[0]
c0 = {
'A': 1.0,
'B': 3.0,
}
t = np.linspace(0.0, .1)
xout, yout, info = odesys.integrate(t, rsys.as_per_substance_array(c0), {
'doserate': 2.72,
'density': .998
})
yref = np.zeros((t.size, 2))
k = 3.14 * 2.72 * .998
yref[:, 0] = 1 - k * t
yref[:, 1] = 3 + k * t
assert np.allclose(yout, yref)