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_ArrheniusParamWithUnits():
_2 = _get_ref2_units()
ap = ArrheniusParamWithUnits(_2.A, _2.Ea)
k = ap(_2.T)
assert abs((k - _2.k)/_2.k) < 1e-4
r = Reaction({'H2O2': 1}, {'OH': 2}, ap)
ratc = r.rate_expr().rate_coeff({'temperature': _2.T})
assert allclose(ratc, _2.k, rtol=1e-4)
def test_get_ode__ArrheniusParam():
rxn = Reaction({'A': 1}, {'B': 1}, None)
rxn.param = ArrheniusParam(1e10, 40e3)
rsys = ReactionSystem([rxn], 'A B')
odesys = get_odesys(rsys, include_params=True)[0]
conc = {'A': 3, 'B': 5}
x, y, p = odesys.pre_process(-37, conc, {'temperature': 200})
fout = odesys.f_cb(x, y, p)
ref = 3 * 1e10 * np.exp(-40e3 / 8.314472 / 200)
assert abs((fout[0] + ref) / ref) < 1e-14
assert abs((fout[1] - ref) / ref) < 1e-14
def test_get_ode__ArrheniusParam():
rxn = Reaction({'A': 1}, {'B': 1}, None)
rxn.param = ArrheniusParam(1e10, 40e3)
rsys = ReactionSystem([rxn], 'A B')
odesys = get_odesys(rsys, include_params=True)[0]
conc = {'A': 3, 'B': 5}
x, y, p = odesys.pre_process(-37, conc, {'temperature': 200})
fout = odesys.f_cb(x, y, p)
ref = 3*1e10*np.exp(-40e3/8.314472/200)
assert abs((fout[0] + ref)/ref) < 1e-14
assert abs((fout[1] - ref)/ref) < 1e-14
def test_ArrheniusParamWithUnits():
s = u.second
mol = u.mol
J = u.joule
K = u.kelvin
act_J__mol = 42e3
ap = ArrheniusParamWithUnits(1e10 / s, act_J__mol * J / mol)
freezing_K = 273.15
k = ap(freezing_K * K)
ref = 1e10 / s * math.exp(-act_J__mol / (8.3145 * freezing_K))
assert abs((k - ref) / ref) < 1e-4
r = Reaction({'H2O2': 1}, {'OH': 2}, ap)
ratc = r.rate_expr().rate_coeff({'temperature': freezing_K * u.K})
assert allclose(ratc, ref, rtol=1e-4)
def test_get_ode__Radiolytic__substitutions__units():
rad = Radiolytic([2.4e-7 * u.mol / u.joule])
rxn = Reaction({'A': 4, 'B': 1}, {'C': 3, 'D': 2}, rad)
rsys = ReactionSystem([rxn], 'A B C D')
g_dm3 = u.gram / u.decimetre**3
kg_dm3 = u.kg / u.decimetre**3
substance_rho = Density(
[1 * kg_dm3, -1 * g_dm3 / u.kelvin, 273.15 * u.kelvin])
odesys = get_odesys(rsys,
include_params=True,
unit_registry=SI_base_registry,
substitutions={'density': substance_rho})[0]
conc = {
'A': 3 * u.molar,
'B': 5 * u.molar,
'C': 11 * u.molar,
'D': 13 * u.molar
}
x, y, p = odesys.pre_process(-37 * u.second, conc, {
'doserate': 0.4 * u.gray / u.second,
'temperature': 298.15 * u.kelvin
})
fout = odesys.f_cb(x, y, p)
r = 2.4e-7 * 0.4 * 0.975 * 1e3 # mol/m3/s
ref = [-4 * r, -r, 3 * r, 2 * r]
assert np.all(abs((fout - ref) / ref) < 1e-14)
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_ode_with_global_parameters():
ratex = ArrheniusMassAction([1e10, 40e3 / 8.3145])
rxn = Reaction({'A': 1}, {'B': 1}, ratex)
rsys = ReactionSystem([rxn], 'A B')
odesys = get_odesys(rsys, include_params=True)[0]
conc = {'A': 3, 'B': 5}
x, y, p = odesys.pre_process(-37, conc, {'temperature': 298.15})
fout = odesys.f_cb(x, y, p)
ref = 3 * 1e10 * np.exp(-40e3 / 8.3145 / 298.15)
assert abs((fout[0] + ref) / ref) < 1e-14
assert abs((fout[1] - ref) / ref) < 1e-14
def test_get_ode__Radiolytic():
rad = Radiolytic([2.4e-7])
rxn = Reaction({'A': 4, 'B': 1}, {'C': 3, 'D': 2}, rad)
rsys = ReactionSystem([rxn], 'A B C D')
odesys = get_odesys(rsys, include_params=True)[0]
c = {'A': 3, 'B': 5, 'C': 11, 'D': 13}
x, y, p = odesys.pre_process(-37, c, {'doserate': 0.4, 'density': 0.998})
fout = odesys.f_cb(x, y, p)
r = 2.4e-7 * 0.4 * 0.998
ref = [-4 * r, -r, 3 * r, 2 * r]
assert np.all(abs((fout - ref) / ref) < 1e-14)
def test_get_ode__Radiolytic__substitutions():
rad = Radiolytic([2.4e-7])
rxn = Reaction({'A': 4, 'B': 1}, {'C': 3, 'D': 2}, rad)
rsys = ReactionSystem([rxn], 'A B C D')
substance_rho = Density([1, -1e-3, 273.15])
odesys = get_odesys(rsys,
include_params=True,
substitutions={'density': substance_rho})[0]
conc = {'A': 3, 'B': 5, 'C': 11, 'D': 13}
state = {'doserate': 0.4, 'temperature': 298.15}
x, y, p = odesys.pre_process(-37, conc, state)
fout = odesys.f_cb(x, y, p)
r = 2.4e-7 * 0.4 * substance_rho({'temperature': 298.15})
ref = [-4 * r, -r, 3 * r, 2 * r]
assert np.all(abs((fout - ref) / ref) < 1e-14)
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_ode__TPoly():
rate = TPolyMassAction(
[273.15 * u.K, 10 / u.molar / u.s, 2 / u.molar / u.s / u.K])
rxn = Reaction({'A': 1, 'B': 1}, {'C': 3, 'D': 2}, rate, {'A': 3})
rsys = ReactionSystem([rxn], 'A B C D')
odesys = get_odesys(rsys, unit_registry=SI_base_registry)[0]
conc = {
'A': 3 * u.molar,
'B': 5 * u.molar,
'C': 11 * u.molar,
'D': 13 * u.molar
}
x, y, p = odesys.pre_process(-37 * u.second, conc,
{'temperature': 298.15 * u.kelvin})
fout = odesys.f_cb(x, y, p)
r = 3 * 5 * (10 + 2 * 25) * 1000 # mol/m3/s
ref = [-4 * r, -r, 3 * r, 2 * r]
assert np.all(abs((fout - ref) / ref) < 1e-14)
def test_get_odesys__time_dep_rate():
class RampedRate(MassAction):
argument_names = ('rate_constant', 'ramping_rate')
def rate_coeff(self, variables, backend=math):
rate_constant, ramping_rate = self.all_args(variables,
backend=backend)
return rate_constant * ramping_rate * variables['time']
rate = RampedRate([7, 2])
rxn = Reaction({'A': 1}, {'B': 3}, rate)
rsys = ReactionSystem([rxn], 'A B')
odesys = get_odesys(rsys)[0]
conc = {'A': 3, 'B': 11}
x, y, p = odesys.pre_process([5, 13, 17], conc)
fout = odesys.f_cb(x, y, p)
r = 2 * 7 * 3
ref = np.array([[-r * 5, -r * 13, -r * 17],
[r * 5 * 3, r * 13 * 3, r * 17 * 3]]).T
assert np.allclose(fout, ref)
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)
def test_get_ode__Radiolytic__units():
rad = Radiolytic([2.4e-7 * u.mol / u.joule])
rxn = Reaction({'A': 4, 'B': 1}, {'C': 3, 'D': 2}, rad)
rsys = ReactionSystem([rxn], 'A B C D')
odesys = get_odesys(rsys,
include_params=True,
unit_registry=SI_base_registry)[0]
conc = {
'A': 3 * u.molar,
'B': 5 * u.molar,
'C': 11 * u.molar,
'D': 13 * u.molar
}
x, y, p = odesys.pre_process(
-37 * u.second, conc, {
'doserate': 0.4 * u.gray / u.second,
'density': 0.998 * u.kg / u.decimetre**3
})
fout = odesys.f_cb(x, y, p) # f_cb does not carry any units
r = 2.4e-7 * 0.4 * 0.998 * 1e3 # mol/m3
ref = [-4 * r, -r, 3 * r, 2 * r]
assert np.all(abs((fout - ref) / ref) < 1e-14)
def _get_rsys():
r1 = Reaction({'A': 2}, {'B': 1}, param=3.0)
A = Substance('A', latex_name='\\boldsymbol{A}')
B = Substance('B', latex_name='\\boldsymbol{B}')
rsys = ReactionSystem([r1], [A, B])
return rsys
