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
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.to_arrays(-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 np.all(abs(fout[:, 0] - r2 + r1)) < 1e-10
assert np.all(abs(fout[:, 1] - r1 + r2)) < 1e-10
assert np.all(abs(fout[:, 2] - r1 + r2)) < 1e-10
def test_create_odesys__ShiftedTPoly():
rxn = Reaction({'A': 1, 'B': 1}, {'C': 3, 'D': 2}, 'k_bi', {'A': 3})
rsys = ReactionSystem([rxn], 'A B C D')
_k0, _k1, T0C = 10, 2, 273.15
rate = MassAction(ShiftedTPoly([T0C*u.K, _k0/u.molar/u.s, _k1/u.molar/u.s/u.K]))
T_C = 25
T = (T0C+T_C)*u.kelvin
p1 = rate.rate_coeff({'temperature': T})
assert allclose(p1, (_k0 + _k1*T_C)/u.molar/u.s)
odesys, odesys_extra = create_odesys(rsys)
ics = {'A': 3*u.molar, 'B': 5*u.molar, 'C': 11*u.molar, 'D': 13*u.molar}
pars = dict(k_bi=p1)
validation = odesys_extra['validate'](dict(ics, **pars))
assert set(map(str, validation['not_seen'])) == {'C', 'D'}
dedim_ctx = _mk_dedim(SI_base_registry)
(t, c, _p), dedim_extra = dedim_ctx['dedim_tcp'](-37*u.s, [ics[k] for k in odesys.names], pars)
fout = odesys.f_cb(t, c, [_p[pk] for pk in odesys.param_names])
r = 3*5*(_k0 + _k1*25)*1000 # mol/m3/s
ref = [-4*r, -r, 3*r, 2*r]
assert np.all(abs((fout - ref)/ref) < 1e-14)
odesys.integrate(t, c, _p)
def test_get_odesys__late_binding():
def _gibbs(args, T, R, backend, **kwargs):
H, S = args
return backend.exp(-(H - T*S)/(R*T))
def _eyring(args, T, R, k_B, h, backend, **kwargs):
H, S = args
return k_B/h*T*backend.exp(-(H - T*S)/(R*T))
gibbs_pk = ('temperature', 'molar_gas_constant')
eyring_pk = gibbs_pk + ('Boltzmann_constant', 'Planck_constant')
GibbsEC = MassActionEq.from_callback(_gibbs, argument_names=('H', 'S'), parameter_keys=gibbs_pk)
EyringMA = MassAction.from_callback(_eyring, argument_names=('H', 'S'), parameter_keys=eyring_pk)
uk_equil = ('He_assoc', 'Se_assoc')
beta = GibbsEC(unique_keys=uk_equil) # equilibrium parameters
uk_kinet = ('Ha_assoc', 'Sa_assoc')
bimol_barrier = EyringMA(unique_keys=uk_kinet) # activation parameters
eq = Equilibrium({'Fe+3', 'SCN-'}, {'FeSCN+2'}, beta)
rsys = ReactionSystem(eq.as_reactions(kf=bimol_barrier))
odesys, extra = get_odesys(rsys, include_params=False)
pk, unique, p_units = map(extra.get, 'param_keys unique p_units'.split())
assert sorted(unique) == sorted(uk_equil + uk_kinet)
assert sorted(pk) == sorted(eyring_pk)
def test_get_odesys__Expr_as_param__unique_as_param():
def _eyring_pe_coupled(args, T, S, backend=math, **kwargs):
freq, = args
return freq*T/S
EyringPreExpCoupled = Expr.from_callback(_eyring_pe_coupled, argument_names=('freq',),
parameter_keys=('temperature', 'S_u'))
def _k(args, T, backend=math, **kwargs):
A, H, S = args
return A*backend.exp(-(H - T*S)/(8.314511*T))
EyringMA = MassAction.from_callback(_k, parameter_keys=('temperature',),
argument_names=('Aa', 'Ha', 'Sa'))
kb_h = 2.08e10
rxn = Reaction({'A'}, {'B'}, EyringMA(unique_keys=('A_u', 'H_u', 'S_u')))
rsys = ReactionSystem([rxn], ['A', 'B'])
odesys2, extra2 = get_odesys(rsys, include_params=False,
substitutions={'A_u': EyringPreExpCoupled(kb_h)})
y0 = defaultdict(float, {'A': 7.0})
rt = 293.15
xout2, yout2, info2 = odesys2.integrate(5, y0, {'H_u': 107e3, 'S_u': 150, 'temperature': rt},
integrator='cvode', atol=1e-12, rtol=1e-10, nsteps=1000)
kref2 = kb_h*rt*np.exp(-(107e3 - rt*150)/(8.314511*rt))/150
ref2 = y0['A']*np.exp(-kref2*xout2)
assert np.allclose(yout2[:, 0], ref2)
assert np.allclose(yout2[:, 1], y0['A'] - ref2)
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.to_arrays(-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 decompose_yields(yields, rxns, atol=1e-10):
""" Decomposes yields into mass-action reactions
This function offers a way to express a reaction with non-integer
stoichiometric coefficients as a linear combination of production reactions
with integer coefficients.
Ak = y
A is (n_species x n_reactions) matrix, k is "rate coefficient", y is yields
Parameters
----------
yields: OrderedDict
specie names as keys and yields as values
rxns: iterable :class:`Reaction` instances
dict keys must match those of ``yields`` each pair
of dictionaries gives stoichiometry
(1st is reactant, 2nd is products)
atol: float
absolute tolerance for residuals
Examples
--------
>>> from chempy import Reaction
>>> h2a = Reaction({'H2O': 1}, {'H2': 1, 'O': 1})
>>> h2b = Reaction({'H2O': 1}, {'H2': 1, 'H2O2': 1}, inact_reac={'H2O': 1})
>>> decompose_yields({'H2': 3, 'O': 2, 'H2O2': 1}, [h2a, h2b])
array([ 2., 1.])
Raises
------
ValueError
When atol is exceeded
numpy.LinAlgError
When numpy.linalg.lstsq fails to converge
Returns
-------
1-dimensional array of effective rate coefficients.
"""
from chempy import ReactionSystem
# Sanity check:
rxn_keys = set.union(*(rxn.keys() for rxn in rxns))
for key in yields.keys():
if key not in rxn_keys:
raise ValueError("Substance key: %s not in reactions" % key)
rsys = ReactionSystem(rxns, rxn_keys)
A = rsys.net_stoichs(yields.keys())
b = list(yields.values())
unit = unit_of(b[0])
x, residuals, rank, s = np.linalg.lstsq(A.T, to_unitless(b, unit))
if len(residuals) > 0:
if np.any(residuals > atol):
raise ValueError("atol not satisfied")
return x*unit
def test_get_odesys__Equilibrium_as_reactions():
from chempy import Equilibrium, ReactionSystem
eq = Equilibrium({'Fe+3', 'SCN-'}, {'FeSCN+2'}, 10**2)
substances = 'Fe+3 SCN- FeSCN+2'.split()
rsys = ReactionSystem(eq.as_reactions(kf=3.0), substances)
odesys, extra = get_odesys(rsys)
init_conc = {'Fe+3': 1.0, 'SCN-': .3, 'FeSCN+2': 0}
tout, Cout, info = odesys.integrate(5, init_conc, integrator='cvode', atol=1e-11, rtol=1e-12)
cmplx_ref = binary_rev(tout, 3, 3.0/100, init_conc['FeSCN+2'], init_conc['Fe+3'], init_conc['SCN-'])
assert np.allclose(Cout[:, 2], cmplx_ref)
def get_rsys():
r1 = Reaction({'A'}, {'B'},
MassAction([4. / 100], unique_keys=['k1']),
name='R1: A cons.')
r2 = Reaction({'B', 'C'}, {'A', 'C'},
MassAction([1e4], unique_keys=['k2']),
name='R2: A reform.')
r3 = Reaction({'B': 2}, {'B', 'C'},
MassAction([3e7], unique_keys=['k3']),
name='R3: C form.')
return ReactionSystem([r1, r2, r3])
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.to_arrays(-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():
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.to_arrays(-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__TPoly():
rate = MassAction(ShiftedTPoly([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.to_arrays(-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_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.to_arrays(-37, conc, {'temperature': 200})
fout = odesys.f_cb(x, y, p)
ref = 3*1e10*np.exp(-40e3/8.314472/200)
assert np.all(abs((fout[:, 0] + ref)/ref) < 1e-14)
assert np.all(abs((fout[:, 1] - ref)/ref) < 1e-14)
def test_ode_with_global_parameters():
ratex = MassAction(Arrhenius([1e10, 40e3/8.3145]))
rxn = Reaction({'A': 1}, {'B': 1}, ratex)
rsys = ReactionSystem([rxn], 'A B')
odesys, extra = get_odesys(rsys, include_params=False)
param_keys, unique_keys, p_units = map(extra.get, 'param_keys unique p_units'.split())
conc = {'A': 3, 'B': 5}
x, y, p = odesys.to_arrays(-37, conc, {'temperature': 298.15})
fout = odesys.f_cb(x, y, p)
ref = 3*1e10*np.exp(-40e3/8.3145/298.15)
assert np.all(abs((fout[:, 0] + ref)/ref) < 1e-14)
assert np.all(abs((fout[:, 1] - ref)/ref) < 1e-14)
def get_rsys():
r1 = Reaction(
{"A"}, {"B"}, MassAction([4.0 / 100], unique_keys=["k1"]), name="R1: A cons."
)
r2 = Reaction(
{"B", "C"},
{"A", "C"},
MassAction([1e4], unique_keys=["k2"]),
name="R2: A reform.",
)
r3 = Reaction(
{"B": 2}, {"B", "C"}, MassAction([3e7], unique_keys=["k3"]), name="R3: C form."
)
return ReactionSystem([r1, r2, r3])
def test_EyringMassAction():
args = kB_h_times_exp_dS_R, dH_over_R, c0 = 1.2e11 / 273.15, 40e3 / 8, 1
ama = MassAction(Eyring(args, ("Sfreq", "Hact")))
rxn1 = Reaction({"A": 2, "B": 1}, {"C": 1}, ama, {"B": 1})
T_ = "temperature"
def ref(v):
return (v.get("Sfreq", 1.2e11 / 273.15) * v[T_] *
math.exp(-v.get("Hact", 40e3 / 8) / v[T_]) * v["B"] *
v["A"]**2)
for params in [(11.0, 13.0, 17.0, 311.2), (12, 8, 5, 270)]:
var = dict(zip(["A", "B", "C", T_], params))
ref_val = ref(var)
assert abs((ama(var, reaction=rxn1) - ref_val) / ref_val) < 1e-14
with pytest.raises(ValueError):
MassAction(Eyring([1, 1, 1, 1, 1]))
# assert ama.as_mass_action({T_: 273.15}).args[0] == 1.2e11*math.exp(-40e3/8/273.15)
ama2 = MassAction(
Eyring4([1.2e11 / 273, 40e3 / 8, 1.2, 1e3],
("Sfreq", "Hact", "Sref", "Href")))
rxn2 = Reaction({"C": 1}, {"A": 2, "B": 2}, ama2)
var2 = {"C": 29, "temperature": 273}
def ref2(var):
return (var["C"] * var.get("temperature", 273) *
var.get("Sfreq", 1.2e11 / 273) / var.get("Sref", 1.2) *
math.exp((var.get("Href", 1e3) - var.get("Hact", 5e3)) /
var.get("temperature", 273)))
r2 = ref2(var2)
assert abs((ama2(var2, reaction=rxn2) - r2) / r2) < 1e-14
rsys = ReactionSystem([rxn1, rxn2])
var3 = {
"A": 11,
"B": 13,
"C": 17,
"temperature": 298,
"Sfreq": 1.2e11 / 298
}
rates = rsys.rates(var3)
rf3 = ref(var3)
rb3 = ref2(var3)
ref_rates = {"A": 2 * (rb3 - rf3), "B": 2 * (rb3 - rf3), "C": rf3 - rb3}
for k, v in ref_rates.items():
assert abs((rates[k] - v) / v) < 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.to_arrays(-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_EyringMassAction():
args = kB_h_times_exp_dS_R, dH_over_R, c0 = 1.2e11 / 273.15, 40e3 / 8, 1
ama = MassAction(Eyring(args, ('Sfreq', 'Hact')))
rxn1 = Reaction({'A': 2, 'B': 1}, {'C': 1}, ama, {'B': 1})
T_ = 'temperature'
def ref(v):
return v.get('Sfreq', 1.2e11 / 273.15) * v[T_] * math.exp(
-v.get('Hact', 40e3 / 8) / v[T_]) * v['B'] * v['A']**2
for params in [(11., 13., 17., 311.2), (12, 8, 5, 270)]:
var = dict(zip(['A', 'B', 'C', T_], params))
ref_val = ref(var)
assert abs((ama(var, reaction=rxn1) - ref_val) / ref_val) < 1e-14
with pytest.raises(ValueError):
MassAction(Eyring([1, 1, 1, 1, 1]))
# assert ama.as_mass_action({T_: 273.15}).args[0] == 1.2e11*math.exp(-40e3/8/273.15)
ama2 = MassAction(
Eyring4([1.2e11 / 273, 40e3 / 8, 1.2, 1e3],
('Sfreq', 'Hact', 'Sref', 'Href')))
rxn2 = Reaction({'C': 1}, {'A': 2, 'B': 2}, ama2)
var2 = {'C': 29, 'temperature': 273}
def ref2(var):
return var['C'] * var.get('temperature', 273) * var.get(
'Sfreq', 1.2e11 / 273) / var.get('Sref', 1.2) * math.exp(
(var.get('Href', 1e3) - var.get('Hact', 5e3)) /
var.get('temperature', 273))
r2 = ref2(var2)
assert abs((ama2(var2, reaction=rxn2) - r2) / r2) < 1e-14
rsys = ReactionSystem([rxn1, rxn2])
var3 = {
'A': 11,
'B': 13,
'C': 17,
'temperature': 298,
'Sfreq': 1.2e11 / 298
}
rates = rsys.rates(var3)
rf3 = ref(var3)
rb3 = ref2(var3)
ref_rates = {'A': 2 * (rb3 - rf3), 'B': 2 * (rb3 - rf3), 'C': rf3 - rb3}
for k, v in ref_rates.items():
assert abs((rates[k] - v) / v) < 1e-14
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.to_arrays(-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 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.to_arrays(-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__Equilibrium_as_reactions():
from chempy import Equilibrium, ReactionSystem
eq = Equilibrium({"Fe+3", "SCN-"}, {"FeSCN+2"}, 10 ** 2)
substances = "Fe+3 SCN- FeSCN+2".split()
rsys = ReactionSystem(eq.as_reactions(kf=3.0), substances)
odesys, extra = get_odesys(rsys)
init_conc = {"Fe+3": 1.0, "SCN-": 0.3, "FeSCN+2": 0}
tout, Cout, info = odesys.integrate(
5, init_conc, integrator="cvode", atol=1e-11, rtol=1e-12
)
cmplx_ref = binary_rev(
tout, 3, 3.0 / 100, init_conc["FeSCN+2"], init_conc["Fe+3"], init_conc["SCN-"]
)
assert np.allclose(Cout[:, 2], cmplx_ref)
def test_chained_parameter_variation():
ratex = MassAction(Arrhenius([1e10, 63e3 / 8.3145]))
rxn = Reaction({'A': 1}, {'B': 1}, ratex)
rsys = ReactionSystem([rxn], 'A B')
odesys, extra = get_odesys(rsys, include_params=False)
param_keys, unique_keys, p_units = map(extra.get,
'param_keys unique p_units'.split())
conc = {'A': 3.17, 'B': 5.03}
Ts = (294, 304, 317)
times = [3.1, 2.1, 5.3]
kw = dict(integrator='cvode', atol=1e-12, rtol=1e-13, first_step=1e-14)
tout, cout, info = chained_parameter_variation(odesys,
times,
conc, {'temperature': Ts},
{},
integrate_kwargs=kw)
assert len(info['nfev']) == 3
assert info['nfev'][0] > 2
assert info['nfev'][1] > 2
assert info['nfev'][2] > 2
assert np.all(np.diff(tout) > 0)
tout1 = tout[tout <= times[0]]
tout23 = tout[tout > times[0]]
tout2 = tout23[tout23 <= times[0] + times[1]]
tout3 = tout23[tout23 > times[0] + times[1]]
def _ref(y0, x, T, x0):
k = 1e10 * np.exp(-63e3 / 8.3145 / T)
return y0 * np.exp(-k * (x - x0))
Aref1 = _ref(conc['A'], tout1, Ts[0], tout1[0])
Bref1 = conc['B'] + conc['A'] - Aref1
Aref2 = _ref(Aref1[-1], tout2, Ts[1], tout1[-1])
Bref2 = Bref1[-1] + Aref1[-1] - Aref2
Aref3 = _ref(Aref2[-1], tout3, Ts[2], tout2[-1])
Bref3 = Bref2[-1] + Aref2[-1] - Aref3
cref = np.concatenate([
np.vstack((a, b)).T
for a, b in [(Aref1, Bref1), (Aref2, Bref2), (Aref3, Bref3)]
])
forgive = 27 * 1.1
assert np.allclose(cref,
cout,
atol=kw['atol'] * forgive,
rtol=kw['rtol'] * forgive)
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 = MassAction(Arrhenius([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, extra = get_odesys(rsys, False, substitutions={'temperature': rt})
all_pk, unique, p_units = map(extra.get,
'param_keys unique p_units'.split())
conc = {'A': A0, 'B': B0}
tout = [2, 5, 10]
for ramp_rate in [2, 3, 4]:
unique['ramp_rate'] = ramp_rate
xout, yout, info = odesys.integrate(10,
conc,
unique,
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)
unique['ramp_rate'] = 2
x, y, p = odesys.to_arrays(tout, conc, unique)
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)
def test_get_odesys__rate_exprs_cb():
k = .2
a = Substance('A')
b = Substance('B')
r = Reaction({'A': 1}, {'B': 1}, param=k)
rsys = ReactionSystem([r], [a, b])
assert sorted(rsys.substances.keys()) == ['A', 'B']
odesys, extra = get_odesys(rsys)
c0 = {'A': 1.0, 'B': 3.0}
t = np.linspace(0.0, 10.0)
res = odesys.integrate(t, c0)
yref = np.zeros((t.size, 2))
yref[:, 0] = np.exp(-k*t)
yref[:, 1] = 4 - np.exp(-k*t)
assert np.allclose(res.yout, yref)
rate = extra['rate_exprs_cb'](res.xout, res.yout, res.params)
assert np.allclose(rate[:, 0], k*yref[:, 0])
def test_get_ode__Radiolytic__units__multi():
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}
doserates = [dr * u.gray / u.second for dr in [0.1, 0.2, 0.3, 0.4]]
results = odesys.integrate(
37 * u.second,
conc,
{"doserate": doserates, "density": 0.998 * u.kg / u.decimetre ** 3},
)
assert len(results) == 4
for i, r in enumerate(results):
dr = r.params[odesys.param_names.index("doserate")]
assert dr.ndim == 0 or len(dr) == 1
assert dr == doserates[i]
def test_get_ode__Radiolytic__units__multi():
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}
doserates = [dr*u.gray/u.second for dr in [.1, .2, .3, .4]]
results = odesys.integrate(37*u.second, conc, {
'doserate': doserates,
'density': 0.998*u.kg/u.decimetre**3
})
assert len(results) == 4
for i, r in enumerate(results):
dr = r.params[odesys.param_names.index('doserate')]
assert dr.ndim == 0 or len(dr) == 1
assert dr == doserates[i]
def test_get_odesys__time_dep_rate():
class RampedRate(Expr):
argument_names = ("rate_constant", "ramping_rate")
def __call__(self, variables, reaction, backend=math):
rate_constant, ramping_rate = self.all_args(variables, backend=backend)
return rate_constant * ramping_rate * variables["time"]
rate = MassAction(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.to_arrays([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_1():
k = .2
a = Substance('A')
b = Substance('B')
r = Reaction({'A': 1}, {'B': 1}, param=k)
rsys = ReactionSystem([r], [a, b])
assert sorted(rsys.substances.keys()) == ['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, 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_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, 0.1)
xout, yout, info = odesys.integrate(
t, rsys.as_per_substance_array(c0), {"doserate": 2.72, "density": 0.998}
)
yref = np.zeros((t.size, 2))
k = 3.14 * 2.72 * 0.998
yref[:, 0] = 1 - k * t
yref[:, 1] = 3 + k * t
assert np.allclose(yout, yref)