# -*- coding: utf-8 -*-

from collections import defaultdict, OrderedDict
from itertools import permutations
import math

import pytest

try:
    import numpy as np
except ImportError:
    np = None


from chempy import Equilibrium, Reaction, ReactionSystem, Substance
from chempy.thermodynamics.expressions import MassActionEq
from chempy.units import (
    SI_base_registry,
    get_derived_unit,
    allclose,
    units_library,
    linspace,
    to_unitless,
    default_constants as const,
    default_units as u,
)
from chempy.util._expr import Expr
from chempy.util.testing import requires
from .test_rates import _get_SpecialFraction_rsys
from ..arrhenius import ArrheniusParam
from ..rates import Arrhenius, MassAction, Radiolytic, RampedTemp
from .._rates import ShiftedTPoly
from ..ode import (
    get_odesys,
    chained_parameter_variation,
    _mk_dedim,
    _create_odesys as create_odesys,
)
from ..integrated import dimerization_irrev, binary_rev


@requires("numpy", "pyodesys")
def test_get_odesys_1():
    k = 0.2
    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)


@requires("numpy", "pyodesys", "sympy")
def test_get_odesys__rate_exprs_cb():
    k = 0.2
    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])


@requires("numpy", "pyodesys")
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)


@requires(units_library, "pyodesys")
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


@requires(units_library, "pyodesys")
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": 0.2 * 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)


@requires("numpy", "pyodesys")
def test_SpecialFraction():
    k, kprime = 3.142, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)

    odesys = get_odesys(rsys, include_params=True)[0]
    c0 = {"H2": 13, "Br2": 17, "HBr": 19}
    r = k * c0["H2"] * c0["Br2"] ** (3 / 2) / (c0["Br2"] + kprime * c0["HBr"])
    ref = rsys.as_per_substance_array({"H2": -r, "Br2": -r, "HBr": 2 * r})
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0))
    assert np.allclose(res, ref)


@requires(units_library, "pyodesys")
def test_SpecialFraction_with_units():
    k, kprime = 3.142 * u.s ** -1 * u.molar ** -0.5, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)
    odesys = get_odesys(rsys, include_params=True, unit_registry=SI_base_registry)[0]
    c0 = {"H2": 13 * u.molar, "Br2": 16 * u.molar, "HBr": 19 * u.molar}
    r = k * c0["H2"] * c0["Br2"] ** (3 / 2) / (c0["Br2"] + kprime * c0["HBr"])
    conc_unit = u.mol / u.metre ** 3
    rate_unit = conc_unit / u.second
    ref = rsys.as_per_substance_array(
        {"H2": -r, "Br2": -r, "HBr": 2 * r}, unit=rate_unit
    )
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0, unit=conc_unit))
    assert allclose(to_unitless(ref, rate_unit), res)


@requires("pyodesys")
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)


@requires("pyodesys")
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)


@requires("pyodesys")
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)


@requires("pyodesys", units_library)
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)


@requires("pyodesys", units_library)
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]


class Density(Expr):
    """Arguments: rho0 drhodT T0"""

    parameter_keys = ("temperature",)
    kw = {}

    def __call__(self, variables, backend=None):
        rho0, drhodT, T0 = self.all_args(variables)
        return rho0 + drhodT * (variables["temperature"] - T0)


@requires("pyodesys")
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)


@requires("pyodesys", units_library)
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)


@requires("pyodesys", units_library)
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)


@requires("pyodesys", units_library)
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)


@requires("pyodesys", units_library)
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)


@requires("numpy", "pyodesys")
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)


@requires("numpy", "pyodesys")
def test_get_odesys__ScaledSys():
    from pyodesys.symbolic import ScaledSys

    k = 0.2
    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, SymbolicSys=ScaledSys)[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)


@requires("numpy", "pyodesys", "sympy")
def test_get_odesys__max_euler_step_cb():
    rsys = ReactionSystem.from_string(
        "\n".join(["H2O -> H+ + OH-; 1e-4", "OH- + H+ -> H2O; 1e10"])
    )
    odesys, extra = get_odesys(rsys)
    r1 = 1.01e-4
    r2 = 6e-4
    dH2Odt = r2 - r1
    euler_ref = 2e-7 / dH2Odt
    assert (
        abs(
            extra["max_euler_step_cb"](0, {"H2O": 1.01, "H+": 2e-7, "OH-": 3e-7})
            - euler_ref
        )
        / euler_ref
        < 1e-8
    )


@requires("numpy", "pyodesys", "sympy")
@pytest.mark.parametrize("substances", permutations(["H2O", "H+", "OH-"]))
def test_get_odesys__linear_dependencies__preferred(substances):
    rsys = ReactionSystem.from_string(
        "\n".join(["H2O -> H+ + OH-; 1e-4", "OH- + H+ -> H2O; 1e10"]), substances
    )
    assert isinstance(rsys.substances, OrderedDict)
    odesys, extra = get_odesys(rsys)

    af_H2O_H = extra["linear_dependencies"](["H+", "H2O"])
    import sympy

    y0 = {k: sympy.Symbol(k + "0") for k in rsys.substances}
    af_H2O_H(
        None, {odesys[k]: v for k, v in y0.items()}, None, sympy
    )  # ensure idempotent
    exprs_H2O_H = af_H2O_H(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    ref_H2O_H = {
        "H2O": y0["H2O"] + y0["OH-"] - odesys["OH-"],  # oxygen
        "H+": 2 * y0["H2O"]
        + y0["H+"]
        + y0["OH-"]
        - odesys["OH-"]
        - 2 * (y0["H2O"] + y0["OH-"] - odesys["OH-"]),  # hydrogen
    }
    for k, v in ref_H2O_H.items():
        assert (exprs_H2O_H[odesys[k]] - v) == 0


@requires("numpy", "pyodesys", "sympy", "pycvodes")
@pytest.mark.parametrize(
    "preferred", [None, ["H+", "OH-"], ["H2O", "H+"], ["H2O", "OH-"]]
)
def test_get_odesys__linear_dependencies__PartiallySolvedSystem(preferred):
    import sympy
    from pyodesys.symbolic import PartiallySolvedSystem

    rsys = ReactionSystem.from_string(
        "\n".join(["H2O -> H+ + OH-; 1e-4", "OH- + H+ -> H2O; 1e10"])
    )
    odesys, extra = get_odesys(rsys)
    c0 = {"H2O": 0, "H+": 2e-7, "OH-": 3e-7}
    h0max = extra["max_euler_step_cb"](0, c0)
    analytic_factory = extra["linear_dependencies"]()
    y0 = {k: sympy.Symbol(k + "0") for k in rsys.substances}
    analytic_factory(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    psys = PartiallySolvedSystem(odesys, analytic_factory)
    xout, yout, info = psys.integrate(
        1, c0, atol=1e-12, rtol=1e-10, first_step=h0max * 1e-12, integrator="cvode"
    )
    c_reac = c0["H+"], c0["OH-"]
    H2O_ref = binary_rev(xout, 1e10, 1e-4, c0["H2O"], max(c_reac), min(c_reac))
    assert np.allclose(yout[:, psys.names.index("H2O")], H2O_ref)
    assert np.allclose(yout[:, psys.names.index("H+")], c0["H+"] + c0["H2O"] - H2O_ref)
    assert np.allclose(
        yout[:, psys.names.index("OH-")], c0["OH-"] + c0["H2O"] - H2O_ref
    )


@requires("numpy", "pyodesys", "sympy", "pycvodes")
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)


@requires("numpy", "pyodesys", "sympy", "pycvodes")
def test_get_odesys__Expr_as_param():
    def _eyring_pe(args, T, backend=math, **kwargs):
        (freq,) = args
        return freq * T

    EyringPreExp = Expr.from_callback(
        _eyring_pe, argument_names=("freq",), parameter_keys=("temperature",)
    )

    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"])
    odesys, extra = get_odesys(
        rsys, include_params=False, substitutions={"A_u": EyringPreExp(kb_h)}
    )
    y0 = defaultdict(float, {"A": 7.0})
    rt = 293.15
    xout, yout, info = odesys.integrate(
        5,
        y0,
        {"H_u": 117e3, "S_u": 150, "temperature": rt},
        integrator="cvode",
        atol=1e-12,
        rtol=1e-10,
        nsteps=1000,
    )
    kref = kb_h * rt * np.exp(-(117e3 - rt * 150) / (8.314511 * rt))
    ref = y0["A"] * np.exp(-kref * xout)
    assert np.allclose(yout[:, 0], ref)
    assert np.allclose(yout[:, 1], y0["A"] - ref)


@requires("numpy", "pyodesys", "sympy", "pycvodes")
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)


@requires("pyodesys", "pycvodes")
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 _check_cstr(odesys, fr, fc, extra_pars=None):
    tout, c0 = np.linspace(0, 0.13, 7), {"H2O2": 2, "O2": 4, "H2O": 3}
    params = {fr: 13, fc["H2O2"]: 11, fc["O2"]: 43, fc["H2O"]: 45}
    params.update(extra_pars or {})
    res = odesys.integrate(tout, c0, params)
    from chempy.kinetics.integrated import binary_irrev_cstr

    def get_analytic(result, k, n):
        ref = binary_irrev_cstr(
            result.xout,
            5,
            result.named_dep("H2O2")[0],
            result.named_dep(k)[0],
            result.named_param(fc["H2O2"]),
            result.named_param(fc[k]),
            result.named_param(fr),
            n,
        )
        return np.array(ref).T

    ref_O2 = get_analytic(res, "O2", 1)
    ref_H2O = get_analytic(res, "H2O", 2)
    assert np.allclose(res.named_dep("H2O2"), ref_O2[:, 0])
    assert np.allclose(res.named_dep("H2O2"), ref_H2O[:, 0])
    assert np.allclose(res.named_dep("O2"), ref_O2[:, 1])
    assert np.allclose(res.named_dep("H2O"), ref_H2O[:, 1])


@requires("pyodesys", "scipy", "sym")
def test_get_odesys__cstr():
    rsys = ReactionSystem.from_string("2 H2O2 -> O2 + 2 H2O; 5")
    odesys, extra = get_odesys(rsys, cstr=True)
    fr, fc = extra["cstr_fr_fc"]
    _check_cstr(odesys, fr, fc)


@requires("pyodesys", "scipy", "sym")
def test_create_odesys__cstr():
    rsys = ReactionSystem.from_string("2 H2O2 -> O2 + 2 H2O; 'k2'")
    fr, fc = "feedratio", OrderedDict([(sk, "fc_%s" % sk) for sk in rsys.substances])
    odesys, extra = create_odesys(rsys, rates_kw=dict(cstr_fr_fc=(fr, fc)))
    _check_cstr(odesys, fr, fc, extra_pars=dict(k2=5))


@requires("pygslodeiv2", "sym", units_library)
def test_get_odesys_rsys_with_units():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 0.096/s
    B + C -> P; 4e3/M/s
    """,
        substance_factory=Substance,
    )
    with pytest.raises(Exception):
        get_odesys(
            rsys
        )  # not a strict test, SI_base_registry could be made the default

    odesys, extra = get_odesys(rsys, unit_registry=SI_base_registry)
    tend = 10
    tend_units = tend * u.s
    c0 = {"A": 1e-6, "B": 0, "C": 1, "P": 0}
    c0_units = {k: v * u.molar for k, v in c0.items()}
    result1 = odesys.integrate(tend_units, c0_units, integrator="gsl")
    assert result1.info["success"]

    with pytest.raises(Exception):
        odesys.integrate(tend, c0, integrator="gsl")


@requires("pyodeint", "sym", units_library)
def test_get_odesys_rsys_with_units__named_params():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 'k1'
    B + C -> P; 'k2'
    """,
        substance_factory=Substance,
    )
    odesys, extra = get_odesys(
        rsys, include_params=False, unit_registry=SI_base_registry
    )
    tend = 10
    tend_units = tend * u.s
    c0 = {"A": 1e-6, "B": 0, "C": 1, "P": 0}
    p = {"k1": 3, "k2": 4}
    p_units = {"k1": 3 / u.s, "k2": 4 / u.M / u.s}
    c0_units = {k: v * u.molar for k, v in c0.items()}
    result1 = odesys.integrate(tend_units, c0_units, p_units, integrator="odeint")
    assert result1.info["success"]

    with pytest.raises(Exception):
        odesys.integrate(tend, c0, p, integrator="odeint")


@requires("pycvodes", "sym", units_library)
def test_get_odesys__Eyring():
    R = 8.314472
    T_K = 300
    dH = 80e3
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """.format(
            dH=dH, dS=dS
        ),
        substances="NOBr NO Br".split(),
    )
    kref = 20836643994.118652 * T_K * np.exp(-(dH - T_K * dS) / (R * T_K))
    NOBr0_M = 0.7
    init_cond = dict(NOBr=NOBr0_M * u.M, NO=0 * u.M, Br=0 * u.M)
    t = 5 * u.second
    params = dict(temperature=T_K * u.K)

    def check(rsys):
        odesys, extra = get_odesys(
            rsys, unit_registry=SI_base_registry, constants=const
        )
        res = odesys.integrate(t, init_cond, params, integrator="cvode")
        NOBr_ref = NOBr0_M * np.exp(-kref * to_unitless(res.xout, u.second))
        ref = np.array([NOBr_ref] + [NOBr0_M - NOBr_ref] * 2).T
        cmp = to_unitless(res.yout, u.M)
        assert np.allclose(cmp, ref)

    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """.format(
            dH=dH, dS=dS
        ),
        substances="NOBr NO Br".split(),
    )
    check(rsys2)


@requires("pycvodes", "sym", units_library)
def test_get_odesys__Eyring_2nd_order():
    R = 8.314472
    T_K = 300
    dH = 80e3
    dS = 10
    rsys1b = ReactionSystem.from_string(
        """
    NO + Br -> NOBr; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """.format(
            dH=dH, dS=dS
        )
    )
    c0 = 1  # mol/dm3 === 1000 mol/m3
    kbref = 20836643994.118652 * T_K * np.exp(-(dH - T_K * dS) / (R * T_K)) / c0
    NO0_M = 1.5
    Br0_M = 0.7
    init_cond = dict(NOBr=0 * u.M, NO=NO0_M * u.M, Br=Br0_M * u.M)
    t = 5 * u.second
    params = dict(temperature=T_K * u.K)

    def analytic_b(t):
        U, V = NO0_M, Br0_M
        d = U - V
        return (U * (1 - np.exp(-kbref * t * d))) / (U / V - np.exp(-kbref * t * d))

    def check(rsys):
        odesys, extra = get_odesys(
            rsys, unit_registry=SI_base_registry, constants=const
        )
        res = odesys.integrate(t, init_cond, params, integrator="cvode")
        t_sec = to_unitless(res.xout, u.second)
        NOBr_ref = analytic_b(t_sec)
        cmp = to_unitless(res.yout, u.M)
        ref = np.empty_like(cmp)
        ref[:, odesys.names.index("NOBr")] = NOBr_ref
        ref[:, odesys.names.index("Br")] = Br0_M - NOBr_ref
        ref[:, odesys.names.index("NO")] = NO0_M - NOBr_ref
        assert np.allclose(cmp, ref)

    check(rsys1b)
    rsys2b = ReactionSystem.from_string(
        """
    NO + Br -> NOBr; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """.format(
            dH=dH, dS=dS
        )
    )
    check(rsys2b)


@requires("pycvodes", "sym", "scipy", units_library)
def test_get_odesys__Eyring_1st_order_linearly_ramped_temperature():
    from scipy.special import expi

    def analytic_unit0(t, T0, dH, dS):
        R = 8.314472
        kB = 1.3806504e-23
        h = 6.62606896e-34
        A = kB / h * np.exp(dS / R)
        B = dH / R
        return np.exp(
            A
            * (
                (-(B ** 2) * np.exp(B / T0) * expi(-B / T0) - T0 * (B - T0))
                * np.exp(-B / T0)
                + (
                    B ** 2 * np.exp(B / (t + T0)) * expi(-B / (t + T0))
                    - (t + T0) * (-B + t + T0)
                )
                * np.exp(-B / (t + T0))
            )
            / 2
        )

    T_K = 290
    dH = 80e3
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """.format(
            dH=dH, dS=dS
        )
    )

    NOBr0_M = 0.7
    init_cond = dict(NOBr=NOBr0_M * u.M, NO=0 * u.M, Br=0 * u.M)
    t = 20 * u.second

    def check(rsys):
        odes, extra = get_odesys(
            rsys,
            unit_registry=SI_base_registry,
            constants=const,
            substitutions={"temperature": RampedTemp([T_K * u.K, 1 * u.K / u.s])},
        )
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, integrator="cvode")
            t_sec = to_unitless(res.xout, u.second)
            NOBr_ref = NOBr0_M * analytic_unit0(t_sec, T_K, dH, dS)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index("NOBr")] = NOBr_ref
            ref[:, odesys.names.index("Br")] = NOBr0_M - NOBr_ref
            ref[:, odesys.names.index("NO")] = NOBr0_M - NOBr_ref
            assert np.allclose(cmp, ref)

    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """.format(
            dH=dH, dS=dS
        )
    )
    check(rsys2)


@requires("pycvodes", "sym", "scipy", units_library)
def test_get_odesys__Eyring_2nd_order_linearly_ramped_temperature():
    from scipy.special import expi

    def analytic_unit0(t, k, m, dH, dS):
        R = 8.314472
        kB = 1.3806504e-23
        h = 6.62606896e-34
        A = kB / h * np.exp(dS / R)
        B = dH / R
        return (
            k
            * np.exp(B * (k * t + 2 * m) / (m * (k * t + m)))
            / (
                A
                * (
                    -(B ** 2) * np.exp(B / (k * t + m)) * expi(-B / (k * t + m))
                    - B * k * t
                    - B * m
                    + k ** 2 * t ** 2
                    + 2 * k * m * t
                    + m ** 2
                )
                * np.exp(B / m)
                + (
                    A * B ** 2 * np.exp(B / m) * expi(-B / m)
                    - A * m * (-B + m)
                    + k * np.exp(B / m)
                )
                * np.exp(B / (k * t + m))
            )
        )

    T_K = 290
    dTdt_Ks = 3
    dH = 80e3
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    2 NO2 -> N2O4; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """.format(
            dH=dH, dS=dS
        )
    )

    NO2_M = 1.0
    init_cond = dict(NO2=NO2_M * u.M, N2O4=0 * u.M)
    t = 20 * u.second

    def check(rsys):
        odes, extra = get_odesys(
            rsys,
            unit_registry=SI_base_registry,
            constants=const,
            substitutions={"temperature": RampedTemp([T_K * u.K, dTdt_Ks * u.K / u.s])},
        )
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, integrator="cvode")
            t_sec = to_unitless(res.xout, u.second)
            NO2_ref = analytic_unit0(t_sec, dTdt_Ks, T_K, dH, dS)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index("NO2")] = NO2_ref
            ref[:, odesys.names.index("N2O4")] = (NO2_M - NO2_ref) / 2
            assert np.allclose(cmp, ref)

    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    2 NO2 -> N2O4; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """.format(
            dH=dH, dS=dS
        )
    )
    check(rsys2)


@requires("pycvodes", "sym", units_library)
def test_get_odesys__Eyring_2nd_order_reversible():
    R = 8.314472
    T_K = 273.15 + 20  # 20 degree celsius
    kB = 1.3806504e-23
    h = 6.62606896e-34

    dHf = 74e3
    dSf = R * np.log(h / kB / T_K * 1e16)

    dHb = 79e3
    dSb = dSf - 23

    rsys1 = ReactionSystem.from_string(
        """
    Fe+3 + SCN- -> FeSCN+2; EyringParam(dH={dHf}*J/mol, dS={dSf}*J/K/mol)
    FeSCN+2 -> Fe+3 + SCN-; EyringParam(dH={dHb}*J/mol, dS={dSb}*J/K/mol)
    """.format(
            dHf=dHf, dSf=dSf, dHb=dHb, dSb=dSb
        )
    )
    kf_ref = 20836643994.118652 * T_K * np.exp(-(dHf - T_K * dSf) / (R * T_K))
    kb_ref = 20836643994.118652 * T_K * np.exp(-(dHb - T_K * dSb) / (R * T_K))
    Fe0 = 6e-3
    SCN0 = 2e-3
    init_cond = {"Fe+3": Fe0 * u.M, "SCN-": SCN0 * u.M, "FeSCN+2": 0 * u.M}
    t = 3 * u.second

    def check(rsys, params):
        odes, extra = get_odesys(
            rsys, include_params=False, unit_registry=SI_base_registry, constants=const
        )
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, params, integrator="cvode")
            t_sec = to_unitless(res.xout, u.second)
            FeSCN_ref = binary_rev(t_sec, kf_ref, kb_ref, 0, Fe0, SCN0)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index("FeSCN+2")] = FeSCN_ref
            ref[:, odesys.names.index("Fe+3")] = Fe0 - FeSCN_ref
            ref[:, odesys.names.index("SCN-")] = SCN0 - FeSCN_ref
            assert np.allclose(cmp, ref)

    check(rsys1, {"temperature": T_K * u.K})
    rsys2 = ReactionSystem.from_string(
        """
    Fe+3 + SCN- -> FeSCN+2; MassAction(EyringHS([{dHf}*J/mol, {dSf}*J/K/mol]))
    FeSCN+2 -> Fe+3 + SCN-; MassAction(EyringHS([{dHb}*J/mol, {dSb}*J/K/mol]))
    """.format(
            dHf=dHf, dSf=dSf, dHb=dHb, dSb=dSb
        )
    )
    check(rsys2, {"temperature": T_K * u.K})
    rsys3 = ReactionSystem.from_string(
        """
    Fe+3 + SCN- -> FeSCN+2; MassAction(EyringHS.fk('dHf', 'dSf'))
    FeSCN+2 -> Fe+3 + SCN-; MassAction(EyringHS.fk('dHb', 'dSb'))
    """
    )
    check(
        rsys3,
        dict(
            temperature=T_K * u.K,
            dHf=dHf * u.J / u.mol,
            dSf=dSf * u.J / u.mol / u.K,
            dHb=dHb * u.J / u.mol,
            dSb=dSb * u.J / u.mol / u.K,
        ),
    )


@requires("numpy", "pyodesys", "sympy", "pycvodes")
def test_create_odesys():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 'k1'
    B + C -> P; 'k2'
    """,
        substance_factory=Substance,
    )

    odesys, odesys_extra = create_odesys(rsys, unit_registry=SI_base_registry)

    tend_ul = 10
    init_conc_ul = {"A": 1e-6, "B": 0, "C": 1}
    params_ul = dict(k1=3, k2=4)

    tend = tend_ul * u.s
    params = {"k1": params_ul["k1"] / u.s, "k2": params_ul["k2"] / u.M / u.s}
    init_conc = {k: v * u.molar for k, v in init_conc_ul.items()}

    validation = odesys_extra["validate"](dict(init_conc, **params))
    (P,) = validation["not_seen"]
    assert P == "P"

    ref_rates = {
        "A": -params["k1"] * init_conc["A"],
        "P": params["k2"] * init_conc["B"] * init_conc["C"],
    }
    ref_rates["B"] = -ref_rates["A"] - ref_rates["P"]
    ref_rates["C"] = -ref_rates["P"]
    assert validation["rates"] == ref_rates

    result1, result1_extra = odesys_extra["unit_aware_solve"](
        tend, defaultdict(lambda: 0 * u.molar, init_conc), params, integrator="cvode"
    )
    assert result1.info["success"]

    result2 = odesys.integrate(
        tend_ul, defaultdict(lambda: 0, init_conc_ul), params_ul, integrator="cvode"
    )
    assert np.allclose(result2.yout[-1, :], to_unitless(result1.yout[-1, :], u.molar))


@requires("pycvodes", "sym", units_library)
def test_create_odesys__Radiolytic():
    rsys1 = ReactionSystem.from_string(
        """
    -> e-(aq); Radiolytic.fk('g_emaq')
    """,
        checks=(),
    )
    ic1 = {"e-(aq)": 0.0}
    t1 = 5
    p1 = dict(g_emaq=42.0, doserate=17.0, density=5.0)
    odesys1, odesys_extra = create_odesys(rsys1)
    result1 = odesys1.integrate(t1, ic1, p1)
    yref1 = result1.xout * p1["g_emaq"] * p1["doserate"] * p1["density"]
    assert np.allclose(yref1, result1.yout.squeeze())


@requires("pycvodes", "sym", units_library)
def test_create_odesys__validate__catalyst():
    rsys1 = ReactionSystem.from_string(
        """
    H2O2 + Pt -> 2 OH + Pt; 'k_decomp'
    """
    )
    ic1 = defaultdict(lambda: 0 * u.molar, {"H2O2": 3.0 * u.molar, "Pt": 0.5 * u.molar})
    t1 = linspace(0 * u.s, 0.3 * u.s, 7)
    p1 = dict(k_decomp=42 / u.second / u.molar)
    odesys1, odesys_extra = create_odesys(rsys1)
    validation = odesys_extra["validate"](dict(ic1, **p1))
    assert validation["not_seen"] == {"OH"}

    dedim_ctx = _mk_dedim(SI_base_registry)
    (t, c, _p), dedim_extra = dedim_ctx["dedim_tcp"](
        t1, [ic1[k] for k in odesys1.names], p1
    )
    result1 = odesys1.integrate(t, c, _p)
    tout = result1.xout * dedim_extra["unit_time"]
    cout = result1.yout * dedim_extra["unit_conc"]
    yref1 = ic1["H2O2"] * np.exp(-tout * ic1["Pt"] * p1["k_decomp"])
    assert allclose(yref1, cout[:, odesys1.names.index("H2O2")], rtol=1e-6)


@requires("pyodesys", units_library)
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)

4540873c7d825b87051ab54132dd3eda4063911e
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@requires('numpy', 'pyodesys')
def test_get_odesys_1():
    k = 0.2
    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)


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@requires('numpy', 'pyodesys')
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)


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@requires(units_library, 'pyodesys')
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=0.001 / 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': 0.2 * 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-06, 13.0)
    yref = np.zeros((xout.size, 2))
    yref[:, 0] = Aref
    yref[:, 1] = 200 + (13 - Aref) / 2
    assert allclose(yout, yref * conc_unit)


@requires('numpy', 'pyodesys')
def test_SpecialFraction():
    k, kprime = 3.142, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)
    odesys = get_odesys(rsys, include_params=True)[0]
    c0 = {'H2': 13, 'Br2': 17, 'HBr': 19}
    r = k * c0['H2'] * c0['Br2'] ** (3 / 2) / (c0['Br2'] + kprime * c0['HBr'])
    ref = rsys.as_per_substance_array({'H2': -r, 'Br2': -r, 'HBr': 2 * r})
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0))
    assert np.allclose(res, ref)


@requires(units_library, 'pyodesys')
def test_SpecialFraction_with_units():
    k, kprime = 3.142 * u.s ** -1 * u.molar ** -0.5, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)
    odesys = get_odesys(rsys, include_params=True, unit_registry=
        SI_base_registry)[0]
    c0 = {'H2': 13 * u.molar, 'Br2': 16 * u.molar, 'HBr': 19 * u.molar}
    r = k * c0['H2'] * c0['Br2'] ** (3 / 2) / (c0['Br2'] + kprime * c0['HBr'])
    conc_unit = u.mol / u.metre ** 3
    rate_unit = conc_unit / u.second
    ref = rsys.as_per_substance_array({'H2': -r, 'Br2': -r, 'HBr': 2 * r},
        unit=rate_unit)
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0, unit=conc_unit))
    assert allclose(to_unitless(ref, rate_unit), res)


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@requires('pyodesys')
def test_get_ode__ArrheniusParam():
    rxn = Reaction({'A': 1}, {'B': 1}, None)
    rxn.param = ArrheniusParam(10000000000.0, 40000.0)
    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 * 10000000000.0 * np.exp(-40000.0 / 8.314472 / 200)
    assert np.all(abs((fout[:, 0] + ref) / ref) < 1e-14)
    assert np.all(abs((fout[:, 1] - ref) / ref) < 1e-14)


@requires('pyodesys')
def test_get_ode__Radiolytic():
    rad = Radiolytic([2.4e-07])
    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-07 * 0.4 * 0.998
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)


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class Density(Expr):
    """Arguments: rho0 drhodT T0"""
    parameter_keys = 'temperature',
    kw = {}

    def __call__(self, variables, backend=None):
        rho0, drhodT, T0 = self.all_args(variables)
        return rho0 + drhodT * (variables['temperature'] - T0)


@requires('pyodesys')
def test_get_ode__Radiolytic__substitutions():
    rad = Radiolytic([2.4e-07])
    rxn = Reaction({'A': 4, 'B': 1}, {'C': 3, 'D': 2}, rad)
    rsys = ReactionSystem([rxn], 'A B C D')
    substance_rho = Density([1, -0.001, 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-07 * 0.4 * substance_rho({'temperature': 298.15})
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)


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@requires('numpy', 'pyodesys')
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)
    uk_kinet = 'Ha_assoc', 'Sa_assoc'
    bimol_barrier = EyringMA(unique_keys=uk_kinet)
    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)


@requires('numpy', 'pyodesys')
def test_get_odesys__ScaledSys():
    from pyodesys.symbolic import ScaledSys
    k = 0.2
    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, SymbolicSys=ScaledSys)[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)


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@requires('numpy', 'pyodesys', 'sympy')
@pytest.mark.parametrize('substances', permutations(['H2O', 'H+', 'OH-']))
def test_get_odesys__linear_dependencies__preferred(substances):
    rsys = ReactionSystem.from_string('\n'.join(['H2O -> H+ + OH-; 1e-4',
        'OH- + H+ -> H2O; 1e10']), substances)
    assert isinstance(rsys.substances, OrderedDict)
    odesys, extra = get_odesys(rsys)
    af_H2O_H = extra['linear_dependencies'](['H+', 'H2O'])
    import sympy
    y0 = {k: sympy.Symbol(k + '0') for k in rsys.substances}
    af_H2O_H(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    exprs_H2O_H = af_H2O_H(None, {odesys[k]: v for k, v in y0.items()},
        None, sympy)
    ref_H2O_H = {'H2O': y0['H2O'] + y0['OH-'] - odesys['OH-'], 'H+': 2 * y0
        ['H2O'] + y0['H+'] + y0['OH-'] - odesys['OH-'] - 2 * (y0['H2O'] +
        y0['OH-'] - odesys['OH-'])}
    for k, v in ref_H2O_H.items():
        assert exprs_H2O_H[odesys[k]] - v == 0


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
@pytest.mark.parametrize('preferred', [None, ['H+', 'OH-'], ['H2O', 'H+'],
    ['H2O', 'OH-']])
def test_get_odesys__linear_dependencies__PartiallySolvedSystem(preferred):
    import sympy
    from pyodesys.symbolic import PartiallySolvedSystem
    rsys = ReactionSystem.from_string('\n'.join(['H2O -> H+ + OH-; 1e-4',
        'OH- + H+ -> H2O; 1e10']))
    odesys, extra = get_odesys(rsys)
    c0 = {'H2O': 0, 'H+': 2e-07, 'OH-': 3e-07}
    h0max = extra['max_euler_step_cb'](0, c0)
    analytic_factory = extra['linear_dependencies']()
    y0 = {k: sympy.Symbol(k + '0') for k in rsys.substances}
    analytic_factory(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    psys = PartiallySolvedSystem(odesys, analytic_factory)
    xout, yout, info = psys.integrate(1, c0, atol=1e-12, rtol=1e-10,
        first_step=h0max * 1e-12, integrator='cvode')
    c_reac = c0['H+'], c0['OH-']
    H2O_ref = binary_rev(xout, 10000000000.0, 0.0001, c0['H2O'], max(c_reac
        ), min(c_reac))
    assert np.allclose(yout[:, psys.names.index('H2O')], H2O_ref)
    assert np.allclose(yout[:, psys.names.index('H+')], c0['H+'] + c0['H2O'
        ] - H2O_ref)
    assert np.allclose(yout[:, psys.names.index('OH-')], c0['OH-'] + c0[
        'H2O'] - H2O_ref)


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
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)


<mask token>


def _check_cstr(odesys, fr, fc, extra_pars=None):
    tout, c0 = np.linspace(0, 0.13, 7), {'H2O2': 2, 'O2': 4, 'H2O': 3}
    params = {fr: 13, fc['H2O2']: 11, fc['O2']: 43, fc['H2O']: 45}
    params.update(extra_pars or {})
    res = odesys.integrate(tout, c0, params)
    from chempy.kinetics.integrated import binary_irrev_cstr

    def get_analytic(result, k, n):
        ref = binary_irrev_cstr(result.xout, 5, result.named_dep('H2O2')[0],
            result.named_dep(k)[0], result.named_param(fc['H2O2']), result.
            named_param(fc[k]), result.named_param(fr), n)
        return np.array(ref).T
    ref_O2 = get_analytic(res, 'O2', 1)
    ref_H2O = get_analytic(res, 'H2O', 2)
    assert np.allclose(res.named_dep('H2O2'), ref_O2[:, 0])
    assert np.allclose(res.named_dep('H2O2'), ref_H2O[:, 0])
    assert np.allclose(res.named_dep('O2'), ref_O2[:, 1])
    assert np.allclose(res.named_dep('H2O'), ref_H2O[:, 1])


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@requires('pyodesys', 'scipy', 'sym')
def test_create_odesys__cstr():
    rsys = ReactionSystem.from_string("2 H2O2 -> O2 + 2 H2O; 'k2'")
    fr, fc = 'feedratio', OrderedDict([(sk, 'fc_%s' % sk) for sk in rsys.
        substances])
    odesys, extra = create_odesys(rsys, rates_kw=dict(cstr_fr_fc=(fr, fc)))
    _check_cstr(odesys, fr, fc, extra_pars=dict(k2=5))


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@requires('pycvodes', 'sym', 'scipy', units_library)
def test_get_odesys__Eyring_1st_order_linearly_ramped_temperature():
    from scipy.special import expi

    def analytic_unit0(t, T0, dH, dS):
        R = 8.314472
        kB = 1.3806504e-23
        h = 6.62606896e-34
        A = kB / h * np.exp(dS / R)
        B = dH / R
        return np.exp(A * ((-B ** 2 * np.exp(B / T0) * expi(-B / T0) - T0 *
            (B - T0)) * np.exp(-B / T0) + (B ** 2 * np.exp(B / (t + T0)) *
            expi(-B / (t + T0)) - (t + T0) * (-B + t + T0)) * np.exp(-B / (
            t + T0))) / 2)
    T_K = 290
    dH = 80000.0
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """
        .format(dH=dH, dS=dS))
    NOBr0_M = 0.7
    init_cond = dict(NOBr=NOBr0_M * u.M, NO=0 * u.M, Br=0 * u.M)
    t = 20 * u.second

    def check(rsys):
        odes, extra = get_odesys(rsys, unit_registry=SI_base_registry,
            constants=const, substitutions={'temperature': RampedTemp([T_K *
            u.K, 1 * u.K / u.s])})
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, integrator='cvode')
            t_sec = to_unitless(res.xout, u.second)
            NOBr_ref = NOBr0_M * analytic_unit0(t_sec, T_K, dH, dS)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index('NOBr')] = NOBr_ref
            ref[:, odesys.names.index('Br')] = NOBr0_M - NOBr_ref
            ref[:, odesys.names.index('NO')] = NOBr0_M - NOBr_ref
            assert np.allclose(cmp, ref)
    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """
        .format(dH=dH, dS=dS))
    check(rsys2)


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@requires('pycvodes', 'sym', units_library)
def test_create_odesys__Radiolytic():
    rsys1 = ReactionSystem.from_string(
        """
    -> e-(aq); Radiolytic.fk('g_emaq')
    """, checks=())
    ic1 = {'e-(aq)': 0.0}
    t1 = 5
    p1 = dict(g_emaq=42.0, doserate=17.0, density=5.0)
    odesys1, odesys_extra = create_odesys(rsys1)
    result1 = odesys1.integrate(t1, ic1, p1)
    yref1 = result1.xout * p1['g_emaq'] * p1['doserate'] * p1['density']
    assert np.allclose(yref1, result1.yout.squeeze())


@requires('pycvodes', 'sym', units_library)
def test_create_odesys__validate__catalyst():
    rsys1 = ReactionSystem.from_string(
        """
    H2O2 + Pt -> 2 OH + Pt; 'k_decomp'
    """)
    ic1 = defaultdict(lambda : 0 * u.molar, {'H2O2': 3.0 * u.molar, 'Pt': 
        0.5 * u.molar})
    t1 = linspace(0 * u.s, 0.3 * u.s, 7)
    p1 = dict(k_decomp=42 / u.second / u.molar)
    odesys1, odesys_extra = create_odesys(rsys1)
    validation = odesys_extra['validate'](dict(ic1, **p1))
    assert validation['not_seen'] == {'OH'}
    dedim_ctx = _mk_dedim(SI_base_registry)
    (t, c, _p), dedim_extra = dedim_ctx['dedim_tcp'](t1, [ic1[k] for k in
        odesys1.names], p1)
    result1 = odesys1.integrate(t, c, _p)
    tout = result1.xout * dedim_extra['unit_time']
    cout = result1.yout * dedim_extra['unit_conc']
    yref1 = ic1['H2O2'] * np.exp(-tout * ic1['Pt'] * p1['k_decomp'])
    assert allclose(yref1, cout[:, odesys1.names.index('H2O2')], rtol=1e-06)


@requires('pyodesys', units_library)
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
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)
    odesys.integrate(t, c, _p)

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@requires('numpy', 'pyodesys')
def test_get_odesys_1():
    k = 0.2
    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)


@requires('numpy', 'pyodesys', 'sympy')
def test_get_odesys__rate_exprs_cb():
    k = 0.2
    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])


@requires('numpy', 'pyodesys')
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)


<mask token>


@requires(units_library, 'pyodesys')
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=0.001 / 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': 0.2 * 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-06, 13.0)
    yref = np.zeros((xout.size, 2))
    yref[:, 0] = Aref
    yref[:, 1] = 200 + (13 - Aref) / 2
    assert allclose(yout, yref * conc_unit)


@requires('numpy', 'pyodesys')
def test_SpecialFraction():
    k, kprime = 3.142, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)
    odesys = get_odesys(rsys, include_params=True)[0]
    c0 = {'H2': 13, 'Br2': 17, 'HBr': 19}
    r = k * c0['H2'] * c0['Br2'] ** (3 / 2) / (c0['Br2'] + kprime * c0['HBr'])
    ref = rsys.as_per_substance_array({'H2': -r, 'Br2': -r, 'HBr': 2 * r})
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0))
    assert np.allclose(res, ref)


@requires(units_library, 'pyodesys')
def test_SpecialFraction_with_units():
    k, kprime = 3.142 * u.s ** -1 * u.molar ** -0.5, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)
    odesys = get_odesys(rsys, include_params=True, unit_registry=
        SI_base_registry)[0]
    c0 = {'H2': 13 * u.molar, 'Br2': 16 * u.molar, 'HBr': 19 * u.molar}
    r = k * c0['H2'] * c0['Br2'] ** (3 / 2) / (c0['Br2'] + kprime * c0['HBr'])
    conc_unit = u.mol / u.metre ** 3
    rate_unit = conc_unit / u.second
    ref = rsys.as_per_substance_array({'H2': -r, 'Br2': -r, 'HBr': 2 * r},
        unit=rate_unit)
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0, unit=conc_unit))
    assert allclose(to_unitless(ref, rate_unit), res)


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@requires('pyodesys')
def test_get_ode__ArrheniusParam():
    rxn = Reaction({'A': 1}, {'B': 1}, None)
    rxn.param = ArrheniusParam(10000000000.0, 40000.0)
    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 * 10000000000.0 * np.exp(-40000.0 / 8.314472 / 200)
    assert np.all(abs((fout[:, 0] + ref) / ref) < 1e-14)
    assert np.all(abs((fout[:, 1] - ref) / ref) < 1e-14)


@requires('pyodesys')
def test_get_ode__Radiolytic():
    rad = Radiolytic([2.4e-07])
    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-07 * 0.4 * 0.998
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)


<mask token>


class Density(Expr):
    """Arguments: rho0 drhodT T0"""
    parameter_keys = 'temperature',
    kw = {}

    def __call__(self, variables, backend=None):
        rho0, drhodT, T0 = self.all_args(variables)
        return rho0 + drhodT * (variables['temperature'] - T0)


@requires('pyodesys')
def test_get_ode__Radiolytic__substitutions():
    rad = Radiolytic([2.4e-07])
    rxn = Reaction({'A': 4, 'B': 1}, {'C': 3, 'D': 2}, rad)
    rsys = ReactionSystem([rxn], 'A B C D')
    substance_rho = Density([1, -0.001, 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-07 * 0.4 * substance_rho({'temperature': 298.15})
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)


<mask token>


@requires('numpy', 'pyodesys')
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)
    uk_kinet = 'Ha_assoc', 'Sa_assoc'
    bimol_barrier = EyringMA(unique_keys=uk_kinet)
    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)


@requires('numpy', 'pyodesys')
def test_get_odesys__ScaledSys():
    from pyodesys.symbolic import ScaledSys
    k = 0.2
    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, SymbolicSys=ScaledSys)[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)


<mask token>


@requires('numpy', 'pyodesys', 'sympy')
@pytest.mark.parametrize('substances', permutations(['H2O', 'H+', 'OH-']))
def test_get_odesys__linear_dependencies__preferred(substances):
    rsys = ReactionSystem.from_string('\n'.join(['H2O -> H+ + OH-; 1e-4',
        'OH- + H+ -> H2O; 1e10']), substances)
    assert isinstance(rsys.substances, OrderedDict)
    odesys, extra = get_odesys(rsys)
    af_H2O_H = extra['linear_dependencies'](['H+', 'H2O'])
    import sympy
    y0 = {k: sympy.Symbol(k + '0') for k in rsys.substances}
    af_H2O_H(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    exprs_H2O_H = af_H2O_H(None, {odesys[k]: v for k, v in y0.items()},
        None, sympy)
    ref_H2O_H = {'H2O': y0['H2O'] + y0['OH-'] - odesys['OH-'], 'H+': 2 * y0
        ['H2O'] + y0['H+'] + y0['OH-'] - odesys['OH-'] - 2 * (y0['H2O'] +
        y0['OH-'] - odesys['OH-'])}
    for k, v in ref_H2O_H.items():
        assert exprs_H2O_H[odesys[k]] - v == 0


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
@pytest.mark.parametrize('preferred', [None, ['H+', 'OH-'], ['H2O', 'H+'],
    ['H2O', 'OH-']])
def test_get_odesys__linear_dependencies__PartiallySolvedSystem(preferred):
    import sympy
    from pyodesys.symbolic import PartiallySolvedSystem
    rsys = ReactionSystem.from_string('\n'.join(['H2O -> H+ + OH-; 1e-4',
        'OH- + H+ -> H2O; 1e10']))
    odesys, extra = get_odesys(rsys)
    c0 = {'H2O': 0, 'H+': 2e-07, 'OH-': 3e-07}
    h0max = extra['max_euler_step_cb'](0, c0)
    analytic_factory = extra['linear_dependencies']()
    y0 = {k: sympy.Symbol(k + '0') for k in rsys.substances}
    analytic_factory(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    psys = PartiallySolvedSystem(odesys, analytic_factory)
    xout, yout, info = psys.integrate(1, c0, atol=1e-12, rtol=1e-10,
        first_step=h0max * 1e-12, integrator='cvode')
    c_reac = c0['H+'], c0['OH-']
    H2O_ref = binary_rev(xout, 10000000000.0, 0.0001, c0['H2O'], max(c_reac
        ), min(c_reac))
    assert np.allclose(yout[:, psys.names.index('H2O')], H2O_ref)
    assert np.allclose(yout[:, psys.names.index('H+')], c0['H+'] + c0['H2O'
        ] - H2O_ref)
    assert np.allclose(yout[:, psys.names.index('OH-')], c0['OH-'] + c0[
        'H2O'] - H2O_ref)


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
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)


<mask token>


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
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 = 20800000000.0
    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': 107000.0, 'S_u':
        150, 'temperature': rt}, integrator='cvode', atol=1e-12, rtol=1e-10,
        nsteps=1000)
    kref2 = kb_h * rt * np.exp(-(107000.0 - 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)


@requires('pyodesys', 'pycvodes')
def test_chained_parameter_variation():
    ratex = MassAction(Arrhenius([10000000000.0, 63000.0 / 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 = 10000000000.0 * np.exp(-63000.0 / 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 _check_cstr(odesys, fr, fc, extra_pars=None):
    tout, c0 = np.linspace(0, 0.13, 7), {'H2O2': 2, 'O2': 4, 'H2O': 3}
    params = {fr: 13, fc['H2O2']: 11, fc['O2']: 43, fc['H2O']: 45}
    params.update(extra_pars or {})
    res = odesys.integrate(tout, c0, params)
    from chempy.kinetics.integrated import binary_irrev_cstr

    def get_analytic(result, k, n):
        ref = binary_irrev_cstr(result.xout, 5, result.named_dep('H2O2')[0],
            result.named_dep(k)[0], result.named_param(fc['H2O2']), result.
            named_param(fc[k]), result.named_param(fr), n)
        return np.array(ref).T
    ref_O2 = get_analytic(res, 'O2', 1)
    ref_H2O = get_analytic(res, 'H2O', 2)
    assert np.allclose(res.named_dep('H2O2'), ref_O2[:, 0])
    assert np.allclose(res.named_dep('H2O2'), ref_H2O[:, 0])
    assert np.allclose(res.named_dep('O2'), ref_O2[:, 1])
    assert np.allclose(res.named_dep('H2O'), ref_H2O[:, 1])


<mask token>


@requires('pyodesys', 'scipy', 'sym')
def test_create_odesys__cstr():
    rsys = ReactionSystem.from_string("2 H2O2 -> O2 + 2 H2O; 'k2'")
    fr, fc = 'feedratio', OrderedDict([(sk, 'fc_%s' % sk) for sk in rsys.
        substances])
    odesys, extra = create_odesys(rsys, rates_kw=dict(cstr_fr_fc=(fr, fc)))
    _check_cstr(odesys, fr, fc, extra_pars=dict(k2=5))


<mask token>


@requires('pyodeint', 'sym', units_library)
def test_get_odesys_rsys_with_units__named_params():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 'k1'
    B + C -> P; 'k2'
    """,
        substance_factory=Substance)
    odesys, extra = get_odesys(rsys, include_params=False, unit_registry=
        SI_base_registry)
    tend = 10
    tend_units = tend * u.s
    c0 = {'A': 1e-06, 'B': 0, 'C': 1, 'P': 0}
    p = {'k1': 3, 'k2': 4}
    p_units = {'k1': 3 / u.s, 'k2': 4 / u.M / u.s}
    c0_units = {k: (v * u.molar) for k, v in c0.items()}
    result1 = odesys.integrate(tend_units, c0_units, p_units, integrator=
        'odeint')
    assert result1.info['success']
    with pytest.raises(Exception):
        odesys.integrate(tend, c0, p, integrator='odeint')


<mask token>


@requires('pycvodes', 'sym', units_library)
def test_get_odesys__Eyring_2nd_order():
    R = 8.314472
    T_K = 300
    dH = 80000.0
    dS = 10
    rsys1b = ReactionSystem.from_string(
        """
    NO + Br -> NOBr; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """
        .format(dH=dH, dS=dS))
    c0 = 1
    kbref = 20836643994.118652 * T_K * np.exp(-(dH - T_K * dS) / (R * T_K)
        ) / c0
    NO0_M = 1.5
    Br0_M = 0.7
    init_cond = dict(NOBr=0 * u.M, NO=NO0_M * u.M, Br=Br0_M * u.M)
    t = 5 * u.second
    params = dict(temperature=T_K * u.K)

    def analytic_b(t):
        U, V = NO0_M, Br0_M
        d = U - V
        return U * (1 - np.exp(-kbref * t * d)) / (U / V - np.exp(-kbref *
            t * d))

    def check(rsys):
        odesys, extra = get_odesys(rsys, unit_registry=SI_base_registry,
            constants=const)
        res = odesys.integrate(t, init_cond, params, integrator='cvode')
        t_sec = to_unitless(res.xout, u.second)
        NOBr_ref = analytic_b(t_sec)
        cmp = to_unitless(res.yout, u.M)
        ref = np.empty_like(cmp)
        ref[:, odesys.names.index('NOBr')] = NOBr_ref
        ref[:, odesys.names.index('Br')] = Br0_M - NOBr_ref
        ref[:, odesys.names.index('NO')] = NO0_M - NOBr_ref
        assert np.allclose(cmp, ref)
    check(rsys1b)
    rsys2b = ReactionSystem.from_string(
        """
    NO + Br -> NOBr; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """
        .format(dH=dH, dS=dS))
    check(rsys2b)


@requires('pycvodes', 'sym', 'scipy', units_library)
def test_get_odesys__Eyring_1st_order_linearly_ramped_temperature():
    from scipy.special import expi

    def analytic_unit0(t, T0, dH, dS):
        R = 8.314472
        kB = 1.3806504e-23
        h = 6.62606896e-34
        A = kB / h * np.exp(dS / R)
        B = dH / R
        return np.exp(A * ((-B ** 2 * np.exp(B / T0) * expi(-B / T0) - T0 *
            (B - T0)) * np.exp(-B / T0) + (B ** 2 * np.exp(B / (t + T0)) *
            expi(-B / (t + T0)) - (t + T0) * (-B + t + T0)) * np.exp(-B / (
            t + T0))) / 2)
    T_K = 290
    dH = 80000.0
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """
        .format(dH=dH, dS=dS))
    NOBr0_M = 0.7
    init_cond = dict(NOBr=NOBr0_M * u.M, NO=0 * u.M, Br=0 * u.M)
    t = 20 * u.second

    def check(rsys):
        odes, extra = get_odesys(rsys, unit_registry=SI_base_registry,
            constants=const, substitutions={'temperature': RampedTemp([T_K *
            u.K, 1 * u.K / u.s])})
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, integrator='cvode')
            t_sec = to_unitless(res.xout, u.second)
            NOBr_ref = NOBr0_M * analytic_unit0(t_sec, T_K, dH, dS)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index('NOBr')] = NOBr_ref
            ref[:, odesys.names.index('Br')] = NOBr0_M - NOBr_ref
            ref[:, odesys.names.index('NO')] = NOBr0_M - NOBr_ref
            assert np.allclose(cmp, ref)
    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """
        .format(dH=dH, dS=dS))
    check(rsys2)


<mask token>


@requires('pycvodes', 'sym', units_library)
def test_create_odesys__Radiolytic():
    rsys1 = ReactionSystem.from_string(
        """
    -> e-(aq); Radiolytic.fk('g_emaq')
    """, checks=())
    ic1 = {'e-(aq)': 0.0}
    t1 = 5
    p1 = dict(g_emaq=42.0, doserate=17.0, density=5.0)
    odesys1, odesys_extra = create_odesys(rsys1)
    result1 = odesys1.integrate(t1, ic1, p1)
    yref1 = result1.xout * p1['g_emaq'] * p1['doserate'] * p1['density']
    assert np.allclose(yref1, result1.yout.squeeze())


@requires('pycvodes', 'sym', units_library)
def test_create_odesys__validate__catalyst():
    rsys1 = ReactionSystem.from_string(
        """
    H2O2 + Pt -> 2 OH + Pt; 'k_decomp'
    """)
    ic1 = defaultdict(lambda : 0 * u.molar, {'H2O2': 3.0 * u.molar, 'Pt': 
        0.5 * u.molar})
    t1 = linspace(0 * u.s, 0.3 * u.s, 7)
    p1 = dict(k_decomp=42 / u.second / u.molar)
    odesys1, odesys_extra = create_odesys(rsys1)
    validation = odesys_extra['validate'](dict(ic1, **p1))
    assert validation['not_seen'] == {'OH'}
    dedim_ctx = _mk_dedim(SI_base_registry)
    (t, c, _p), dedim_extra = dedim_ctx['dedim_tcp'](t1, [ic1[k] for k in
        odesys1.names], p1)
    result1 = odesys1.integrate(t, c, _p)
    tout = result1.xout * dedim_extra['unit_time']
    cout = result1.yout * dedim_extra['unit_conc']
    yref1 = ic1['H2O2'] * np.exp(-tout * ic1['Pt'] * p1['k_decomp'])
    assert allclose(yref1, cout[:, odesys1.names.index('H2O2')], rtol=1e-06)


@requires('pyodesys', units_library)
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
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)
    odesys.integrate(t, c, _p)

<mask token>


@requires('numpy', 'pyodesys')
def test_get_odesys_1():
    k = 0.2
    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)


@requires('numpy', 'pyodesys', 'sympy')
def test_get_odesys__rate_exprs_cb():
    k = 0.2
    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])


@requires('numpy', 'pyodesys')
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)


@requires(units_library, 'pyodesys')
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-05 / s)
    recombination = Reaction({'H+': 1, 'OH-': 1}, {'H2O': 1}, 
        137000000000.0 / 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-07 * M, 'OH-': 0.0001 * 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-05 * M / s, conc_unit / time_unit)
    r2 = to_unitless(1e-14 * 137000000000.0 * 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


@requires(units_library, 'pyodesys')
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=0.001 / 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': 0.2 * 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-06, 13.0)
    yref = np.zeros((xout.size, 2))
    yref[:, 0] = Aref
    yref[:, 1] = 200 + (13 - Aref) / 2
    assert allclose(yout, yref * conc_unit)


@requires('numpy', 'pyodesys')
def test_SpecialFraction():
    k, kprime = 3.142, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)
    odesys = get_odesys(rsys, include_params=True)[0]
    c0 = {'H2': 13, 'Br2': 17, 'HBr': 19}
    r = k * c0['H2'] * c0['Br2'] ** (3 / 2) / (c0['Br2'] + kprime * c0['HBr'])
    ref = rsys.as_per_substance_array({'H2': -r, 'Br2': -r, 'HBr': 2 * r})
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0))
    assert np.allclose(res, ref)


@requires(units_library, 'pyodesys')
def test_SpecialFraction_with_units():
    k, kprime = 3.142 * u.s ** -1 * u.molar ** -0.5, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)
    odesys = get_odesys(rsys, include_params=True, unit_registry=
        SI_base_registry)[0]
    c0 = {'H2': 13 * u.molar, 'Br2': 16 * u.molar, 'HBr': 19 * u.molar}
    r = k * c0['H2'] * c0['Br2'] ** (3 / 2) / (c0['Br2'] + kprime * c0['HBr'])
    conc_unit = u.mol / u.metre ** 3
    rate_unit = conc_unit / u.second
    ref = rsys.as_per_substance_array({'H2': -r, 'Br2': -r, 'HBr': 2 * r},
        unit=rate_unit)
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0, unit=conc_unit))
    assert allclose(to_unitless(ref, rate_unit), res)


<mask token>


@requires('pyodesys')
def test_get_ode__ArrheniusParam():
    rxn = Reaction({'A': 1}, {'B': 1}, None)
    rxn.param = ArrheniusParam(10000000000.0, 40000.0)
    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 * 10000000000.0 * np.exp(-40000.0 / 8.314472 / 200)
    assert np.all(abs((fout[:, 0] + ref) / ref) < 1e-14)
    assert np.all(abs((fout[:, 1] - ref) / ref) < 1e-14)


@requires('pyodesys')
def test_get_ode__Radiolytic():
    rad = Radiolytic([2.4e-07])
    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-07 * 0.4 * 0.998
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)


<mask token>


class Density(Expr):
    """Arguments: rho0 drhodT T0"""
    parameter_keys = 'temperature',
    kw = {}

    def __call__(self, variables, backend=None):
        rho0, drhodT, T0 = self.all_args(variables)
        return rho0 + drhodT * (variables['temperature'] - T0)


@requires('pyodesys')
def test_get_ode__Radiolytic__substitutions():
    rad = Radiolytic([2.4e-07])
    rxn = Reaction({'A': 4, 'B': 1}, {'C': 3, 'D': 2}, rad)
    rsys = ReactionSystem([rxn], 'A B C D')
    substance_rho = Density([1, -0.001, 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-07 * 0.4 * substance_rho({'temperature': 298.15})
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)


<mask token>


@requires('numpy', 'pyodesys')
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)
    uk_kinet = 'Ha_assoc', 'Sa_assoc'
    bimol_barrier = EyringMA(unique_keys=uk_kinet)
    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)


@requires('numpy', 'pyodesys')
def test_get_odesys__ScaledSys():
    from pyodesys.symbolic import ScaledSys
    k = 0.2
    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, SymbolicSys=ScaledSys)[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)


<mask token>


@requires('numpy', 'pyodesys', 'sympy')
@pytest.mark.parametrize('substances', permutations(['H2O', 'H+', 'OH-']))
def test_get_odesys__linear_dependencies__preferred(substances):
    rsys = ReactionSystem.from_string('\n'.join(['H2O -> H+ + OH-; 1e-4',
        'OH- + H+ -> H2O; 1e10']), substances)
    assert isinstance(rsys.substances, OrderedDict)
    odesys, extra = get_odesys(rsys)
    af_H2O_H = extra['linear_dependencies'](['H+', 'H2O'])
    import sympy
    y0 = {k: sympy.Symbol(k + '0') for k in rsys.substances}
    af_H2O_H(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    exprs_H2O_H = af_H2O_H(None, {odesys[k]: v for k, v in y0.items()},
        None, sympy)
    ref_H2O_H = {'H2O': y0['H2O'] + y0['OH-'] - odesys['OH-'], 'H+': 2 * y0
        ['H2O'] + y0['H+'] + y0['OH-'] - odesys['OH-'] - 2 * (y0['H2O'] +
        y0['OH-'] - odesys['OH-'])}
    for k, v in ref_H2O_H.items():
        assert exprs_H2O_H[odesys[k]] - v == 0


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
@pytest.mark.parametrize('preferred', [None, ['H+', 'OH-'], ['H2O', 'H+'],
    ['H2O', 'OH-']])
def test_get_odesys__linear_dependencies__PartiallySolvedSystem(preferred):
    import sympy
    from pyodesys.symbolic import PartiallySolvedSystem
    rsys = ReactionSystem.from_string('\n'.join(['H2O -> H+ + OH-; 1e-4',
        'OH- + H+ -> H2O; 1e10']))
    odesys, extra = get_odesys(rsys)
    c0 = {'H2O': 0, 'H+': 2e-07, 'OH-': 3e-07}
    h0max = extra['max_euler_step_cb'](0, c0)
    analytic_factory = extra['linear_dependencies']()
    y0 = {k: sympy.Symbol(k + '0') for k in rsys.substances}
    analytic_factory(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    psys = PartiallySolvedSystem(odesys, analytic_factory)
    xout, yout, info = psys.integrate(1, c0, atol=1e-12, rtol=1e-10,
        first_step=h0max * 1e-12, integrator='cvode')
    c_reac = c0['H+'], c0['OH-']
    H2O_ref = binary_rev(xout, 10000000000.0, 0.0001, c0['H2O'], max(c_reac
        ), min(c_reac))
    assert np.allclose(yout[:, psys.names.index('H2O')], H2O_ref)
    assert np.allclose(yout[:, psys.names.index('H+')], c0['H+'] + c0['H2O'
        ] - H2O_ref)
    assert np.allclose(yout[:, psys.names.index('OH-')], c0['OH-'] + c0[
        'H2O'] - H2O_ref)


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
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)


<mask token>


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
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 = 20800000000.0
    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': 107000.0, 'S_u':
        150, 'temperature': rt}, integrator='cvode', atol=1e-12, rtol=1e-10,
        nsteps=1000)
    kref2 = kb_h * rt * np.exp(-(107000.0 - 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)


@requires('pyodesys', 'pycvodes')
def test_chained_parameter_variation():
    ratex = MassAction(Arrhenius([10000000000.0, 63000.0 / 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 = 10000000000.0 * np.exp(-63000.0 / 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 _check_cstr(odesys, fr, fc, extra_pars=None):
    tout, c0 = np.linspace(0, 0.13, 7), {'H2O2': 2, 'O2': 4, 'H2O': 3}
    params = {fr: 13, fc['H2O2']: 11, fc['O2']: 43, fc['H2O']: 45}
    params.update(extra_pars or {})
    res = odesys.integrate(tout, c0, params)
    from chempy.kinetics.integrated import binary_irrev_cstr

    def get_analytic(result, k, n):
        ref = binary_irrev_cstr(result.xout, 5, result.named_dep('H2O2')[0],
            result.named_dep(k)[0], result.named_param(fc['H2O2']), result.
            named_param(fc[k]), result.named_param(fr), n)
        return np.array(ref).T
    ref_O2 = get_analytic(res, 'O2', 1)
    ref_H2O = get_analytic(res, 'H2O', 2)
    assert np.allclose(res.named_dep('H2O2'), ref_O2[:, 0])
    assert np.allclose(res.named_dep('H2O2'), ref_H2O[:, 0])
    assert np.allclose(res.named_dep('O2'), ref_O2[:, 1])
    assert np.allclose(res.named_dep('H2O'), ref_H2O[:, 1])


<mask token>


@requires('pyodesys', 'scipy', 'sym')
def test_create_odesys__cstr():
    rsys = ReactionSystem.from_string("2 H2O2 -> O2 + 2 H2O; 'k2'")
    fr, fc = 'feedratio', OrderedDict([(sk, 'fc_%s' % sk) for sk in rsys.
        substances])
    odesys, extra = create_odesys(rsys, rates_kw=dict(cstr_fr_fc=(fr, fc)))
    _check_cstr(odesys, fr, fc, extra_pars=dict(k2=5))


<mask token>


@requires('pyodeint', 'sym', units_library)
def test_get_odesys_rsys_with_units__named_params():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 'k1'
    B + C -> P; 'k2'
    """,
        substance_factory=Substance)
    odesys, extra = get_odesys(rsys, include_params=False, unit_registry=
        SI_base_registry)
    tend = 10
    tend_units = tend * u.s
    c0 = {'A': 1e-06, 'B': 0, 'C': 1, 'P': 0}
    p = {'k1': 3, 'k2': 4}
    p_units = {'k1': 3 / u.s, 'k2': 4 / u.M / u.s}
    c0_units = {k: (v * u.molar) for k, v in c0.items()}
    result1 = odesys.integrate(tend_units, c0_units, p_units, integrator=
        'odeint')
    assert result1.info['success']
    with pytest.raises(Exception):
        odesys.integrate(tend, c0, p, integrator='odeint')


<mask token>


@requires('pycvodes', 'sym', units_library)
def test_get_odesys__Eyring_2nd_order():
    R = 8.314472
    T_K = 300
    dH = 80000.0
    dS = 10
    rsys1b = ReactionSystem.from_string(
        """
    NO + Br -> NOBr; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """
        .format(dH=dH, dS=dS))
    c0 = 1
    kbref = 20836643994.118652 * T_K * np.exp(-(dH - T_K * dS) / (R * T_K)
        ) / c0
    NO0_M = 1.5
    Br0_M = 0.7
    init_cond = dict(NOBr=0 * u.M, NO=NO0_M * u.M, Br=Br0_M * u.M)
    t = 5 * u.second
    params = dict(temperature=T_K * u.K)

    def analytic_b(t):
        U, V = NO0_M, Br0_M
        d = U - V
        return U * (1 - np.exp(-kbref * t * d)) / (U / V - np.exp(-kbref *
            t * d))

    def check(rsys):
        odesys, extra = get_odesys(rsys, unit_registry=SI_base_registry,
            constants=const)
        res = odesys.integrate(t, init_cond, params, integrator='cvode')
        t_sec = to_unitless(res.xout, u.second)
        NOBr_ref = analytic_b(t_sec)
        cmp = to_unitless(res.yout, u.M)
        ref = np.empty_like(cmp)
        ref[:, odesys.names.index('NOBr')] = NOBr_ref
        ref[:, odesys.names.index('Br')] = Br0_M - NOBr_ref
        ref[:, odesys.names.index('NO')] = NO0_M - NOBr_ref
        assert np.allclose(cmp, ref)
    check(rsys1b)
    rsys2b = ReactionSystem.from_string(
        """
    NO + Br -> NOBr; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """
        .format(dH=dH, dS=dS))
    check(rsys2b)


@requires('pycvodes', 'sym', 'scipy', units_library)
def test_get_odesys__Eyring_1st_order_linearly_ramped_temperature():
    from scipy.special import expi

    def analytic_unit0(t, T0, dH, dS):
        R = 8.314472
        kB = 1.3806504e-23
        h = 6.62606896e-34
        A = kB / h * np.exp(dS / R)
        B = dH / R
        return np.exp(A * ((-B ** 2 * np.exp(B / T0) * expi(-B / T0) - T0 *
            (B - T0)) * np.exp(-B / T0) + (B ** 2 * np.exp(B / (t + T0)) *
            expi(-B / (t + T0)) - (t + T0) * (-B + t + T0)) * np.exp(-B / (
            t + T0))) / 2)
    T_K = 290
    dH = 80000.0
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """
        .format(dH=dH, dS=dS))
    NOBr0_M = 0.7
    init_cond = dict(NOBr=NOBr0_M * u.M, NO=0 * u.M, Br=0 * u.M)
    t = 20 * u.second

    def check(rsys):
        odes, extra = get_odesys(rsys, unit_registry=SI_base_registry,
            constants=const, substitutions={'temperature': RampedTemp([T_K *
            u.K, 1 * u.K / u.s])})
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, integrator='cvode')
            t_sec = to_unitless(res.xout, u.second)
            NOBr_ref = NOBr0_M * analytic_unit0(t_sec, T_K, dH, dS)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index('NOBr')] = NOBr_ref
            ref[:, odesys.names.index('Br')] = NOBr0_M - NOBr_ref
            ref[:, odesys.names.index('NO')] = NOBr0_M - NOBr_ref
            assert np.allclose(cmp, ref)
    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """
        .format(dH=dH, dS=dS))
    check(rsys2)


<mask token>


@requires('pycvodes', 'sym', units_library)
def test_create_odesys__Radiolytic():
    rsys1 = ReactionSystem.from_string(
        """
    -> e-(aq); Radiolytic.fk('g_emaq')
    """, checks=())
    ic1 = {'e-(aq)': 0.0}
    t1 = 5
    p1 = dict(g_emaq=42.0, doserate=17.0, density=5.0)
    odesys1, odesys_extra = create_odesys(rsys1)
    result1 = odesys1.integrate(t1, ic1, p1)
    yref1 = result1.xout * p1['g_emaq'] * p1['doserate'] * p1['density']
    assert np.allclose(yref1, result1.yout.squeeze())


@requires('pycvodes', 'sym', units_library)
def test_create_odesys__validate__catalyst():
    rsys1 = ReactionSystem.from_string(
        """
    H2O2 + Pt -> 2 OH + Pt; 'k_decomp'
    """)
    ic1 = defaultdict(lambda : 0 * u.molar, {'H2O2': 3.0 * u.molar, 'Pt': 
        0.5 * u.molar})
    t1 = linspace(0 * u.s, 0.3 * u.s, 7)
    p1 = dict(k_decomp=42 / u.second / u.molar)
    odesys1, odesys_extra = create_odesys(rsys1)
    validation = odesys_extra['validate'](dict(ic1, **p1))
    assert validation['not_seen'] == {'OH'}
    dedim_ctx = _mk_dedim(SI_base_registry)
    (t, c, _p), dedim_extra = dedim_ctx['dedim_tcp'](t1, [ic1[k] for k in
        odesys1.names], p1)
    result1 = odesys1.integrate(t, c, _p)
    tout = result1.xout * dedim_extra['unit_time']
    cout = result1.yout * dedim_extra['unit_conc']
    yref1 = ic1['H2O2'] * np.exp(-tout * ic1['Pt'] * p1['k_decomp'])
    assert allclose(yref1, cout[:, odesys1.names.index('H2O2')], rtol=1e-06)


@requires('pyodesys', units_library)
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
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)
    odesys.integrate(t, c, _p)

<mask token>


@requires('numpy', 'pyodesys')
def test_get_odesys_1():
    k = 0.2
    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)


@requires('numpy', 'pyodesys', 'sympy')
def test_get_odesys__rate_exprs_cb():
    k = 0.2
    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])


@requires('numpy', 'pyodesys')
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)


@requires(units_library, 'pyodesys')
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-05 / s)
    recombination = Reaction({'H+': 1, 'OH-': 1}, {'H2O': 1}, 
        137000000000.0 / 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-07 * M, 'OH-': 0.0001 * 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-05 * M / s, conc_unit / time_unit)
    r2 = to_unitless(1e-14 * 137000000000.0 * 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


@requires(units_library, 'pyodesys')
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=0.001 / 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': 0.2 * 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-06, 13.0)
    yref = np.zeros((xout.size, 2))
    yref[:, 0] = Aref
    yref[:, 1] = 200 + (13 - Aref) / 2
    assert allclose(yout, yref * conc_unit)


@requires('numpy', 'pyodesys')
def test_SpecialFraction():
    k, kprime = 3.142, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)
    odesys = get_odesys(rsys, include_params=True)[0]
    c0 = {'H2': 13, 'Br2': 17, 'HBr': 19}
    r = k * c0['H2'] * c0['Br2'] ** (3 / 2) / (c0['Br2'] + kprime * c0['HBr'])
    ref = rsys.as_per_substance_array({'H2': -r, 'Br2': -r, 'HBr': 2 * r})
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0))
    assert np.allclose(res, ref)


@requires(units_library, 'pyodesys')
def test_SpecialFraction_with_units():
    k, kprime = 3.142 * u.s ** -1 * u.molar ** -0.5, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)
    odesys = get_odesys(rsys, include_params=True, unit_registry=
        SI_base_registry)[0]
    c0 = {'H2': 13 * u.molar, 'Br2': 16 * u.molar, 'HBr': 19 * u.molar}
    r = k * c0['H2'] * c0['Br2'] ** (3 / 2) / (c0['Br2'] + kprime * c0['HBr'])
    conc_unit = u.mol / u.metre ** 3
    rate_unit = conc_unit / u.second
    ref = rsys.as_per_substance_array({'H2': -r, 'Br2': -r, 'HBr': 2 * r},
        unit=rate_unit)
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0, unit=conc_unit))
    assert allclose(to_unitless(ref, rate_unit), res)


@requires('pyodesys')
def test_ode_with_global_parameters():
    ratex = MassAction(Arrhenius([10000000000.0, 40000.0 / 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 * 10000000000.0 * np.exp(-40000.0 / 8.3145 / 298.15)
    assert np.all(abs((fout[:, 0] + ref) / ref) < 1e-14)
    assert np.all(abs((fout[:, 1] - ref) / ref) < 1e-14)


@requires('pyodesys')
def test_get_ode__ArrheniusParam():
    rxn = Reaction({'A': 1}, {'B': 1}, None)
    rxn.param = ArrheniusParam(10000000000.0, 40000.0)
    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 * 10000000000.0 * np.exp(-40000.0 / 8.314472 / 200)
    assert np.all(abs((fout[:, 0] + ref) / ref) < 1e-14)
    assert np.all(abs((fout[:, 1] - ref) / ref) < 1e-14)


@requires('pyodesys')
def test_get_ode__Radiolytic():
    rad = Radiolytic([2.4e-07])
    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-07 * 0.4 * 0.998
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)


<mask token>


class Density(Expr):
    """Arguments: rho0 drhodT T0"""
    parameter_keys = 'temperature',
    kw = {}

    def __call__(self, variables, backend=None):
        rho0, drhodT, T0 = self.all_args(variables)
        return rho0 + drhodT * (variables['temperature'] - T0)


@requires('pyodesys')
def test_get_ode__Radiolytic__substitutions():
    rad = Radiolytic([2.4e-07])
    rxn = Reaction({'A': 4, 'B': 1}, {'C': 3, 'D': 2}, rad)
    rsys = ReactionSystem([rxn], 'A B C D')
    substance_rho = Density([1, -0.001, 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-07 * 0.4 * substance_rho({'temperature': 298.15})
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)


@requires('pyodesys', units_library)
def test_get_ode__Radiolytic__substitutions__units():
    rad = Radiolytic([2.4e-07 * 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-07 * 0.4 * 0.975 * 1000.0
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)


<mask token>


@requires('pyodesys', units_library)
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)


@requires('pyodesys', units_library)
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, 10000000000.0, 56000.0 / 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])
        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
    ref = np.array([[-r(2), -r(5), -r(10)], [3 * r(2), 3 * r(5), 3 * r(10)]]).T
    assert np.allclose(fout, ref)


@requires('numpy', 'pyodesys')
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)
    uk_kinet = 'Ha_assoc', 'Sa_assoc'
    bimol_barrier = EyringMA(unique_keys=uk_kinet)
    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)


@requires('numpy', 'pyodesys')
def test_get_odesys__ScaledSys():
    from pyodesys.symbolic import ScaledSys
    k = 0.2
    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, SymbolicSys=ScaledSys)[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)


@requires('numpy', 'pyodesys', 'sympy')
def test_get_odesys__max_euler_step_cb():
    rsys = ReactionSystem.from_string('\n'.join(['H2O -> H+ + OH-; 1e-4',
        'OH- + H+ -> H2O; 1e10']))
    odesys, extra = get_odesys(rsys)
    r1 = 0.000101
    r2 = 0.0006
    dH2Odt = r2 - r1
    euler_ref = 2e-07 / dH2Odt
    assert abs(extra['max_euler_step_cb'](0, {'H2O': 1.01, 'H+': 2e-07,
        'OH-': 3e-07}) - euler_ref) / euler_ref < 1e-08


@requires('numpy', 'pyodesys', 'sympy')
@pytest.mark.parametrize('substances', permutations(['H2O', 'H+', 'OH-']))
def test_get_odesys__linear_dependencies__preferred(substances):
    rsys = ReactionSystem.from_string('\n'.join(['H2O -> H+ + OH-; 1e-4',
        'OH- + H+ -> H2O; 1e10']), substances)
    assert isinstance(rsys.substances, OrderedDict)
    odesys, extra = get_odesys(rsys)
    af_H2O_H = extra['linear_dependencies'](['H+', 'H2O'])
    import sympy
    y0 = {k: sympy.Symbol(k + '0') for k in rsys.substances}
    af_H2O_H(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    exprs_H2O_H = af_H2O_H(None, {odesys[k]: v for k, v in y0.items()},
        None, sympy)
    ref_H2O_H = {'H2O': y0['H2O'] + y0['OH-'] - odesys['OH-'], 'H+': 2 * y0
        ['H2O'] + y0['H+'] + y0['OH-'] - odesys['OH-'] - 2 * (y0['H2O'] +
        y0['OH-'] - odesys['OH-'])}
    for k, v in ref_H2O_H.items():
        assert exprs_H2O_H[odesys[k]] - v == 0


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
@pytest.mark.parametrize('preferred', [None, ['H+', 'OH-'], ['H2O', 'H+'],
    ['H2O', 'OH-']])
def test_get_odesys__linear_dependencies__PartiallySolvedSystem(preferred):
    import sympy
    from pyodesys.symbolic import PartiallySolvedSystem
    rsys = ReactionSystem.from_string('\n'.join(['H2O -> H+ + OH-; 1e-4',
        'OH- + H+ -> H2O; 1e10']))
    odesys, extra = get_odesys(rsys)
    c0 = {'H2O': 0, 'H+': 2e-07, 'OH-': 3e-07}
    h0max = extra['max_euler_step_cb'](0, c0)
    analytic_factory = extra['linear_dependencies']()
    y0 = {k: sympy.Symbol(k + '0') for k in rsys.substances}
    analytic_factory(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    psys = PartiallySolvedSystem(odesys, analytic_factory)
    xout, yout, info = psys.integrate(1, c0, atol=1e-12, rtol=1e-10,
        first_step=h0max * 1e-12, integrator='cvode')
    c_reac = c0['H+'], c0['OH-']
    H2O_ref = binary_rev(xout, 10000000000.0, 0.0001, c0['H2O'], max(c_reac
        ), min(c_reac))
    assert np.allclose(yout[:, psys.names.index('H2O')], H2O_ref)
    assert np.allclose(yout[:, psys.names.index('H+')], c0['H+'] + c0['H2O'
        ] - H2O_ref)
    assert np.allclose(yout[:, psys.names.index('OH-')], c0['OH-'] + c0[
        'H2O'] - H2O_ref)


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
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)


<mask token>


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
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 = 20800000000.0
    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': 107000.0, 'S_u':
        150, 'temperature': rt}, integrator='cvode', atol=1e-12, rtol=1e-10,
        nsteps=1000)
    kref2 = kb_h * rt * np.exp(-(107000.0 - 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)


@requires('pyodesys', 'pycvodes')
def test_chained_parameter_variation():
    ratex = MassAction(Arrhenius([10000000000.0, 63000.0 / 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 = 10000000000.0 * np.exp(-63000.0 / 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 _check_cstr(odesys, fr, fc, extra_pars=None):
    tout, c0 = np.linspace(0, 0.13, 7), {'H2O2': 2, 'O2': 4, 'H2O': 3}
    params = {fr: 13, fc['H2O2']: 11, fc['O2']: 43, fc['H2O']: 45}
    params.update(extra_pars or {})
    res = odesys.integrate(tout, c0, params)
    from chempy.kinetics.integrated import binary_irrev_cstr

    def get_analytic(result, k, n):
        ref = binary_irrev_cstr(result.xout, 5, result.named_dep('H2O2')[0],
            result.named_dep(k)[0], result.named_param(fc['H2O2']), result.
            named_param(fc[k]), result.named_param(fr), n)
        return np.array(ref).T
    ref_O2 = get_analytic(res, 'O2', 1)
    ref_H2O = get_analytic(res, 'H2O', 2)
    assert np.allclose(res.named_dep('H2O2'), ref_O2[:, 0])
    assert np.allclose(res.named_dep('H2O2'), ref_H2O[:, 0])
    assert np.allclose(res.named_dep('O2'), ref_O2[:, 1])
    assert np.allclose(res.named_dep('H2O'), ref_H2O[:, 1])


@requires('pyodesys', 'scipy', 'sym')
def test_get_odesys__cstr():
    rsys = ReactionSystem.from_string('2 H2O2 -> O2 + 2 H2O; 5')
    odesys, extra = get_odesys(rsys, cstr=True)
    fr, fc = extra['cstr_fr_fc']
    _check_cstr(odesys, fr, fc)


@requires('pyodesys', 'scipy', 'sym')
def test_create_odesys__cstr():
    rsys = ReactionSystem.from_string("2 H2O2 -> O2 + 2 H2O; 'k2'")
    fr, fc = 'feedratio', OrderedDict([(sk, 'fc_%s' % sk) for sk in rsys.
        substances])
    odesys, extra = create_odesys(rsys, rates_kw=dict(cstr_fr_fc=(fr, fc)))
    _check_cstr(odesys, fr, fc, extra_pars=dict(k2=5))


@requires('pygslodeiv2', 'sym', units_library)
def test_get_odesys_rsys_with_units():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 0.096/s
    B + C -> P; 4e3/M/s
    """,
        substance_factory=Substance)
    with pytest.raises(Exception):
        get_odesys(rsys)
    odesys, extra = get_odesys(rsys, unit_registry=SI_base_registry)
    tend = 10
    tend_units = tend * u.s
    c0 = {'A': 1e-06, 'B': 0, 'C': 1, 'P': 0}
    c0_units = {k: (v * u.molar) for k, v in c0.items()}
    result1 = odesys.integrate(tend_units, c0_units, integrator='gsl')
    assert result1.info['success']
    with pytest.raises(Exception):
        odesys.integrate(tend, c0, integrator='gsl')


@requires('pyodeint', 'sym', units_library)
def test_get_odesys_rsys_with_units__named_params():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 'k1'
    B + C -> P; 'k2'
    """,
        substance_factory=Substance)
    odesys, extra = get_odesys(rsys, include_params=False, unit_registry=
        SI_base_registry)
    tend = 10
    tend_units = tend * u.s
    c0 = {'A': 1e-06, 'B': 0, 'C': 1, 'P': 0}
    p = {'k1': 3, 'k2': 4}
    p_units = {'k1': 3 / u.s, 'k2': 4 / u.M / u.s}
    c0_units = {k: (v * u.molar) for k, v in c0.items()}
    result1 = odesys.integrate(tend_units, c0_units, p_units, integrator=
        'odeint')
    assert result1.info['success']
    with pytest.raises(Exception):
        odesys.integrate(tend, c0, p, integrator='odeint')


@requires('pycvodes', 'sym', units_library)
def test_get_odesys__Eyring():
    R = 8.314472
    T_K = 300
    dH = 80000.0
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """
        .format(dH=dH, dS=dS), substances='NOBr NO Br'.split())
    kref = 20836643994.118652 * T_K * np.exp(-(dH - T_K * dS) / (R * T_K))
    NOBr0_M = 0.7
    init_cond = dict(NOBr=NOBr0_M * u.M, NO=0 * u.M, Br=0 * u.M)
    t = 5 * u.second
    params = dict(temperature=T_K * u.K)

    def check(rsys):
        odesys, extra = get_odesys(rsys, unit_registry=SI_base_registry,
            constants=const)
        res = odesys.integrate(t, init_cond, params, integrator='cvode')
        NOBr_ref = NOBr0_M * np.exp(-kref * to_unitless(res.xout, u.second))
        ref = np.array([NOBr_ref] + [NOBr0_M - NOBr_ref] * 2).T
        cmp = to_unitless(res.yout, u.M)
        assert np.allclose(cmp, ref)
    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """
        .format(dH=dH, dS=dS), substances='NOBr NO Br'.split())
    check(rsys2)


@requires('pycvodes', 'sym', units_library)
def test_get_odesys__Eyring_2nd_order():
    R = 8.314472
    T_K = 300
    dH = 80000.0
    dS = 10
    rsys1b = ReactionSystem.from_string(
        """
    NO + Br -> NOBr; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """
        .format(dH=dH, dS=dS))
    c0 = 1
    kbref = 20836643994.118652 * T_K * np.exp(-(dH - T_K * dS) / (R * T_K)
        ) / c0
    NO0_M = 1.5
    Br0_M = 0.7
    init_cond = dict(NOBr=0 * u.M, NO=NO0_M * u.M, Br=Br0_M * u.M)
    t = 5 * u.second
    params = dict(temperature=T_K * u.K)

    def analytic_b(t):
        U, V = NO0_M, Br0_M
        d = U - V
        return U * (1 - np.exp(-kbref * t * d)) / (U / V - np.exp(-kbref *
            t * d))

    def check(rsys):
        odesys, extra = get_odesys(rsys, unit_registry=SI_base_registry,
            constants=const)
        res = odesys.integrate(t, init_cond, params, integrator='cvode')
        t_sec = to_unitless(res.xout, u.second)
        NOBr_ref = analytic_b(t_sec)
        cmp = to_unitless(res.yout, u.M)
        ref = np.empty_like(cmp)
        ref[:, odesys.names.index('NOBr')] = NOBr_ref
        ref[:, odesys.names.index('Br')] = Br0_M - NOBr_ref
        ref[:, odesys.names.index('NO')] = NO0_M - NOBr_ref
        assert np.allclose(cmp, ref)
    check(rsys1b)
    rsys2b = ReactionSystem.from_string(
        """
    NO + Br -> NOBr; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """
        .format(dH=dH, dS=dS))
    check(rsys2b)


@requires('pycvodes', 'sym', 'scipy', units_library)
def test_get_odesys__Eyring_1st_order_linearly_ramped_temperature():
    from scipy.special import expi

    def analytic_unit0(t, T0, dH, dS):
        R = 8.314472
        kB = 1.3806504e-23
        h = 6.62606896e-34
        A = kB / h * np.exp(dS / R)
        B = dH / R
        return np.exp(A * ((-B ** 2 * np.exp(B / T0) * expi(-B / T0) - T0 *
            (B - T0)) * np.exp(-B / T0) + (B ** 2 * np.exp(B / (t + T0)) *
            expi(-B / (t + T0)) - (t + T0) * (-B + t + T0)) * np.exp(-B / (
            t + T0))) / 2)
    T_K = 290
    dH = 80000.0
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """
        .format(dH=dH, dS=dS))
    NOBr0_M = 0.7
    init_cond = dict(NOBr=NOBr0_M * u.M, NO=0 * u.M, Br=0 * u.M)
    t = 20 * u.second

    def check(rsys):
        odes, extra = get_odesys(rsys, unit_registry=SI_base_registry,
            constants=const, substitutions={'temperature': RampedTemp([T_K *
            u.K, 1 * u.K / u.s])})
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, integrator='cvode')
            t_sec = to_unitless(res.xout, u.second)
            NOBr_ref = NOBr0_M * analytic_unit0(t_sec, T_K, dH, dS)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index('NOBr')] = NOBr_ref
            ref[:, odesys.names.index('Br')] = NOBr0_M - NOBr_ref
            ref[:, odesys.names.index('NO')] = NOBr0_M - NOBr_ref
            assert np.allclose(cmp, ref)
    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """
        .format(dH=dH, dS=dS))
    check(rsys2)


@requires('pycvodes', 'sym', 'scipy', units_library)
def test_get_odesys__Eyring_2nd_order_linearly_ramped_temperature():
    from scipy.special import expi

    def analytic_unit0(t, k, m, dH, dS):
        R = 8.314472
        kB = 1.3806504e-23
        h = 6.62606896e-34
        A = kB / h * np.exp(dS / R)
        B = dH / R
        return k * np.exp(B * (k * t + 2 * m) / (m * (k * t + m))) / (A * (
            -B ** 2 * np.exp(B / (k * t + m)) * expi(-B / (k * t + m)) - B *
            k * t - B * m + k ** 2 * t ** 2 + 2 * k * m * t + m ** 2) * np.
            exp(B / m) + (A * B ** 2 * np.exp(B / m) * expi(-B / m) - A * m *
            (-B + m) + k * np.exp(B / m)) * np.exp(B / (k * t + m)))
    T_K = 290
    dTdt_Ks = 3
    dH = 80000.0
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    2 NO2 -> N2O4; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """
        .format(dH=dH, dS=dS))
    NO2_M = 1.0
    init_cond = dict(NO2=NO2_M * u.M, N2O4=0 * u.M)
    t = 20 * u.second

    def check(rsys):
        odes, extra = get_odesys(rsys, unit_registry=SI_base_registry,
            constants=const, substitutions={'temperature': RampedTemp([T_K *
            u.K, dTdt_Ks * u.K / u.s])})
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, integrator='cvode')
            t_sec = to_unitless(res.xout, u.second)
            NO2_ref = analytic_unit0(t_sec, dTdt_Ks, T_K, dH, dS)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index('NO2')] = NO2_ref
            ref[:, odesys.names.index('N2O4')] = (NO2_M - NO2_ref) / 2
            assert np.allclose(cmp, ref)
    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    2 NO2 -> N2O4; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """
        .format(dH=dH, dS=dS))
    check(rsys2)


<mask token>


@requires('numpy', 'pyodesys', 'sympy', 'pycvodes')
def test_create_odesys():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 'k1'
    B + C -> P; 'k2'
    """,
        substance_factory=Substance)
    odesys, odesys_extra = create_odesys(rsys, unit_registry=SI_base_registry)
    tend_ul = 10
    init_conc_ul = {'A': 1e-06, 'B': 0, 'C': 1}
    params_ul = dict(k1=3, k2=4)
    tend = tend_ul * u.s
    params = {'k1': params_ul['k1'] / u.s, 'k2': params_ul['k2'] / u.M / u.s}
    init_conc = {k: (v * u.molar) for k, v in init_conc_ul.items()}
    validation = odesys_extra['validate'](dict(init_conc, **params))
    P, = validation['not_seen']
    assert P == 'P'
    ref_rates = {'A': -params['k1'] * init_conc['A'], 'P': params['k2'] *
        init_conc['B'] * init_conc['C']}
    ref_rates['B'] = -ref_rates['A'] - ref_rates['P']
    ref_rates['C'] = -ref_rates['P']
    assert validation['rates'] == ref_rates
    result1, result1_extra = odesys_extra['unit_aware_solve'](tend,
        defaultdict(lambda : 0 * u.molar, init_conc), params, integrator=
        'cvode')
    assert result1.info['success']
    result2 = odesys.integrate(tend_ul, defaultdict(lambda : 0,
        init_conc_ul), params_ul, integrator='cvode')
    assert np.allclose(result2.yout[-1, :], to_unitless(result1.yout[-1, :],
        u.molar))


@requires('pycvodes', 'sym', units_library)
def test_create_odesys__Radiolytic():
    rsys1 = ReactionSystem.from_string(
        """
    -> e-(aq); Radiolytic.fk('g_emaq')
    """, checks=())
    ic1 = {'e-(aq)': 0.0}
    t1 = 5
    p1 = dict(g_emaq=42.0, doserate=17.0, density=5.0)
    odesys1, odesys_extra = create_odesys(rsys1)
    result1 = odesys1.integrate(t1, ic1, p1)
    yref1 = result1.xout * p1['g_emaq'] * p1['doserate'] * p1['density']
    assert np.allclose(yref1, result1.yout.squeeze())


@requires('pycvodes', 'sym', units_library)
def test_create_odesys__validate__catalyst():
    rsys1 = ReactionSystem.from_string(
        """
    H2O2 + Pt -> 2 OH + Pt; 'k_decomp'
    """)
    ic1 = defaultdict(lambda : 0 * u.molar, {'H2O2': 3.0 * u.molar, 'Pt': 
        0.5 * u.molar})
    t1 = linspace(0 * u.s, 0.3 * u.s, 7)
    p1 = dict(k_decomp=42 / u.second / u.molar)
    odesys1, odesys_extra = create_odesys(rsys1)
    validation = odesys_extra['validate'](dict(ic1, **p1))
    assert validation['not_seen'] == {'OH'}
    dedim_ctx = _mk_dedim(SI_base_registry)
    (t, c, _p), dedim_extra = dedim_ctx['dedim_tcp'](t1, [ic1[k] for k in
        odesys1.names], p1)
    result1 = odesys1.integrate(t, c, _p)
    tout = result1.xout * dedim_extra['unit_time']
    cout = result1.yout * dedim_extra['unit_conc']
    yref1 = ic1['H2O2'] * np.exp(-tout * ic1['Pt'] * p1['k_decomp'])
    assert allclose(yref1, cout[:, odesys1.names.index('H2O2')], rtol=1e-06)


@requires('pyodesys', units_library)
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
    ref = [-4 * r, -r, 3 * r, 2 * r]
    assert np.all(abs((fout - ref) / ref) < 1e-14)
    odesys.integrate(t, c, _p)

# -*- coding: utf-8 -*-

from collections import defaultdict, OrderedDict
from itertools import permutations
import math

import pytest

try:
    import numpy as np
except ImportError:
    np = None


from chempy import Equilibrium, Reaction, ReactionSystem, Substance
from chempy.thermodynamics.expressions import MassActionEq
from chempy.units import (
    SI_base_registry,
    get_derived_unit,
    allclose,
    units_library,
    linspace,
    to_unitless,
    default_constants as const,
    default_units as u,
)
from chempy.util._expr import Expr
from chempy.util.testing import requires
from .test_rates import _get_SpecialFraction_rsys
from ..arrhenius import ArrheniusParam
from ..rates import Arrhenius, MassAction, Radiolytic, RampedTemp
from .._rates import ShiftedTPoly
from ..ode import (
    get_odesys,
    chained_parameter_variation,
    _mk_dedim,
    _create_odesys as create_odesys,
)
from ..integrated import dimerization_irrev, binary_rev


@requires("numpy", "pyodesys")
def test_get_odesys_1():
    k = 0.2
    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)


@requires("numpy", "pyodesys", "sympy")
def test_get_odesys__rate_exprs_cb():
    k = 0.2
    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])


@requires("numpy", "pyodesys")
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)


@requires(units_library, "pyodesys")
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


@requires(units_library, "pyodesys")
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": 0.2 * 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)


@requires("numpy", "pyodesys")
def test_SpecialFraction():
    k, kprime = 3.142, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)

    odesys = get_odesys(rsys, include_params=True)[0]
    c0 = {"H2": 13, "Br2": 17, "HBr": 19}
    r = k * c0["H2"] * c0["Br2"] ** (3 / 2) / (c0["Br2"] + kprime * c0["HBr"])
    ref = rsys.as_per_substance_array({"H2": -r, "Br2": -r, "HBr": 2 * r})
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0))
    assert np.allclose(res, ref)


@requires(units_library, "pyodesys")
def test_SpecialFraction_with_units():
    k, kprime = 3.142 * u.s ** -1 * u.molar ** -0.5, 2.718
    rsys = _get_SpecialFraction_rsys(k, kprime)
    odesys = get_odesys(rsys, include_params=True, unit_registry=SI_base_registry)[0]
    c0 = {"H2": 13 * u.molar, "Br2": 16 * u.molar, "HBr": 19 * u.molar}
    r = k * c0["H2"] * c0["Br2"] ** (3 / 2) / (c0["Br2"] + kprime * c0["HBr"])
    conc_unit = u.mol / u.metre ** 3
    rate_unit = conc_unit / u.second
    ref = rsys.as_per_substance_array(
        {"H2": -r, "Br2": -r, "HBr": 2 * r}, unit=rate_unit
    )
    res = odesys.f_cb(0, rsys.as_per_substance_array(c0, unit=conc_unit))
    assert allclose(to_unitless(ref, rate_unit), res)


@requires("pyodesys")
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)


@requires("pyodesys")
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)


@requires("pyodesys")
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)


@requires("pyodesys", units_library)
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)


@requires("pyodesys", units_library)
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]


class Density(Expr):
    """Arguments: rho0 drhodT T0"""

    parameter_keys = ("temperature",)
    kw = {}

    def __call__(self, variables, backend=None):
        rho0, drhodT, T0 = self.all_args(variables)
        return rho0 + drhodT * (variables["temperature"] - T0)


@requires("pyodesys")
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)


@requires("pyodesys", units_library)
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)


@requires("pyodesys", units_library)
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)


@requires("pyodesys", units_library)
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)


@requires("pyodesys", units_library)
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)


@requires("numpy", "pyodesys")
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)


@requires("numpy", "pyodesys")
def test_get_odesys__ScaledSys():
    from pyodesys.symbolic import ScaledSys

    k = 0.2
    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, SymbolicSys=ScaledSys)[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)


@requires("numpy", "pyodesys", "sympy")
def test_get_odesys__max_euler_step_cb():
    rsys = ReactionSystem.from_string(
        "\n".join(["H2O -> H+ + OH-; 1e-4", "OH- + H+ -> H2O; 1e10"])
    )
    odesys, extra = get_odesys(rsys)
    r1 = 1.01e-4
    r2 = 6e-4
    dH2Odt = r2 - r1
    euler_ref = 2e-7 / dH2Odt
    assert (
        abs(
            extra["max_euler_step_cb"](0, {"H2O": 1.01, "H+": 2e-7, "OH-": 3e-7})
            - euler_ref
        )
        / euler_ref
        < 1e-8
    )


@requires("numpy", "pyodesys", "sympy")
@pytest.mark.parametrize("substances", permutations(["H2O", "H+", "OH-"]))
def test_get_odesys__linear_dependencies__preferred(substances):
    rsys = ReactionSystem.from_string(
        "\n".join(["H2O -> H+ + OH-; 1e-4", "OH- + H+ -> H2O; 1e10"]), substances
    )
    assert isinstance(rsys.substances, OrderedDict)
    odesys, extra = get_odesys(rsys)

    af_H2O_H = extra["linear_dependencies"](["H+", "H2O"])
    import sympy

    y0 = {k: sympy.Symbol(k + "0") for k in rsys.substances}
    af_H2O_H(
        None, {odesys[k]: v for k, v in y0.items()}, None, sympy
    )  # ensure idempotent
    exprs_H2O_H = af_H2O_H(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    ref_H2O_H = {
        "H2O": y0["H2O"] + y0["OH-"] - odesys["OH-"],  # oxygen
        "H+": 2 * y0["H2O"]
        + y0["H+"]
        + y0["OH-"]
        - odesys["OH-"]
        - 2 * (y0["H2O"] + y0["OH-"] - odesys["OH-"]),  # hydrogen
    }
    for k, v in ref_H2O_H.items():
        assert (exprs_H2O_H[odesys[k]] - v) == 0


@requires("numpy", "pyodesys", "sympy", "pycvodes")
@pytest.mark.parametrize(
    "preferred", [None, ["H+", "OH-"], ["H2O", "H+"], ["H2O", "OH-"]]
)
def test_get_odesys__linear_dependencies__PartiallySolvedSystem(preferred):
    import sympy
    from pyodesys.symbolic import PartiallySolvedSystem

    rsys = ReactionSystem.from_string(
        "\n".join(["H2O -> H+ + OH-; 1e-4", "OH- + H+ -> H2O; 1e10"])
    )
    odesys, extra = get_odesys(rsys)
    c0 = {"H2O": 0, "H+": 2e-7, "OH-": 3e-7}
    h0max = extra["max_euler_step_cb"](0, c0)
    analytic_factory = extra["linear_dependencies"]()
    y0 = {k: sympy.Symbol(k + "0") for k in rsys.substances}
    analytic_factory(None, {odesys[k]: v for k, v in y0.items()}, None, sympy)
    psys = PartiallySolvedSystem(odesys, analytic_factory)
    xout, yout, info = psys.integrate(
        1, c0, atol=1e-12, rtol=1e-10, first_step=h0max * 1e-12, integrator="cvode"
    )
    c_reac = c0["H+"], c0["OH-"]
    H2O_ref = binary_rev(xout, 1e10, 1e-4, c0["H2O"], max(c_reac), min(c_reac))
    assert np.allclose(yout[:, psys.names.index("H2O")], H2O_ref)
    assert np.allclose(yout[:, psys.names.index("H+")], c0["H+"] + c0["H2O"] - H2O_ref)
    assert np.allclose(
        yout[:, psys.names.index("OH-")], c0["OH-"] + c0["H2O"] - H2O_ref
    )


@requires("numpy", "pyodesys", "sympy", "pycvodes")
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)


@requires("numpy", "pyodesys", "sympy", "pycvodes")
def test_get_odesys__Expr_as_param():
    def _eyring_pe(args, T, backend=math, **kwargs):
        (freq,) = args
        return freq * T

    EyringPreExp = Expr.from_callback(
        _eyring_pe, argument_names=("freq",), parameter_keys=("temperature",)
    )

    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"])
    odesys, extra = get_odesys(
        rsys, include_params=False, substitutions={"A_u": EyringPreExp(kb_h)}
    )
    y0 = defaultdict(float, {"A": 7.0})
    rt = 293.15
    xout, yout, info = odesys.integrate(
        5,
        y0,
        {"H_u": 117e3, "S_u": 150, "temperature": rt},
        integrator="cvode",
        atol=1e-12,
        rtol=1e-10,
        nsteps=1000,
    )
    kref = kb_h * rt * np.exp(-(117e3 - rt * 150) / (8.314511 * rt))
    ref = y0["A"] * np.exp(-kref * xout)
    assert np.allclose(yout[:, 0], ref)
    assert np.allclose(yout[:, 1], y0["A"] - ref)


@requires("numpy", "pyodesys", "sympy", "pycvodes")
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)


@requires("pyodesys", "pycvodes")
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 _check_cstr(odesys, fr, fc, extra_pars=None):
    tout, c0 = np.linspace(0, 0.13, 7), {"H2O2": 2, "O2": 4, "H2O": 3}
    params = {fr: 13, fc["H2O2"]: 11, fc["O2"]: 43, fc["H2O"]: 45}
    params.update(extra_pars or {})
    res = odesys.integrate(tout, c0, params)
    from chempy.kinetics.integrated import binary_irrev_cstr

    def get_analytic(result, k, n):
        ref = binary_irrev_cstr(
            result.xout,
            5,
            result.named_dep("H2O2")[0],
            result.named_dep(k)[0],
            result.named_param(fc["H2O2"]),
            result.named_param(fc[k]),
            result.named_param(fr),
            n,
        )
        return np.array(ref).T

    ref_O2 = get_analytic(res, "O2", 1)
    ref_H2O = get_analytic(res, "H2O", 2)
    assert np.allclose(res.named_dep("H2O2"), ref_O2[:, 0])
    assert np.allclose(res.named_dep("H2O2"), ref_H2O[:, 0])
    assert np.allclose(res.named_dep("O2"), ref_O2[:, 1])
    assert np.allclose(res.named_dep("H2O"), ref_H2O[:, 1])


@requires("pyodesys", "scipy", "sym")
def test_get_odesys__cstr():
    rsys = ReactionSystem.from_string("2 H2O2 -> O2 + 2 H2O; 5")
    odesys, extra = get_odesys(rsys, cstr=True)
    fr, fc = extra["cstr_fr_fc"]
    _check_cstr(odesys, fr, fc)


@requires("pyodesys", "scipy", "sym")
def test_create_odesys__cstr():
    rsys = ReactionSystem.from_string("2 H2O2 -> O2 + 2 H2O; 'k2'")
    fr, fc = "feedratio", OrderedDict([(sk, "fc_%s" % sk) for sk in rsys.substances])
    odesys, extra = create_odesys(rsys, rates_kw=dict(cstr_fr_fc=(fr, fc)))
    _check_cstr(odesys, fr, fc, extra_pars=dict(k2=5))


@requires("pygslodeiv2", "sym", units_library)
def test_get_odesys_rsys_with_units():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 0.096/s
    B + C -> P; 4e3/M/s
    """,
        substance_factory=Substance,
    )
    with pytest.raises(Exception):
        get_odesys(
            rsys
        )  # not a strict test, SI_base_registry could be made the default

    odesys, extra = get_odesys(rsys, unit_registry=SI_base_registry)
    tend = 10
    tend_units = tend * u.s
    c0 = {"A": 1e-6, "B": 0, "C": 1, "P": 0}
    c0_units = {k: v * u.molar for k, v in c0.items()}
    result1 = odesys.integrate(tend_units, c0_units, integrator="gsl")
    assert result1.info["success"]

    with pytest.raises(Exception):
        odesys.integrate(tend, c0, integrator="gsl")


@requires("pyodeint", "sym", units_library)
def test_get_odesys_rsys_with_units__named_params():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 'k1'
    B + C -> P; 'k2'
    """,
        substance_factory=Substance,
    )
    odesys, extra = get_odesys(
        rsys, include_params=False, unit_registry=SI_base_registry
    )
    tend = 10
    tend_units = tend * u.s
    c0 = {"A": 1e-6, "B": 0, "C": 1, "P": 0}
    p = {"k1": 3, "k2": 4}
    p_units = {"k1": 3 / u.s, "k2": 4 / u.M / u.s}
    c0_units = {k: v * u.molar for k, v in c0.items()}
    result1 = odesys.integrate(tend_units, c0_units, p_units, integrator="odeint")
    assert result1.info["success"]

    with pytest.raises(Exception):
        odesys.integrate(tend, c0, p, integrator="odeint")


@requires("pycvodes", "sym", units_library)
def test_get_odesys__Eyring():
    R = 8.314472
    T_K = 300
    dH = 80e3
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """.format(
            dH=dH, dS=dS
        ),
        substances="NOBr NO Br".split(),
    )
    kref = 20836643994.118652 * T_K * np.exp(-(dH - T_K * dS) / (R * T_K))
    NOBr0_M = 0.7
    init_cond = dict(NOBr=NOBr0_M * u.M, NO=0 * u.M, Br=0 * u.M)
    t = 5 * u.second
    params = dict(temperature=T_K * u.K)

    def check(rsys):
        odesys, extra = get_odesys(
            rsys, unit_registry=SI_base_registry, constants=const
        )
        res = odesys.integrate(t, init_cond, params, integrator="cvode")
        NOBr_ref = NOBr0_M * np.exp(-kref * to_unitless(res.xout, u.second))
        ref = np.array([NOBr_ref] + [NOBr0_M - NOBr_ref] * 2).T
        cmp = to_unitless(res.yout, u.M)
        assert np.allclose(cmp, ref)

    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """.format(
            dH=dH, dS=dS
        ),
        substances="NOBr NO Br".split(),
    )
    check(rsys2)


@requires("pycvodes", "sym", units_library)
def test_get_odesys__Eyring_2nd_order():
    R = 8.314472
    T_K = 300
    dH = 80e3
    dS = 10
    rsys1b = ReactionSystem.from_string(
        """
    NO + Br -> NOBr; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """.format(
            dH=dH, dS=dS
        )
    )
    c0 = 1  # mol/dm3 === 1000 mol/m3
    kbref = 20836643994.118652 * T_K * np.exp(-(dH - T_K * dS) / (R * T_K)) / c0
    NO0_M = 1.5
    Br0_M = 0.7
    init_cond = dict(NOBr=0 * u.M, NO=NO0_M * u.M, Br=Br0_M * u.M)
    t = 5 * u.second
    params = dict(temperature=T_K * u.K)

    def analytic_b(t):
        U, V = NO0_M, Br0_M
        d = U - V
        return (U * (1 - np.exp(-kbref * t * d))) / (U / V - np.exp(-kbref * t * d))

    def check(rsys):
        odesys, extra = get_odesys(
            rsys, unit_registry=SI_base_registry, constants=const
        )
        res = odesys.integrate(t, init_cond, params, integrator="cvode")
        t_sec = to_unitless(res.xout, u.second)
        NOBr_ref = analytic_b(t_sec)
        cmp = to_unitless(res.yout, u.M)
        ref = np.empty_like(cmp)
        ref[:, odesys.names.index("NOBr")] = NOBr_ref
        ref[:, odesys.names.index("Br")] = Br0_M - NOBr_ref
        ref[:, odesys.names.index("NO")] = NO0_M - NOBr_ref
        assert np.allclose(cmp, ref)

    check(rsys1b)
    rsys2b = ReactionSystem.from_string(
        """
    NO + Br -> NOBr; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """.format(
            dH=dH, dS=dS
        )
    )
    check(rsys2b)


@requires("pycvodes", "sym", "scipy", units_library)
def test_get_odesys__Eyring_1st_order_linearly_ramped_temperature():
    from scipy.special import expi

    def analytic_unit0(t, T0, dH, dS):
        R = 8.314472
        kB = 1.3806504e-23
        h = 6.62606896e-34
        A = kB / h * np.exp(dS / R)
        B = dH / R
        return np.exp(
            A
            * (
                (-(B ** 2) * np.exp(B / T0) * expi(-B / T0) - T0 * (B - T0))
                * np.exp(-B / T0)
                + (
                    B ** 2 * np.exp(B / (t + T0)) * expi(-B / (t + T0))
                    - (t + T0) * (-B + t + T0)
                )
                * np.exp(-B / (t + T0))
            )
            / 2
        )

    T_K = 290
    dH = 80e3
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """.format(
            dH=dH, dS=dS
        )
    )

    NOBr0_M = 0.7
    init_cond = dict(NOBr=NOBr0_M * u.M, NO=0 * u.M, Br=0 * u.M)
    t = 20 * u.second

    def check(rsys):
        odes, extra = get_odesys(
            rsys,
            unit_registry=SI_base_registry,
            constants=const,
            substitutions={"temperature": RampedTemp([T_K * u.K, 1 * u.K / u.s])},
        )
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, integrator="cvode")
            t_sec = to_unitless(res.xout, u.second)
            NOBr_ref = NOBr0_M * analytic_unit0(t_sec, T_K, dH, dS)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index("NOBr")] = NOBr_ref
            ref[:, odesys.names.index("Br")] = NOBr0_M - NOBr_ref
            ref[:, odesys.names.index("NO")] = NOBr0_M - NOBr_ref
            assert np.allclose(cmp, ref)

    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    NOBr -> NO + Br; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """.format(
            dH=dH, dS=dS
        )
    )
    check(rsys2)


@requires("pycvodes", "sym", "scipy", units_library)
def test_get_odesys__Eyring_2nd_order_linearly_ramped_temperature():
    from scipy.special import expi

    def analytic_unit0(t, k, m, dH, dS):
        R = 8.314472
        kB = 1.3806504e-23
        h = 6.62606896e-34
        A = kB / h * np.exp(dS / R)
        B = dH / R
        return (
            k
            * np.exp(B * (k * t + 2 * m) / (m * (k * t + m)))
            / (
                A
                * (
                    -(B ** 2) * np.exp(B / (k * t + m)) * expi(-B / (k * t + m))
                    - B * k * t
                    - B * m
                    + k ** 2 * t ** 2
                    + 2 * k * m * t
                    + m ** 2
                )
                * np.exp(B / m)
                + (
                    A * B ** 2 * np.exp(B / m) * expi(-B / m)
                    - A * m * (-B + m)
                    + k * np.exp(B / m)
                )
                * np.exp(B / (k * t + m))
            )
        )

    T_K = 290
    dTdt_Ks = 3
    dH = 80e3
    dS = 10
    rsys1 = ReactionSystem.from_string(
        """
    2 NO2 -> N2O4; EyringParam(dH={dH}*J/mol, dS={dS}*J/K/mol)
    """.format(
            dH=dH, dS=dS
        )
    )

    NO2_M = 1.0
    init_cond = dict(NO2=NO2_M * u.M, N2O4=0 * u.M)
    t = 20 * u.second

    def check(rsys):
        odes, extra = get_odesys(
            rsys,
            unit_registry=SI_base_registry,
            constants=const,
            substitutions={"temperature": RampedTemp([T_K * u.K, dTdt_Ks * u.K / u.s])},
        )
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, integrator="cvode")
            t_sec = to_unitless(res.xout, u.second)
            NO2_ref = analytic_unit0(t_sec, dTdt_Ks, T_K, dH, dS)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index("NO2")] = NO2_ref
            ref[:, odesys.names.index("N2O4")] = (NO2_M - NO2_ref) / 2
            assert np.allclose(cmp, ref)

    check(rsys1)
    rsys2 = ReactionSystem.from_string(
        """
    2 NO2 -> N2O4; MassAction(EyringHS([{dH}*J/mol, {dS}*J/K/mol]))
    """.format(
            dH=dH, dS=dS
        )
    )
    check(rsys2)


@requires("pycvodes", "sym", units_library)
def test_get_odesys__Eyring_2nd_order_reversible():
    R = 8.314472
    T_K = 273.15 + 20  # 20 degree celsius
    kB = 1.3806504e-23
    h = 6.62606896e-34

    dHf = 74e3
    dSf = R * np.log(h / kB / T_K * 1e16)

    dHb = 79e3
    dSb = dSf - 23

    rsys1 = ReactionSystem.from_string(
        """
    Fe+3 + SCN- -> FeSCN+2; EyringParam(dH={dHf}*J/mol, dS={dSf}*J/K/mol)
    FeSCN+2 -> Fe+3 + SCN-; EyringParam(dH={dHb}*J/mol, dS={dSb}*J/K/mol)
    """.format(
            dHf=dHf, dSf=dSf, dHb=dHb, dSb=dSb
        )
    )
    kf_ref = 20836643994.118652 * T_K * np.exp(-(dHf - T_K * dSf) / (R * T_K))
    kb_ref = 20836643994.118652 * T_K * np.exp(-(dHb - T_K * dSb) / (R * T_K))
    Fe0 = 6e-3
    SCN0 = 2e-3
    init_cond = {"Fe+3": Fe0 * u.M, "SCN-": SCN0 * u.M, "FeSCN+2": 0 * u.M}
    t = 3 * u.second

    def check(rsys, params):
        odes, extra = get_odesys(
            rsys, include_params=False, unit_registry=SI_base_registry, constants=const
        )
        for odesys in [odes, odes.as_autonomous()]:
            res = odesys.integrate(t, init_cond, params, integrator="cvode")
            t_sec = to_unitless(res.xout, u.second)
            FeSCN_ref = binary_rev(t_sec, kf_ref, kb_ref, 0, Fe0, SCN0)
            cmp = to_unitless(res.yout, u.M)
            ref = np.empty_like(cmp)
            ref[:, odesys.names.index("FeSCN+2")] = FeSCN_ref
            ref[:, odesys.names.index("Fe+3")] = Fe0 - FeSCN_ref
            ref[:, odesys.names.index("SCN-")] = SCN0 - FeSCN_ref
            assert np.allclose(cmp, ref)

    check(rsys1, {"temperature": T_K * u.K})
    rsys2 = ReactionSystem.from_string(
        """
    Fe+3 + SCN- -> FeSCN+2; MassAction(EyringHS([{dHf}*J/mol, {dSf}*J/K/mol]))
    FeSCN+2 -> Fe+3 + SCN-; MassAction(EyringHS([{dHb}*J/mol, {dSb}*J/K/mol]))
    """.format(
            dHf=dHf, dSf=dSf, dHb=dHb, dSb=dSb
        )
    )
    check(rsys2, {"temperature": T_K * u.K})
    rsys3 = ReactionSystem.from_string(
        """
    Fe+3 + SCN- -> FeSCN+2; MassAction(EyringHS.fk('dHf', 'dSf'))
    FeSCN+2 -> Fe+3 + SCN-; MassAction(EyringHS.fk('dHb', 'dSb'))
    """
    )
    check(
        rsys3,
        dict(
            temperature=T_K * u.K,
            dHf=dHf * u.J / u.mol,
            dSf=dSf * u.J / u.mol / u.K,
            dHb=dHb * u.J / u.mol,
            dSb=dSb * u.J / u.mol / u.K,
        ),
    )


@requires("numpy", "pyodesys", "sympy", "pycvodes")
def test_create_odesys():
    rsys = ReactionSystem.from_string(
        """
    A -> B; 'k1'
    B + C -> P; 'k2'
    """,
        substance_factory=Substance,
    )

    odesys, odesys_extra = create_odesys(rsys, unit_registry=SI_base_registry)

    tend_ul = 10
    init_conc_ul = {"A": 1e-6, "B": 0, "C": 1}
    params_ul = dict(k1=3, k2=4)

    tend = tend_ul * u.s
    params = {"k1": params_ul["k1"] / u.s, "k2": params_ul["k2"] / u.M / u.s}
    init_conc = {k: v * u.molar for k, v in init_conc_ul.items()}

    validation = odesys_extra["validate"](dict(init_conc, **params))
    (P,) = validation["not_seen"]
    assert P == "P"

    ref_rates = {
        "A": -params["k1"] * init_conc["A"],
        "P": params["k2"] * init_conc["B"] * init_conc["C"],
    }
    ref_rates["B"] = -ref_rates["A"] - ref_rates["P"]
    ref_rates["C"] = -ref_rates["P"]
    assert validation["rates"] == ref_rates

    result1, result1_extra = odesys_extra["unit_aware_solve"](
        tend, defaultdict(lambda: 0 * u.molar, init_conc), params, integrator="cvode"
    )
    assert result1.info["success"]

    result2 = odesys.integrate(
        tend_ul, defaultdict(lambda: 0, init_conc_ul), params_ul, integrator="cvode"
    )
    assert np.allclose(result2.yout[-1, :], to_unitless(result1.yout[-1, :], u.molar))


@requires("pycvodes", "sym", units_library)
def test_create_odesys__Radiolytic():
    rsys1 = ReactionSystem.from_string(
        """
    -> e-(aq); Radiolytic.fk('g_emaq')
    """,
        checks=(),
    )
    ic1 = {"e-(aq)": 0.0}
    t1 = 5
    p1 = dict(g_emaq=42.0, doserate=17.0, density=5.0)
    odesys1, odesys_extra = create_odesys(rsys1)
    result1 = odesys1.integrate(t1, ic1, p1)
    yref1 = result1.xout * p1["g_emaq"] * p1["doserate"] * p1["density"]
    assert np.allclose(yref1, result1.yout.squeeze())


@requires("pycvodes", "sym", units_library)
def test_create_odesys__validate__catalyst():
    rsys1 = ReactionSystem.from_string(
        """
    H2O2 + Pt -> 2 OH + Pt; 'k_decomp'
    """
    )
    ic1 = defaultdict(lambda: 0 * u.molar, {"H2O2": 3.0 * u.molar, "Pt": 0.5 * u.molar})
    t1 = linspace(0 * u.s, 0.3 * u.s, 7)
    p1 = dict(k_decomp=42 / u.second / u.molar)
    odesys1, odesys_extra = create_odesys(rsys1)
    validation = odesys_extra["validate"](dict(ic1, **p1))
    assert validation["not_seen"] == {"OH"}

    dedim_ctx = _mk_dedim(SI_base_registry)
    (t, c, _p), dedim_extra = dedim_ctx["dedim_tcp"](
        t1, [ic1[k] for k in odesys1.names], p1
    )
    result1 = odesys1.integrate(t, c, _p)
    tout = result1.xout * dedim_extra["unit_time"]
    cout = result1.yout * dedim_extra["unit_conc"]
    yref1 = ic1["H2O2"] * np.exp(-tout * ic1["Pt"] * p1["k_decomp"])
    assert allclose(yref1, cout[:, odesys1.names.index("H2O2")], rtol=1e-6)


@requires("pyodesys", units_library)
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)
