ThermoPhase.cpp

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/**
 *  @file ThermoPhase.cpp
 * Definition file for class ThermoPhase, the base class for phases with
 * thermodynamic properties
 * (see class @link Cantera::ThermoPhase ThermoPhase@endlink).
 */
 
// This file is part of Cantera. See License.txt in the top-level directory or
// at https://cantera.org/license.txt for license and copyright information.
 
#include "cantera/thermo/ThermoPhase.h"
#include "cantera/base/stringUtils.h"
#include "cantera/thermo/ThermoFactory.h"
#include "cantera/thermo/Species.h"
#include "cantera/thermo/SpeciesThermoInterpType.h"
#include "cantera/equil/ChemEquil.h"
#include "cantera/equil/MultiPhase.h"
 
#include <iomanip>
#include <fstream>
#include <numeric>
 
using namespace std;
 
namespace Cantera
{
 
shared_ptr<ThermoPhase> ThermoPhase::clone() const
{
    AnyMap phase = parameters();
    AnyMap root;
    vector<AnyMap> speciesDefs;
    speciesDefs.reserve(nSpecies());
    for (const auto& name : speciesNames()) {
        speciesDefs.emplace_back(species(name)->parameters(this));
    }
    root["species"] = std::move(speciesDefs);
    phase.applyUnits();
    root.applyUnits();
    return newThermo(phase, root);
}
 
void ThermoPhase::resetHf298(size_t k) {
    if (k != npos) {
        m_spthermo.resetHf298(k);
    } else {
        for (size_t k = 0; k < nSpecies(); k++) {
            m_spthermo.resetHf298(k);
        }
    }
    invalidateCache();
}
 
int ThermoPhase::activityConvention() const
{
    return cAC_CONVENTION_MOLAR;
}
 
int ThermoPhase::standardStateConvention() const
{
    return m_ssConvention;
}
 
Units ThermoPhase::standardConcentrationUnits() const
{
    // kmol/m^3 for bulk phases, kmol/m^2 for surface phases, etc.
    return Units(1.0, 0, -static_cast<double>(nDim()), 0, 0, 0, 1);
}
 
double ThermoPhase::logStandardConc(size_t k) const
{
    return log(standardConcentration(k));
}
 
void ThermoPhase::getActivities(double* a) const
{
    getActivityConcentrations(a);
    for (size_t k = 0; k < nSpecies(); k++) {
        a[k] /= standardConcentration(k);
    }
}
 
void ThermoPhase::getLnActivityCoefficients(double* lnac) const
{
    getActivityCoefficients(lnac);
    for (size_t k = 0; k < m_kk; k++) {
        lnac[k] = std::log(lnac[k]);
    }
}
 
void ThermoPhase::getElectrochemPotentials(double* mu) const
{
    getChemPotentials(mu);
    double ve = Faraday * electricPotential();
    for (size_t k = 0; k < m_kk; k++) {
        mu[k] += ve*charge(k);
    }
}
 
void ThermoPhase::setState_TPX(double t, double p, const double* x)
{
    setMoleFractions(x);
    setState_TP(t,p);
}
 
void ThermoPhase::setState_TPX(double t, double p, const Composition& x)
{
    setMoleFractionsByName(x);
    setState_TP(t,p);
}
 
void ThermoPhase::setState_TPX(double t, double p, const string& x)
{
    setMoleFractionsByName(x);
    setState_TP(t,p);
}
 
void ThermoPhase::setState_TPY(double t, double p, const double* y)
{
    setMassFractions(y);
    setState_TP(t,p);
}
 
void ThermoPhase::setState_TPY(double t, double p, const Composition& y)
{
    setMassFractionsByName(y);
    setState_TP(t,p);
}
 
void ThermoPhase::setState_TPY(double t, double p, const string& y)
{
    setMassFractionsByName(y);
    setState_TP(t,p);
}
 
void ThermoPhase::setState_TP(double t, double p)
{
    vector<double> state(partialStateSize());
    savePartialState(state.size(), state.data());
    try {
        setTemperature(t);
        setPressure(p);
    } catch (std::exception&) {
        restorePartialState(state.size(), state.data());
        throw;
    }
}
 
void ThermoPhase::setState_HP(double Htarget, double p, double rtol)
{
    vector<double> state(partialStateSize());
    savePartialState(state.size(), state.data());
    try {
        setState_HPorUV(Htarget, p, rtol, false);
    } catch (std::exception&) {
        restorePartialState(state.size(), state.data());
        throw;
    }
}
 
void ThermoPhase::setState_UV(double u, double v, double rtol)
{
    assertCompressible("setState_UV");
    vector<double> state(partialStateSize());
    savePartialState(state.size(), state.data());
    try {
        setState_HPorUV(u, v, rtol, true);
    } catch (std::exception&) {
        restorePartialState(state.size(), state.data());
        throw;
    }
}
 
void ThermoPhase::setState(const AnyMap& input_state)
{
    AnyMap state = input_state;
 
    // Remap allowable synonyms
    if (state.hasKey("mass-fractions")) {
        state["Y"] = state["mass-fractions"];
        state.erase("mass-fractions");
    }
    if (state.hasKey("mole-fractions")) {
        state["X"] = state["mole-fractions"];
        state.erase("mole-fractions");
    }
    if (state.hasKey("temperature")) {
        state["T"] = state["temperature"];
    }
    if (state.hasKey("pressure")) {
        state["P"] = state["pressure"];
    }
    if (state.hasKey("enthalpy")) {
        state["H"] = state["enthalpy"];
    }
    if (state.hasKey("int-energy")) {
        state["U"] = state["int-energy"];
    }
    if (state.hasKey("internal-energy")) {
        state["U"] = state["internal-energy"];
    }
    if (state.hasKey("specific-volume")) {
        state["V"] = state["specific-volume"];
    }
    if (state.hasKey("entropy")) {
        state["S"] = state["entropy"];
    }
    if (state.hasKey("density")) {
        state["D"] = state["density"];
    }
    if (state.hasKey("vapor-fraction")) {
        state["Q"] = state["vapor-fraction"];
    }
 
    // Set composition
    if (state.hasKey("X")) {
        if (state["X"].is<string>()) {
            setMoleFractionsByName(state["X"].asString());
        } else {
            setMoleFractionsByName(state["X"].asMap<double>());
        }
        state.erase("X");
    } else if (state.hasKey("Y")) {
        if (state["Y"].is<string>()) {
            setMassFractionsByName(state["Y"].asString());
        } else {
            setMassFractionsByName(state["Y"].asMap<double>());
        }
        state.erase("Y");
    }
    // set thermodynamic state using whichever property set is found
    if (state.size() == 0) {
        setState_TP(298.15, OneAtm);
    } else if (state.hasKey("T") && state.hasKey("P")) {
        double T = state.convert("T", "K");
        double P = state.convert("P", "Pa");
        if (state.hasKey("Q")) {
            setState_TPQ(T, P, state["Q"].asDouble());
        } else {
            setState_TP(T, P);
        }
    } else if (state.hasKey("T") && state.hasKey("D")) {
        setState_TD(state.convert("T", "K"), state.convert("D", "kg/m^3"));
    } else if (state.hasKey("T") && state.hasKey("V")) {
        setState_TV(state.convert("T", "K"), state.convert("V", "m^3/kg"));
    } else if (state.hasKey("H") && state.hasKey("P")) {
        setState_HP(state.convert("H", "J/kg"), state.convert("P", "Pa"));
    } else if (state.hasKey("U") && state.hasKey("V")) {
        setState_UV(state.convert("U", "J/kg"), state.convert("V", "m^3/kg"));
    } else if (state.hasKey("S") && state.hasKey("P")) {
        setState_SP(state.convert("S", "J/kg/K"), state.convert("P", "Pa"));
    } else if (state.hasKey("S") && state.hasKey("V")) {
        setState_SV(state.convert("S", "J/kg/K"), state.convert("V", "m^3/kg"));
    } else if (state.hasKey("S") && state.hasKey("T")) {
        setState_ST(state.convert("S", "J/kg/K"), state.convert("T", "K"));
    } else if (state.hasKey("P") && state.hasKey("V")) {
        setState_PV(state.convert("P", "Pa"), state.convert("V", "m^3/kg"));
    } else if (state.hasKey("U") && state.hasKey("P")) {
        setState_UP(state.convert("U", "J/kg"), state.convert("P", "Pa"));
    } else if (state.hasKey("V") && state.hasKey("H")) {
        setState_VH(state.convert("V", "m^3/kg"), state.convert("H", "J/kg"));
    } else if (state.hasKey("T") && state.hasKey("H")) {
        setState_TH(state.convert("T", "K"), state.convert("H", "J/kg"));
    } else if (state.hasKey("S") && state.hasKey("H")) {
        setState_SH(state.convert("S", "J/kg/K"), state.convert("H", "J/kg"));
    } else if (state.hasKey("D") && state.hasKey("P")) {
        setState_DP(state.convert("D", "kg/m^3"), state.convert("P", "Pa"));
    } else if (state.hasKey("P") && state.hasKey("Q")) {
        setState_Psat(state.convert("P", "Pa"), state["Q"].asDouble());
    } else if (state.hasKey("T") && state.hasKey("Q")) {
        setState_Tsat(state.convert("T", "K"), state["Q"].asDouble());
    } else if (state.hasKey("T")) {
        setState_TP(state.convert("T", "K"), OneAtm);
    } else if (state.hasKey("P")) {
        setState_TP(298.15, state.convert("P", "Pa"));
    } else {
        throw CanteraError("ThermoPhase::setState",
            "'state' did not specify a recognized set of properties.\n"
            "Keys provided were: {}", input_state.keys_str());
    }
}
 
void ThermoPhase::setState_conditional_TP(double t, double p, bool set_p)
{
    setTemperature(t);
    if (set_p) {
        setPressure(p);
    }
}
 
void ThermoPhase::setState_HPorUV(double Htarget, double p,
                                  double rtol, bool doUV)
{
    double dt;
    double v = 0.0;
 
    // Assign the specific volume or pressure and make sure it's positive
    if (doUV) {
        double v = p;
        if (v < 1.0E-300) {
            throw CanteraError("ThermoPhase::setState_HPorUV (UV)",
                               "Input specific volume is too small or negative. v = {}", v);
        }
        setDensity(1.0/v);
    } else {
        if (p < 1.0E-300) {
            throw CanteraError("ThermoPhase::setState_HPorUV (HP)",
                               "Input pressure is too small or negative. p = {}", p);
        }
        setPressure(p);
    }
    double Tmax = maxTemp() + 0.1;
    double Tmin = minTemp() - 0.1;
 
    // Make sure we are within the temperature bounds at the start
    // of the iteration
    double Tnew = temperature();
    double Tinit = Tnew;
    if (Tnew > Tmax) {
        Tnew = Tmax - 1.0;
    } else if (Tnew < Tmin) {
        Tnew = Tmin + 1.0;
    }
    if (Tnew != Tinit) {
        setState_conditional_TP(Tnew, p, !doUV);
    }
 
    double Hnew = (doUV) ? intEnergy_mass() : enthalpy_mass();
    double Cpnew = (doUV) ? cv_mass() : cp_mass();
    double Htop = Hnew;
    double Ttop = Tnew;
    double Hbot = Hnew;
    double Tbot = Tnew;
 
    bool ignoreBounds = false;
    // Unstable phases are those for which cp < 0.0. These are possible for
    // cases where we have passed the spinodal curve.
    bool unstablePhase = false;
    // Counter indicating the last temperature point where the
    // phase was unstable
    double Tunstable = -1.0;
    bool unstablePhaseNew = false;
 
    // Newton iteration
    for (int n = 0; n < 500; n++) {
        double Told = Tnew;
        double Hold = Hnew;
        double cpd = Cpnew;
        if (cpd < 0.0) {
            unstablePhase = true;
            Tunstable = Tnew;
        }
        // limit step size to 100 K
        dt = clip((Htarget - Hold)/cpd, -100.0, 100.0);
 
        // Calculate the new T
        Tnew = Told + dt;
 
        // Limit the step size so that we are convergent This is the step that
        // makes it different from a Newton's algorithm
        if ((dt > 0.0 && unstablePhase) || (dt <= 0.0 && !unstablePhase)) {
            if (Hbot < Htarget && Tnew < (0.75 * Tbot + 0.25 * Told)) {
                dt = 0.75 * (Tbot - Told);
                Tnew = Told + dt;
            }
        } else if (Htop > Htarget && Tnew > (0.75 * Ttop + 0.25 * Told)) {
            dt = 0.75 * (Ttop - Told);
            Tnew = Told + dt;
        }
 
        // Check Max and Min values
        if (Tnew > Tmax && !ignoreBounds) {
            setState_conditional_TP(Tmax, p, !doUV);
            double Hmax = (doUV) ? intEnergy_mass() : enthalpy_mass();
            if (Hmax >= Htarget) {
                if (Htop < Htarget) {
                    Ttop = Tmax;
                    Htop = Hmax;
                }
            } else {
                Tnew = Tmax + 1.0;
                ignoreBounds = true;
            }
        }
        if (Tnew < Tmin && !ignoreBounds) {
            setState_conditional_TP(Tmin, p, !doUV);
            double Hmin = (doUV) ? intEnergy_mass() : enthalpy_mass();
            if (Hmin <= Htarget) {
                if (Hbot > Htarget) {
                    Tbot = Tmin;
                    Hbot = Hmin;
                }
            } else {
                Tnew = Tmin - 1.0;
                ignoreBounds = true;
            }
        }
 
        // Try to keep phase within its region of stability
        // -> Could do a lot better if I calculate the
        //    spinodal value of H.
        for (int its = 0; its < 10; its++) {
            Tnew = Told + dt;
            if (Tnew < Told / 3.0) {
                Tnew = Told / 3.0;
                dt = -2.0 * Told / 3.0;
            }
            setState_conditional_TP(Tnew, p, !doUV);
            if (doUV) {
                Hnew = intEnergy_mass();
                Cpnew = cv_mass();
            } else {
                Hnew = enthalpy_mass();
                Cpnew = cp_mass();
            }
            if (Cpnew < 0.0) {
                unstablePhaseNew = true;
                Tunstable = Tnew;
            } else {
                unstablePhaseNew = false;
                break;
            }
            if (unstablePhase == false && unstablePhaseNew == true) {
                dt *= 0.25;
            }
        }
 
        if (Hnew == Htarget) {
            return;
        } else if (Hnew > Htarget && (Htop < Htarget || Hnew < Htop)) {
            Htop = Hnew;
            Ttop = Tnew;
        } else if (Hnew < Htarget && (Hbot > Htarget || Hnew > Hbot)) {
            Hbot = Hnew;
            Tbot = Tnew;
        }
        // Convergence in H
        double Herr = Htarget - Hnew;
        double acpd = std::max(fabs(cpd), 1.0E-5);
        double denom = std::max(fabs(Htarget), acpd * Tnew);
        double HConvErr = fabs((Herr)/denom);
        if (HConvErr < rtol || fabs(dt/Tnew) < rtol) {
            return;
        }
    }
    // We are here when there hasn't been convergence
 
    // Formulate a detailed error message, since questions seem to arise often
    // about the lack of convergence.
    string ErrString =  "No convergence in 500 iterations\n";
    if (doUV) {
        ErrString += fmt::format(
            "\tTarget Internal Energy  = {}\n"
            "\tCurrent Specific Volume = {}\n"
            "\tStarting Temperature    = {}\n"
            "\tCurrent Temperature     = {}\n"
            "\tCurrent Internal Energy = {}\n"
            "\tCurrent Delta T         = {}\n",
            Htarget, v, Tinit, Tnew, Hnew, dt);
    } else {
        ErrString += fmt::format(
            "\tTarget Enthalpy         = {}\n"
            "\tCurrent Pressure        = {}\n"
            "\tStarting Temperature    = {}\n"
            "\tCurrent Temperature     = {}\n"
            "\tCurrent Enthalpy        = {}\n"
            "\tCurrent Delta T         = {}\n",
            Htarget, p, Tinit, Tnew, Hnew, dt);
    }
    if (unstablePhase) {
        ErrString += fmt::format(
            "\t  - The phase became unstable (Cp < 0) T_unstable_last = {}\n",
            Tunstable);
    }
    if (doUV) {
        throw CanteraError("ThermoPhase::setState_HPorUV (UV)", ErrString);
    } else {
        throw CanteraError("ThermoPhase::setState_HPorUV (HP)", ErrString);
    }
}
 
void ThermoPhase::setState_SP(double Starget, double p, double rtol)
{
    vector<double> state(partialStateSize());
    savePartialState(state.size(), state.data());
    try {
        setState_SPorSV(Starget, p, rtol, false);
    } catch (std::exception&) {
        restorePartialState(state.size(), state.data());
        throw;
    }
}
 
void ThermoPhase::setState_SV(double Starget, double v, double rtol)
{
    assertCompressible("setState_SV");
    vector<double> state(partialStateSize());
    savePartialState(state.size(), state.data());
    try {
        setState_SPorSV(Starget, v, rtol, true);
    } catch (std::exception&) {
        restorePartialState(state.size(), state.data());
        throw;
    }
}
 
void ThermoPhase::setState_SPorSV(double Starget, double p,
                                  double rtol, bool doSV)
{
    double v = 0.0;
    double dt;
    if (doSV) {
        v = p;
        if (v < 1.0E-300) {
            throw CanteraError("ThermoPhase::setState_SPorSV (SV)",
                "Input specific volume is too small or negative. v = {}", v);
        }
        setDensity(1.0/v);
    } else {
        if (p < 1.0E-300) {
            throw CanteraError("ThermoPhase::setState_SPorSV (SP)",
                "Input pressure is too small or negative. p = {}", p);
        }
        setPressure(p);
    }
    double Tmax = maxTemp() + 0.1;
    double Tmin = minTemp() - 0.1;
 
    // Make sure we are within the temperature bounds at the start
    // of the iteration
    double Tnew = temperature();
    double Tinit = Tnew;
    if (Tnew > Tmax) {
        Tnew = Tmax - 1.0;
    } else if (Tnew < Tmin) {
        Tnew = Tmin + 1.0;
    }
    if (Tnew != Tinit) {
        setState_conditional_TP(Tnew, p, !doSV);
    }
 
    double Snew = entropy_mass();
    double Cpnew = (doSV) ? cv_mass() : cp_mass();
    double Stop = Snew;
    double Ttop = Tnew;
    double Sbot = Snew;
    double Tbot = Tnew;
 
    bool ignoreBounds = false;
    // Unstable phases are those for which Cp < 0.0. These are possible for
    // cases where we have passed the spinodal curve.
    bool unstablePhase = false;
    double Tunstable = -1.0;
    bool unstablePhaseNew = false;
 
    // Newton iteration
    for (int n = 0; n < 500; n++) {
        double Told = Tnew;
        double Sold = Snew;
        double cpd = Cpnew;
        if (cpd < 0.0) {
            unstablePhase = true;
            Tunstable = Tnew;
        }
        // limit step size to 100 K
        dt = clip((Starget - Sold)*Told/cpd, -100.0, 100.0);
        Tnew = Told + dt;
 
        // Limit the step size so that we are convergent
        if ((dt > 0.0 && unstablePhase) || (dt <= 0.0 && !unstablePhase)) {
            if (Sbot < Starget && Tnew < Tbot) {
                dt = 0.75 * (Tbot - Told);
                Tnew = Told + dt;
            }
        } else if (Stop > Starget && Tnew > Ttop) {
            dt = 0.75 * (Ttop - Told);
            Tnew = Told + dt;
        }
 
        // Check Max and Min values
        if (Tnew > Tmax && !ignoreBounds) {
            setState_conditional_TP(Tmax, p, !doSV);
            double Smax = entropy_mass();
            if (Smax >= Starget) {
                if (Stop < Starget) {
                    Ttop = Tmax;
                    Stop = Smax;
                }
            } else {
                Tnew = Tmax + 1.0;
                ignoreBounds = true;
            }
        } else if (Tnew < Tmin && !ignoreBounds) {
            setState_conditional_TP(Tmin, p, !doSV);
            double Smin = entropy_mass();
            if (Smin <= Starget) {
                if (Sbot > Starget) {
                    Tbot = Tmin;
                    Sbot = Smin;
                }
            } else {
                Tnew = Tmin - 1.0;
                ignoreBounds = true;
            }
        }
 
        // Try to keep phase within its region of stability
        // -> Could do a lot better if I calculate the
        //    spinodal value of H.
        for (int its = 0; its < 10; its++) {
            Tnew = Told + dt;
            setState_conditional_TP(Tnew, p, !doSV);
            Cpnew = (doSV) ? cv_mass() : cp_mass();
            Snew = entropy_mass();
            if (Cpnew < 0.0) {
                unstablePhaseNew = true;
                Tunstable = Tnew;
            } else {
                unstablePhaseNew = false;
                break;
            }
            if (unstablePhase == false && unstablePhaseNew == true) {
                dt *= 0.25;
            }
        }
 
        if (Snew == Starget) {
            return;
        } else if (Snew > Starget && (Stop < Starget || Snew < Stop)) {
            Stop = Snew;
            Ttop = Tnew;
        } else if (Snew < Starget && (Sbot > Starget || Snew > Sbot)) {
            Sbot = Snew;
            Tbot = Tnew;
        }
        // Convergence in S
        double Serr = Starget - Snew;
        double acpd = std::max(fabs(cpd), 1.0E-5);
        double denom = std::max(fabs(Starget), acpd * Tnew);
        double SConvErr = fabs((Serr * Tnew)/denom);
        if (SConvErr < rtol || fabs(dt/Tnew) < rtol) {
            return;
        }
    }
    // We are here when there hasn't been convergence
 
    // Formulate a detailed error message, since questions seem to arise often
    // about the lack of convergence.
    string ErrString =  "No convergence in 500 iterations\n";
    if (doSV) {
        ErrString += fmt::format(
            "\tTarget Entropy          = {}\n"
            "\tCurrent Specific Volume = {}\n"
            "\tStarting Temperature    = {}\n"
            "\tCurrent Temperature     = {}\n"
            "\tCurrent Entropy         = {}\n"
            "\tCurrent Delta T         = {}\n",
            Starget, v, Tinit, Tnew, Snew, dt);
    } else {
        ErrString += fmt::format(
            "\tTarget Entropy          = {}\n"
            "\tCurrent Pressure        = {}\n"
            "\tStarting Temperature    = {}\n"
            "\tCurrent Temperature     = {}\n"
            "\tCurrent Entropy         = {}\n"
            "\tCurrent Delta T         = {}\n",
            Starget, p, Tinit, Tnew, Snew, dt);
    }
    if (unstablePhase) {
        ErrString += fmt::format("\t  - The phase became unstable (Cp < 0) T_unstable_last = {}\n",
                     Tunstable);
    }
    if (doSV) {
        throw CanteraError("ThermoPhase::setState_SPorSV (SV)", ErrString);
    } else {
        throw CanteraError("ThermoPhase::setState_SPorSV (SP)", ErrString);
    }
}
 
double ThermoPhase::o2Required(const double* y) const
{
    // indices of fuel elements
    size_t iC = elementIndex("C");
    size_t iS = elementIndex("S");
    size_t iH = elementIndex("H");
 
    double o2req = 0.0;
    double sum = 0.0;
    for (size_t k = 0; k != m_kk; ++k) {
        sum += y[k];
        double x = y[k] / molecularWeights()[k];
        if (iC != npos) {
            o2req += x * nAtoms(k, iC);
        }
        if (iS != npos) {
            o2req += x * nAtoms(k, iS);
        }
        if (iH != npos) {
            o2req += x * 0.25 * nAtoms(k, iH);
        }
    }
    if (sum == 0.0) {
        throw CanteraError("ThermoPhase::o2Required",
                           "No composition specified");
    }
    return o2req/sum;
}
 
double ThermoPhase::o2Present(const double* y) const
{
    size_t iO = elementIndex("O");
    double o2pres = 0.0;
    double sum = 0.0;
    for (size_t k = 0; k != m_kk; ++k) {
        sum += y[k];
        o2pres += y[k] / molecularWeights()[k] * nAtoms(k, iO);
    }
    if (sum == 0.0) {
        throw CanteraError("ThermoPhase::o2Present",
                           "No composition specified");
    }
    return 0.5 * o2pres / sum;
}
 
double ThermoPhase::stoichAirFuelRatio(const Composition& fuelComp,
                                       const Composition& oxComp,
                                       ThermoBasis basis) const
{
    vector<double> fuel(getCompositionFromMap(fuelComp));
    vector<double> ox(getCompositionFromMap(oxComp));
    return stoichAirFuelRatio(fuel.data(), ox.data(), basis);
}
 
double ThermoPhase::stoichAirFuelRatio(const string& fuelComp, const string& oxComp,
                                       ThermoBasis basis) const
{
    return stoichAirFuelRatio(
            parseCompString(fuelComp.find(":") != string::npos ? fuelComp : fuelComp+":1.0"),
            parseCompString(oxComp.find(":") != string::npos ? oxComp : oxComp+":1.0"),
            basis);
}
 
double ThermoPhase::stoichAirFuelRatio(const double* fuelComp,
                                          const double* oxComp,
                                          ThermoBasis basis) const
{
    vector<double> fuel, ox;
    if (basis == ThermoBasis::molar) { // convert input compositions to mass fractions
        fuel.resize(m_kk);
        ox.resize(m_kk);
        moleFractionsToMassFractions(fuelComp, fuel.data());
        moleFractionsToMassFractions(oxComp, ox.data());
        fuelComp = fuel.data();
        oxComp = ox.data();
    }
 
    double o2_required_fuel = o2Required(fuelComp) - o2Present(fuelComp);
    double o2_required_ox = o2Required(oxComp) - o2Present(oxComp);
 
    if (o2_required_fuel < 0.0 || o2_required_ox > 0.0) {
        throw CanteraError("ThermoPhase::stoichAirFuelRatio",
                           "Fuel composition contains too much oxygen or "
                           "oxidizer contains not enough oxygen. "
                           "Fuel and oxidizer composition mixed up?");
    }
 
    if (o2_required_ox == 0.0) {
        return std::numeric_limits<double>::infinity();
    }
 
    return o2_required_fuel / (-o2_required_ox);
}
 
void ThermoPhase::setEquivalenceRatio(double phi, const double* fuelComp,
                                      const double* oxComp, ThermoBasis basis)
{
    if (phi < 0.0) {
        throw CanteraError("ThermoPhase::setEquivalenceRatio",
                           "Equivalence ratio phi must be >= 0");
    }
 
    double p = pressure();
 
    vector<double> fuel, ox;
    if (basis == ThermoBasis::molar) { // convert input compositions to mass fractions
        fuel.resize(m_kk);
        ox.resize(m_kk);
        moleFractionsToMassFractions(fuelComp, fuel.data());
        moleFractionsToMassFractions(oxComp, ox.data());
        fuelComp = fuel.data();
        oxComp = ox.data();
    }
 
    double AFR_st = stoichAirFuelRatio(fuelComp, oxComp, ThermoBasis::mass);
 
    double sum_f = std::accumulate(fuelComp, fuelComp+m_kk, 0.0);
    double sum_o = std::accumulate(oxComp, oxComp+m_kk, 0.0);
 
    vector<double> y(m_kk);
    for (size_t k = 0; k != m_kk; ++k) {
        y[k] = phi * fuelComp[k]/sum_f + AFR_st * oxComp[k]/sum_o;
    }
 
    setMassFractions(y.data());
    setPressure(p);
}
 
void ThermoPhase::setEquivalenceRatio(double phi, const string& fuelComp,
                                        const string& oxComp, ThermoBasis basis)
{
    setEquivalenceRatio(phi,
            parseCompString(fuelComp.find(":") != string::npos ? fuelComp : fuelComp+":1.0"),
            parseCompString(oxComp.find(":") != string::npos ? oxComp : oxComp+":1.0"),
            basis);
}
 
void ThermoPhase::setEquivalenceRatio(double phi, const Composition& fuelComp,
                                      const Composition& oxComp, ThermoBasis basis)
{
    vector<double> fuel = getCompositionFromMap(fuelComp);
    vector<double> ox = getCompositionFromMap(oxComp);
    setEquivalenceRatio(phi, fuel.data(), ox.data(), basis);
}
 
double ThermoPhase::equivalenceRatio() const
{
    double o2_required = o2Required(massFractions());
    double o2_present  = o2Present(massFractions());
 
    if (o2_present == 0.0) { // pure fuel
        return std::numeric_limits<double>::infinity();
    }
 
    return o2_required / o2_present;
}
 
double ThermoPhase::equivalenceRatio(const Composition& fuelComp,
                                     const Composition& oxComp,
                                     ThermoBasis basis) const
{
    vector<double> fuel(getCompositionFromMap(fuelComp));
    vector<double> ox(getCompositionFromMap(oxComp));
    return equivalenceRatio(fuel.data(), ox.data(), basis);
}
 
double ThermoPhase::equivalenceRatio(const string& fuelComp, const string& oxComp,
                                     ThermoBasis basis) const
{
    return equivalenceRatio(
        parseCompString(fuelComp.find(":") != string::npos ? fuelComp : fuelComp+":1.0"),
        parseCompString(oxComp.find(":") != string::npos ? oxComp : oxComp+":1.0"),
        basis);
}
 
double ThermoPhase::equivalenceRatio(const double* fuelComp,
                                        const double* oxComp,
                                        ThermoBasis basis) const
{
    double Z = mixtureFraction(fuelComp, oxComp, basis);
 
    if (Z == 0.0) {
        return 0.0; // pure oxidizer
    }
 
    if (Z == 1.0) {
        return std::numeric_limits<double>::infinity(); // pure fuel
    }
 
    vector<double> fuel, ox;
    if (basis == ThermoBasis::molar) { // convert input compositions to mass fractions
        fuel.resize(m_kk);
        ox.resize(m_kk);
        moleFractionsToMassFractions(fuelComp, fuel.data());
        moleFractionsToMassFractions(oxComp, ox.data());
        fuelComp = fuel.data();
        oxComp = ox.data();
    }
 
    double AFR_st = stoichAirFuelRatio(fuelComp, oxComp, ThermoBasis::mass);
 
    return std::max(Z / (1.0 - Z) * AFR_st, 0.0);
}
 
void ThermoPhase::setMixtureFraction(double mixFrac, const Composition& fuelComp,
                                     const Composition& oxComp, ThermoBasis basis)
{
    vector<double> fuel(getCompositionFromMap(fuelComp));
    vector<double> ox(getCompositionFromMap(oxComp));
    setMixtureFraction(mixFrac, fuel.data(), ox.data(), basis);
}
 
void ThermoPhase::setMixtureFraction(double mixFrac, const string& fuelComp,
                                     const string& oxComp, ThermoBasis basis)
{
    setMixtureFraction(mixFrac,
        parseCompString(fuelComp.find(":") != string::npos ? fuelComp : fuelComp+":1.0"),
        parseCompString(oxComp.find(":") != string::npos ? oxComp : oxComp+":1.0"),
        basis);
}
 
void ThermoPhase::setMixtureFraction(double mixFrac, const double* fuelComp,
                                       const double* oxComp, ThermoBasis basis)
{
    if (mixFrac < 0.0 || mixFrac > 1.0) {
        throw CanteraError("ThermoPhase::setMixtureFraction",
                           "Mixture fraction must be between 0 and 1");
    }
 
    vector<double> fuel, ox;
    if (basis == ThermoBasis::molar) { // convert input compositions to mass fractions
        fuel.resize(m_kk);
        ox.resize(m_kk);
        moleFractionsToMassFractions(fuelComp, fuel.data());
        moleFractionsToMassFractions(oxComp, ox.data());
        fuelComp = fuel.data();
        oxComp = ox.data();
    }
 
    double sum_yf = std::accumulate(fuelComp, fuelComp+m_kk, 0.0);
    double sum_yo = std::accumulate(oxComp, oxComp+m_kk, 0.0);
 
    if (sum_yf == 0.0 || sum_yo == 0.0) {
        throw CanteraError("ThermoPhase::setMixtureFraction",
                           "No fuel and/or oxidizer composition specified");
    }
 
    double p = pressure();
 
    vector<double> y(m_kk);
 
    for (size_t k = 0; k != m_kk; ++k) {
        y[k] = mixFrac * fuelComp[k]/sum_yf + (1.0-mixFrac) * oxComp[k]/sum_yo;
    }
 
    setMassFractions_NoNorm(y.data());
    setPressure(p);
}
 
double ThermoPhase::mixtureFraction(const Composition& fuelComp,
                                    const Composition& oxComp,
                                    ThermoBasis basis,
                                    const string& element) const
{
    vector<double> fuel(getCompositionFromMap(fuelComp));
    vector<double> ox(getCompositionFromMap(oxComp));
    return mixtureFraction(fuel.data(), ox.data(), basis, element);
}
 
double ThermoPhase::mixtureFraction(const string& fuelComp, const string& oxComp,
                                    ThermoBasis basis, const string& element) const
{
    return mixtureFraction(
            parseCompString(fuelComp.find(":") != string::npos ? fuelComp : fuelComp+":1.0"),
            parseCompString(oxComp.find(":") != string::npos ? oxComp : oxComp+":1.0"),
            basis, element);
}
 
double ThermoPhase::mixtureFraction(const double* fuelComp, const double* oxComp,
                                    ThermoBasis basis, const string& element) const
{
    vector<double> fuel, ox;
    if (basis == ThermoBasis::molar) { // convert input compositions to mass fractions
        fuel.resize(m_kk);
        ox.resize(m_kk);
        moleFractionsToMassFractions(fuelComp, fuel.data());
        moleFractionsToMassFractions(oxComp, ox.data());
        fuelComp = fuel.data();
        oxComp = ox.data();
    }
 
    if (element == "Bilger") // compute the mixture fraction based on the Bilger mixture fraction
    {
        double o2_required_fuel = o2Required(fuelComp) - o2Present(fuelComp);
        double o2_required_ox   = o2Required(oxComp) - o2Present(oxComp);
        double o2_required_mix  = o2Required(massFractions()) - o2Present(massFractions());
 
        if (o2_required_fuel < 0.0 || o2_required_ox > 0.0) {
            throw CanteraError("ThermoPhase::mixtureFraction",
                               "Fuel composition contains too much oxygen or "
                               "oxidizer contains not enough oxygen. "
                               "Fuel and oxidizer composition mixed up?");
        }
 
        double denominator = o2_required_fuel - o2_required_ox;
 
        if (denominator == 0.0) {
            throw CanteraError("ThermoPhase::mixtureFraction",
                               "Fuel and oxidizer have the same composition");
        }
 
        double Z = (o2_required_mix - o2_required_ox) / denominator;
 
        return std::min(std::max(Z, 0.0), 1.0);
    } else {
        // compute the mixture fraction from a single element
        double sum_yf = std::accumulate(fuelComp, fuelComp+m_kk, 0.0);
        double sum_yo = std::accumulate(oxComp, oxComp+m_kk, 0.0);
 
        if (sum_yf == 0.0 || sum_yo == 0.0) {
            throw CanteraError("ThermoPhase::mixtureFraction",
                               "No fuel and/or oxidizer composition specified");
        }
 
        auto elementalFraction = [this](size_t m, const double* y) {
            double Z_m = 0.0;
            for (size_t k = 0; k != m_kk; ++k) {
                Z_m += y[k] / molecularWeight(k) * nAtoms(k, m);
            }
            return Z_m;
        };
 
        size_t m = elementIndex(element);
        double Z_m_fuel = elementalFraction(m, fuelComp)/sum_yf;
        double Z_m_ox   = elementalFraction(m, oxComp)/sum_yo;
        double Z_m_mix  = elementalFraction(m, massFractions());
 
        if (Z_m_fuel == Z_m_ox) {
            throw CanteraError("ThermoPhase::mixtureFraction",
                               "Fuel and oxidizer have the same composition for element {}",
                               element);
        }
        double Z = (Z_m_mix - Z_m_ox) / (Z_m_fuel - Z_m_ox);
        return std::min(std::max(Z, 0.0), 1.0);
    }
}
 
MultiSpeciesThermo& ThermoPhase::speciesThermo(int k)
{
    return m_spthermo;
}
 
const MultiSpeciesThermo& ThermoPhase::speciesThermo(int k) const
{
    return m_spthermo;
}
 
 
void ThermoPhase::initThermoFile(const string& inputFile, const string& id)
{
    if (inputFile.empty()) {
        // No input file specified - nothing to set up
        return;
    }
    size_t dot = inputFile.find_last_of(".");
    string extension;
    if (dot != npos) {
        extension = inputFile.substr(dot+1);
    }
    if (extension == "xml" || extension == "cti") {
        throw CanteraError("ThermoPhase::initThermoFile",
                           "The CTI and XML formats are no longer supported.");
    }
 
    AnyMap root = AnyMap::fromYamlFile(inputFile);
    auto& phase = root["phases"].getMapWhere("name", id);
    setupPhase(*this, phase, root);
}
 
void ThermoPhase::initThermo()
{
    // Check to see that all of the species thermo objects have been initialized
    if (!m_spthermo.ready(m_kk)) {
        throw CanteraError("ThermoPhase::initThermo()",
                           "Missing species thermo data");
    }
}
 
void ThermoPhase::setState_TPQ(double T, double P, double Q)
{
    if (T > critTemperature()) {
        if (P > critPressure() || Q == 1) {
            setState_TP(T, P);
            return;
        } else {
            throw CanteraError("ThermoPhase::setState_TPQ",
                "Temperature ({}), pressure ({}) and vapor fraction ({}) "
                "are inconsistent, above the critical temperature.",
                T, P, Q);
        }
    }
 
    double Psat = satPressure(T);
    if (std::abs(Psat / P - 1) < 1e-6) {
        setState_Tsat(T, Q);
    } else if ((Q == 0 && P >= Psat) || (Q == 1 && P <= Psat)) {
        setState_TP(T, P);
    } else {
        throw CanteraError("ThermoPhase::setState_TPQ",
            "Temperature ({}), pressure ({}) and vapor fraction ({}) "
            "are inconsistent.\nPsat at this T: {}\n"
            "Consider specifying the state using two fully independent "
            "properties (for example, temperature and density)",
            T, P, Q, Psat);
    }
}
 
bool ThermoPhase::addSpecies(shared_ptr<Species> spec)
{
    if (!spec->thermo) {
        throw CanteraError("ThermoPhase::addSpecies",
            "Species {} has no thermo data", spec->name);
    }
    bool added = Phase::addSpecies(spec);
    if (added) {
        spec->thermo->validate(spec->name);
        m_spthermo.install_STIT(m_kk-1, spec->thermo);
    }
    return added;
}
 
void ThermoPhase::modifySpecies(size_t k, shared_ptr<Species> spec)
{
    if (!spec->thermo) {
        throw CanteraError("ThermoPhase::modifySpecies",
            "Species {} has no thermo data", spec->name);
    }
    Phase::modifySpecies(k, spec);
    if (speciesName(k) != spec->name) {
        throw CanteraError("ThermoPhase::modifySpecies",
            "New species '{}' does not match existing species '{}' at index {}",
                           spec->name, speciesName(k), k);
    }
    spec->thermo->validate(spec->name);
    m_spthermo.modifySpecies(k, spec->thermo);
}
 
void ThermoPhase::setParameters(const AnyMap& phaseNode, const AnyMap& rootNode)
{
    m_input = phaseNode;
}
 
AnyMap ThermoPhase::parameters(bool withInput) const
{
    AnyMap out;
    getParameters(out);
    if (withInput) {
        out.update(m_input);
    }
    return out;
}
 
void ThermoPhase::getParameters(AnyMap& phaseNode) const
{
    phaseNode["name"] = name();
    phaseNode["thermo"] = ThermoFactory::factory()->canonicalize(type());
    vector<string> elementNames;
    for (size_t i = 0; i < nElements(); i++) {
        elementNames.push_back(elementName(i));
    }
    phaseNode["elements"] = elementNames;
    phaseNode["species"] = speciesNames();
 
    AnyMap state;
    auto stateVars = nativeState();
    if (stateVars.count("T")) {
        state["T"].setQuantity(temperature(), "K");
    }
 
    if (stateVars.count("D")) {
        state["density"].setQuantity(density(), "kg/m^3");
    } else if (stateVars.count("P")) {
        state["P"].setQuantity(pressure(), "Pa");
    }
 
    if (stateVars.count("Y")) {
        map<string, double> Y;
        for (size_t k = 0; k < m_kk; k++) {
            double Yk = massFraction(k);
            if (Yk > 0) {
                Y[speciesName(k)] = Yk;
            }
        }
        state["Y"] = Y;
        state["Y"].setFlowStyle();
    } else if (stateVars.count("X")) {
        map<string, double> X;
        for (size_t k = 0; k < m_kk; k++) {
            double Xk = moleFraction(k);
            if (Xk > 0) {
                X[speciesName(k)] = Xk;
            }
        }
        state["X"] = X;
        state["X"].setFlowStyle();
    }
 
    phaseNode["state"] = std::move(state);
 
    static bool reg = AnyMap::addOrderingRules("Phase", {{"tail", "state"}});
    if (reg) {
        phaseNode["__type__"] = "Phase";
    }
}
 
const AnyMap& ThermoPhase::input() const
{
    return m_input;
}
 
AnyMap& ThermoPhase::input()
{
    return m_input;
}
 
void ThermoPhase::invalidateCache() {
    Phase::invalidateCache();
    m_tlast += 0.1234;
}
 
void ThermoPhase::equilibrate(const string& XY, const string& solver,
                              double rtol, int max_steps, int max_iter,
                              int estimate_equil, int log_level)
{
    if (solver == "auto" || solver == "element_potential") {
        vector<double> initial_state;
        saveState(initial_state);
        debuglog("Trying ChemEquil solver\n", log_level);
        try {
            ChemEquil E;
            E.options.maxIterations = max_steps;
            E.options.relTolerance = rtol;
            int ret = E.equilibrate(*this, XY.c_str(), log_level-1);
            if (ret < 0) {
                throw CanteraError("ThermoPhase::equilibrate",
                    "ChemEquil solver failed. Return code: {}", ret);
            }
            debuglog("ChemEquil solver succeeded\n", log_level);
            return;
        } catch (std::exception& err) {
            debuglog("ChemEquil solver failed.\n", log_level);
            debuglog(err.what(), log_level);
            restoreState(initial_state);
            if (solver == "auto") {
            } else {
                throw;
            }
        }
    }
 
    if (solver == "auto" || solver == "vcs" || solver == "gibbs") {
        MultiPhase M;
        M.addPhase(this, 1.0);
        M.init();
        M.equilibrate(XY, solver, rtol, max_steps, max_iter,
                      estimate_equil, log_level);
        return;
    }
 
    if (solver != "auto") {
        throw CanteraError("ThermoPhase::equilibrate",
                           "Invalid solver specified: '{}'", solver);
    }
}
 
void ThermoPhase::getdlnActCoeffdlnN(const size_t ld, double* const dlnActCoeffdlnN)
{
    for (size_t m = 0; m < m_kk; m++) {
        for (size_t k = 0; k < m_kk; k++) {
            dlnActCoeffdlnN[ld * k + m] = 0.0;
        }
    }
    return;
}
 
void ThermoPhase::getdlnActCoeffdlnN_numderiv(const size_t ld,
                                              double* const dlnActCoeffdlnN)
{
    double deltaMoles_j = 0.0;
    double pres = pressure();
 
    // Evaluate the current base activity coefficients if necessary
    vector<double> ActCoeff_Base(m_kk);
    getActivityCoefficients(ActCoeff_Base.data());
    vector<double> Xmol_Base(m_kk);
    getMoleFractions(Xmol_Base.data());
 
    // Make copies of ActCoeff and Xmol_ for use in taking differences
    vector<double> ActCoeff(m_kk);
    vector<double> Xmol(m_kk);
    double v_totalMoles = 1.0;
    double TMoles_base = v_totalMoles;
 
    // Loop over the columns species to be deltad
    for (size_t j = 0; j < m_kk; j++) {
        // Calculate a value for the delta moles of species j
        // -> Note Xmol_[] and Tmoles are always positive or zero quantities.
        // -> experience has shown that you always need to make the deltas
        //    greater than needed to change the other mole fractions in order
        //    to capture some effects.
        double moles_j_base = v_totalMoles * Xmol_Base[j];
        deltaMoles_j = 1.0E-7 * moles_j_base + v_totalMoles * 1.0E-13 + 1.0E-150;
 
        // Now, update the total moles in the phase and all of the mole
        // fractions based on this.
        v_totalMoles = TMoles_base + deltaMoles_j;
        for (size_t k = 0; k < m_kk; k++) {
            Xmol[k] = Xmol_Base[k] * TMoles_base / v_totalMoles;
        }
        Xmol[j] = (moles_j_base + deltaMoles_j) / v_totalMoles;
 
        // Go get new values for the activity coefficients.
        setMoleFractions(Xmol.data());
        setPressure(pres);
        getActivityCoefficients(ActCoeff.data());
 
        // Calculate the column of the matrix
        double* const lnActCoeffCol = dlnActCoeffdlnN + ld * j;
        for (size_t k = 0; k < m_kk; k++) {
            lnActCoeffCol[k] = (2*moles_j_base + deltaMoles_j) *(ActCoeff[k] - ActCoeff_Base[k]) /
                               ((ActCoeff[k] + ActCoeff_Base[k]) * deltaMoles_j);
        }
        // Revert to the base case Xmol_, v_totalMoles
        v_totalMoles = TMoles_base;
        Xmol = Xmol_Base;
    }
    setMoleFractions(Xmol_Base.data());
    setPressure(pres);
}
 
string ThermoPhase::report(bool show_thermo, double threshold) const
{
    if (type() == "none") {
        throw NotImplementedError("ThermoPhase::report",
            "Not implemented for thermo model 'none'");
    }
 
    fmt::memory_buffer b;
    // This is the width of the first column of names in the report.
    int name_width = 18;
 
    string blank_leader = fmt::format("{:{}}", "", name_width);
 
    string string_property = fmt::format("{{:>{}}}   {{}}\n", name_width);
 
    string one_property = fmt::format("{{:>{}}}   {{:<.5g}} {{}}\n", name_width);
 
    constexpr auto two_prop_header = "{}   {:^15}   {:^15}\n";
    string kg_kmol_header = fmt::format(
        two_prop_header, blank_leader, "1 kg", "1 kmol"
    );
    string Y_X_header = fmt::format(
        two_prop_header, blank_leader, "mass frac. Y", "mole frac. X"
    );
    string two_prop_sep = fmt::format(
        "{}   {:-^15}   {:-^15}\n", blank_leader, "", ""
    );
    string two_property = fmt::format(
        "{{:>{}}}   {{:15.5g}}   {{:15.5g}}  {{}}\n", name_width
    );
 
    string three_prop_header = fmt::format(
        "{}   {:^15}   {:^15}   {:^15}\n", blank_leader, "mass frac. Y",
        "mole frac. X", "chem. pot. / RT"
    );
    string three_prop_sep = fmt::format(
        "{}   {:-^15}   {:-^15}   {:-^15}\n", blank_leader, "", "", ""
    );
    string three_property = fmt::format(
        "{{:>{}}}   {{:15.5g}}   {{:15.5g}}   {{:15.5g}}\n", name_width
    );
 
    try {
        if (name() != "") {
            fmt_append(b, "\n  {}:\n", name());
        }
        fmt_append(b, "\n");
        fmt_append(b, one_property, "temperature", temperature(), "K");
        fmt_append(b, one_property, "pressure", pressure(), "Pa");
        fmt_append(b, one_property, "density", density(), "kg/m^3");
        fmt_append(b, one_property,
                   "mean mol. weight", meanMolecularWeight(), "kg/kmol");
 
        double phi = electricPotential();
        if (phi != 0.0) {
            fmt_append(b, one_property, "potential", phi, "V");
        }
 
        fmt_append(b, string_property, "phase of matter", phaseOfMatter());
 
        if (show_thermo) {
            fmt_append(b, "\n");
            fmt_append(b, kg_kmol_header);
            fmt_append(b, two_prop_sep);
            fmt_append(b, two_property,
                       "enthalpy", enthalpy_mass(), enthalpy_mole(), "J");
            fmt_append(b, two_property,
                       "internal energy", intEnergy_mass(), intEnergy_mole(), "J");
            fmt_append(b, two_property,
                       "entropy", entropy_mass(), entropy_mole(), "J/K");
            fmt_append(b, two_property,
                       "Gibbs function", gibbs_mass(), gibbs_mole(), "J");
            fmt_append(b, two_property,
                       "heat capacity c_p", cp_mass(), cp_mole(), "J/K");
            try {
                fmt_append(b, two_property,
                           "heat capacity c_v", cv_mass(), cv_mole(), "J/K");
            } catch (NotImplementedError&) {
                fmt_append(b, string_property,
                           "heat capacity c_v", "<not implemented>");
            }
        }
 
        vector<double> x(m_kk);
        vector<double> y(m_kk);
        vector<double> mu(m_kk);
        getMoleFractions(&x[0]);
        getMassFractions(&y[0]);
        getChemPotentials(&mu[0]);
        int nMinor = 0;
        double xMinor = 0.0;
        double yMinor = 0.0;
        fmt_append(b, "\n");
        if (show_thermo) {
            fmt_append(b, three_prop_header);
            fmt_append(b, three_prop_sep);
            for (size_t k = 0; k < m_kk; k++) {
                if (abs(x[k]) >= threshold) {
                    if (abs(x[k]) > SmallNumber) {
                        fmt_append(b, three_property,
                                   speciesName(k), y[k], x[k], mu[k]/RT());
                    } else {
                        fmt_append(b, two_property, speciesName(k), y[k], x[k], "");
                    }
                } else {
                    nMinor++;
                    xMinor += x[k];
                    yMinor += y[k];
                }
            }
        } else {
            fmt_append(b, Y_X_header);
            fmt_append(b, two_prop_sep);
            for (size_t k = 0; k < m_kk; k++) {
                if (abs(x[k]) >= threshold) {
                    fmt_append(b, two_property, speciesName(k), y[k], x[k], "");
                } else {
                    nMinor++;
                    xMinor += x[k];
                    yMinor += y[k];
                }
            }
        }
        if (nMinor) {
            string minor = fmt::format("[{:+5d} minor]", nMinor);
            fmt_append(b, two_property, minor, yMinor, xMinor, "");
        }
    } catch (CanteraError& err) {
        return to_string(b) + err.what();
    }
    return to_string(b);
}
 
}