vcs_solve.h

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/**
 * @file vcs_solve.h Header file for the internal object that holds the vcs
 *    equilibrium problem (see Class \link Cantera::VCS_SOLVE
 *    VCS_SOLVE\endlink and \ref equilfunctions ).
 */
/*
 * Copyright (2005) Sandia Corporation. Under the terms of
 * Contract DE-AC04-94AL85000 with Sandia Corporation, the
 * U.S. Government retains certain rights in this software.
 */

#ifndef _VCS_SOLVE_H
#define _VCS_SOLVE_H

/*
* Index of Symbols
* -------------------
*     irxn -> refers to the species or rxn between the species and
*             the components in the problem
*     k    -> refers to the species
*     j    -> refers to the element or component
*
*     ###  -> to be eliminated
*/

#include "cantera/base/ct_defs.h"
#include "cantera/equil/vcs_defs.h"
#include "cantera/equil/vcs_internal.h"
#include "cantera/base/Array.h"

namespace Cantera
{
/*
 * Forward references
 */
class vcs_VolPhase;
class VCS_SPECIES_THERMO;
class VCS_PROB;
class VCS_COUNTERS;


//! This is the main structure used to hold the internal data
//! used in vcs_solve_TP(), and to solve TP systems.
/*!
 *  The indices of information in this structure may change when the species
 *  basis changes or when phases pop in and out of existence. Both of these
 *  operations change the species ordering.
 */
class VCS_SOLVE
{
public:
    VCS_SOLVE();

    ~VCS_SOLVE();

    //! Initialize the sizes within the VCS_SOLVE object
    /*!
     *  This resizes all of the internal arrays within the object. This
     *  routine operates in two modes. If all of the parameters are the same
     *  as it currently exists in the object, nothing is done by this routine;
     *  a quick exit is carried out and all of the data in the object
     *  persists.
     *
     *  If any of the parameters are different than currently exists in the
     *  object, then all of the data in the object must be redone. It may not
     *  be zeroed, but it must be redone.
     *
     *  @param nspecies0     Number of species within the object
     *  @param nelements     Number of element constraints within the problem
     *  @param nphase0       Number of phases defined within the problem.
     */
    void vcs_initSizes(const size_t nspecies0, const size_t nelements, const size_t nphase0);

    //! Solve an equilibrium problem
    /*!
     *  This is the main interface routine to the equilibrium solver
     *
     * Input:
     *   @param vprob Object containing the equilibrium Problem statement
     *
     *   @param ifunc Determines the operation to be done: Valid values:
     *            0 -> Solve a new problem by initializing structures
     *                 first. An initial estimate may or may not have
     *                 been already determined. This is indicated in the
     *                 VCS_PROB structure.
     *            1 -> The problem has already been initialized and
     *                 set up. We call this routine to resolve it
     *                 using the problem statement and
     *                 solution estimate contained in
     *                 the VCS_PROB structure.
     *            2 -> Don't solve a problem. Destroy all the private
     *                 structures.
     *
     *  @param ipr Printing of results
     *     ipr = 1 -> Print problem statement and final results to
     *                standard output
     *           0 -> don't report on anything
     *  @param ip1 Printing of intermediate results
     *     IP1 = 1 -> Print intermediate results.
     *
     *  @param maxit  Maximum number of iterations for the algorithm
     *
     * Output:
     *
     *    @return
     *       nonzero value: failure to solve the problem at hand.
     *       zero : success
     */
    int vcs(VCS_PROB* vprob, int ifunc, int ipr, int ip1, int maxit);

    //! Main routine that solves for equilibrium at constant T and P
    //! using a variant of the VCS method
    /*!
     * This is the main routine that solves for equilibrium at constant T and P
     * using a variant of the VCS method. Nonideal phases can be accommodated
     * as well.
     *
     * Any number of single-species phases and  multi-species phases
     * can be handled by the present version.
     *
     * @param print_lvl     1 -> Print results to standard output;
     *                      0 -> don't report on anything
     * @param printDetails  1 -> Print intermediate results.
     * @param maxit         Maximum number of iterations for the algorithm
     *
     * @return
     *     * 0 = Equilibrium Achieved
     *     * 1 = Range space error encountered. The element abundance criteria
     *       are only partially satisfied. Specifically, the first NC= (number
     *       of components) conditions are satisfied. However, the full NE
     *       (number of elements) conditions are not satisfied. The
     *       equilibrium condition is returned.
     *     * -1 = Maximum number of iterations is exceeded. Convergence was
     *       not found.
     */
    int vcs_solve_TP(int print_lvl, int printDetails, int maxit);

    int vcs_PS(VCS_PROB* vprob, int iph, int printLvl, double& feStable);

    /*!
     * We make decisions on the initial mole number, and major-minor status
     * here. We also fix up the total moles in a phase.
     *
     * irxn = id of the noncomponent species formation reaction for the
     *        species to be added in.
     *
     * The algorithm proceeds to implement these decisions in the previous
     * position of the species. Then, vcs_switch_pos is called to move the
     * species into the last active species slot, incrementing the number
     * of active species at the same time.
     *
     * This routine is responsible for the global data manipulation only.
     */
    void vcs_reinsert_deleted(size_t kspec);

    //! Choose the optimum species basis for the calculations
    /*!
     * This is done by choosing the species with the largest mole fraction not
     * currently a linear combination of the previous components. Then,
     * calculate the stoichiometric coefficient matrix for that basis.
     *
     * Rearranges the solution data to put the component data at the
     * front of the species list.
     *
     * Then, calculates m_stoichCoeffRxnMatrix(jcomp,irxn) the formation
     * reactions for all noncomponent species in the mechanism. Also
     * calculates DNG(I) and DNL(I), the net mole change for each formation
     * reaction. Also, initializes IR(I) to the default state.
     *
     * @param[in] doJustComponents  If true, the m_stoichCoeffRxnMatrix and
     *                              m_deltaMolNumPhase are not calculated.
     *
     * @param[in] aw     Vector of mole fractions which will be used to construct an
     *                   optimal basis from.
     *
     * @param[in] sa     Gram-Schmidt orthog work space (nc in length) sa[j]
     * @param[in] ss     Gram-Schmidt orthog work space (nc in length) ss[j]
     * @param[in] sm     QR matrix work space (nc*ne in length)         sm[i+j*ne]
     * @param[in] test   This is a small negative number dependent upon whether
     *                   an estimate is supplied or not.
     * @param[out] usedZeroedSpecies  If true, then a species with a zero
     *                                concentration was used as a component.
     *                                The problem may be converged. Or, the
     *                                problem may have a range space error and
     *                                may not have a proper solution.
     * @return        Returns VCS_SUCCESS if everything went ok. Returns
     *     VCS_FAILED_CONVERGENCE if there is a problem.
     *
     * ### Internal Variables calculated by this routine:
     *
     * - #m_numComponents:  Number of component species. This routine
     *   calculates the #m_numComponents species. It switches their positions
     *   in the species vector so that they occupy the first #m_numComponents
     *   spots in the species vector.
     * - #m_stoichCoeffRxnMatrix(jcomp,irxn) Stoichiometric coefficient
     *   matrix for the reaction mechanism expressed in Reduced Canonical
     *   Form. jcomp refers to the component number, and irxn refers to the
     *   irxn_th non-component species.
     * - #m_deltaMolNumPhase(iphase,irxn): Change in the number of moles in
     *   phase, iphase, due to the noncomponent formation reaction, irxn.
     * - #m_phaseParticipation(iphase,irxn): This is 1 if the phase, iphase,
     *   participates in the formation reaction, irxn, and zero otherwise.
     */
    int vcs_basopt(const bool doJustComponents, double aw[], double sa[], double sm[],
                   double ss[], double test, bool* const usedZeroedSpecies);

    //!  Choose a species to test for the next component
    /*!
     *  We make the choice based on testing (molNum[i] * spSize[i]) for its
     *  maximum value. Preference for single species phases is also made.
     *
     *    @param molNum  Mole number vector
     *    @param j       index into molNum[] that indicates where the search
     *                   will start from Previous successful components are
     *                   swapped into the front of molNum[].
     *    @param n       Length of molNum[]
     */
    size_t vcs_basisOptMax(const double* const molNum, const size_t j, const size_t n);

    //! Evaluate the species category for the indicated species
    /*!
     *  All evaluations are done using the "old" version of the solution.
     *
     *  @param kspec   Species to be evaluated
     *
     * @return Returns the calculated species type
     */
    int vcs_species_type(const size_t kspec) const;

    //!  This routine evaluates the species type for all species
    /*!
     *  - #VCS_SPECIES_MAJOR: Major species
     *  - #VCS_SPECIES_MINOR: Minor species
     *  - #VCS_SPECIES_SMALLMS: The species lies in a multicomponent phase
     *    that exists. Its concentration is currently very low, necessitating
     *    a different method of calculation.
     *  - #VCS_SPECIES_ZEROEDMS: The species lies in a multicomponent phase
     *    which currently doesn't exist. Its concentration is currently zero.
     *  - #VCS_SPECIES_ZEROEDSS: Species lies in a single-species phase which
     *       is currently zeroed out.
     *  - #VCS_SPECIES_DELETED: Species has such a small mole fraction it is
     *    deleted even though its phase may possibly exist. The species is
     *    believed to have such a small mole fraction that it best to throw
     *    the calculation of it out.  It will be added back in at the end of
     *    the calculation.
     *  - #VCS_SPECIES_INTERFACIALVOLTAGE: Species refers to an electron in
     *    the metal The unknown is equal to the interfacial voltage drop
     *    across the interface on the SHE (standard hydrogen electrode) scale
     *    (volts).
     *  - #VCS_SPECIES_ZEROEDPHASE: Species lies in a multicomponent phase
     *    that is zeroed atm  and will stay deleted due to a choice from a
     *    higher level. These species will formally always have zero mole
     *    numbers in the solution vector.
     *  - #VCS_SPECIES_ACTIVEBUTZERO: The species lies in a multicomponent
     *    phase which currently does exist.  Its concentration is currently
     *    identically zero, though the phase exists. Note, this is a temporary
     *    condition that exists at the start of an equilibrium problem. The
     *    species is soon "birthed" or "deleted".
     *  - #VCS_SPECIES_STOICHZERO: The species lies in a multicomponent phase
     *    which currently does exist.  Its concentration is currently
     *    identically zero, though the phase exists. This is a permanent
     *    condition due to stoich constraints
     */
    bool vcs_evaluate_speciesType();

    //! We calculate the dimensionless chemical potentials of all species
    //! in a single phase.
    /*!
     * Note, for multispecies phases which are currently zeroed out, the
     * chemical potential is filled out with the standard chemical potential.
     *
     * For species in multispecies phases whose concentration is zero, we need
     * to set the mole fraction to a very low value. Its chemical potential is
     * then calculated using the #VCS_DELETE_MINORSPECIES_CUTOFF concentration
     * to keep numbers positive.
     *
     * # Formula:
     *
     * ## Ideal Mixtures:
     *
     *      m_feSpecies(I) = m_SSfeSpecies(I) + ln(z(I)) - ln(m_tPhaseMoles[iph])
     *                     + m_chargeSpecies[I] * Faraday_dim * m_phasePhi[iphase];
     *
     * (This is equivalent to the adding the log of the mole fraction onto
     *  the standard chemical potential. )
     *
     * ## Non-Ideal Mixtures:
     *
     * ### ActivityConvention = 0: molarity activity formulation
     *
     *     m_feSpecies(I) = m_SSfeSpecies(I)
     *                    + ln(ActCoeff[I] * z(I)) - ln(m_tPhaseMoles[iph])
     *                    + m_chargeSpecies[I] * Faraday_dim * m_phasePhi[iphase];
     *
     * ( This is equivalent to the adding the log of the mole fraction
     *   multiplied by the activity coefficient onto the standard chemical
     *   potential. )
     *
     * ### ActivityConvention = 1: molality activity formulation
     *
     *     m_feSpecies(I) = m_SSfeSpecies(I)
     *                      + ln(ActCoeff[I] * z(I)) - ln(m_tPhaseMoles[iph])
     *                      - ln(Mnaught * m_units)
     *                      + m_chargeSpecies[I] * Faraday_dim * m_phasePhi[iphase];
     *
     * Note: `m_SSfeSpecies(I)` is the molality based standard state. However,
     * `ActCoeff[I]` is the molar based activity coefficient We have used the
     * formulas:
     *
     *     ActCoeff_M[I] =  ActCoeff[I] / Xmol[N]
     *
     * where `Xmol[N]` is the mole fraction of the solvent and `ActCoeff_M[I]`
     * is the molality based act coeff.
     *
     * Note: This is equivalent to the "normal" molality formulation:
     *
     *     m_feSpecies(I) = m_SSfeSpecies(I)
     *                    + ln(ActCoeff_M[I] * m(I))
     *                    + m_chargeSpecies[I] * Faraday_dim * m_phasePhi[iphase]
     *
     * where `m[I]` is the molality of the ith solute
     *
     *     m[I] = Xmol[I] / ( Xmol[N] * Mnaught * m_units)
     *
     * `z(I)/tPhMoles_ptr[iph] = Xmol[i]` is the mole fraction of i in the phase.
     *
     *
     * NOTE: As per the discussion in vcs_dfe(), for small species where the
     * mole fraction is small:
     *
     *     z(i) < VCS_DELETE_MINORSPECIES_CUTOFF
     *
     * The chemical potential is calculated as:
     *
     *     m_feSpecies(I) = m_SSfeSpecies(I)
     *                    + ln(ActCoeff[i](VCS_DELETE_MINORSPECIES_CUTOFF))
     *
     *  @param[in] iph        Phase to be calculated
     *  @param[in] molNum     Number of moles of species i (VCS species order)
     *  @param[out] ac        Activity coefficients for species in phase (VCS
     *                        species order)
     *  @param[out] mu_i      Dimensionless chemical potentials for phase
     *                        species (VCS species order)
     */
    void vcs_chemPotPhase(const int stateCalc, const size_t iph, const double* const molNum,
                          double* const ac, double* const mu_i,
                          const bool do_deleted = false);

    //! Calculate the dimensionless chemical potentials of all species or
    //! of certain groups of species, at a fixed temperature and pressure.
    /*!
     * We calculate the dimensionless chemical potentials of all species
     * or certain groups of species here, at a fixed temperature and pressure,
     * for the input mole vector z[] in the parameter list.
     * Nondimensionalization is achieved by division by RT.
     *
     * Note, for multispecies phases which are currently zeroed out,
     * the chemical potential is filled out with the standard chemical
     * potential.
     *
     * For species in multispecies phases whose concentration is zero, we need
     * to set the mole fraction to a very low value. Its chemical potential is
     * then calculated using the VCS_DELETE_MINORSPECIES_CUTOFF concentration
     * to keep numbers positive.
     *
     * For formulas, see vcs_chemPotPhase().
     *
     *  Handling of Small Species:
     * ------------------------------
     * As per the discussion above, for small species where the mole fraction
     *
     *     z(i) < VCS_DELETE_MINORSPECIES_CUTOFF
     *
     * The chemical potential is calculated as:
     *
     *      m_feSpecies(I)(I) = m_SSfeSpecies(I) + ln(ActCoeff[i](VCS_DELETE_MINORSPECIES_CUTOFF))
     *
     * Species in the following categories are treated as "small species"
     *   - #VCS_SPECIES_DELETED
     *   - #VCS_SPECIES_ACTIVEBUTZERO
     *
     * For species in multispecies phases which are currently not active, the
     * treatment is different. These species are in the following species
     * categories:
     *   - #VCS_SPECIES_ZEROEDMS
     *   - #VCS_SPECIES_ZEROEDPHASE
     *
     * For these species, the `ln( ActCoeff[I] X[I])` term is dropped
     * altogether. The following equation is used:
     *
     *     m_feSpecies(I) = m_SSfeSpecies(I)
     *                    + Charge[I] * Faraday_dim * phasePhi[iphase];
     *
     * Handling of "Species" Representing Interfacial Voltages
     * ---------------------------------------------------------
     *
     * These species have species types of
     * #VCS_SPECIES_TYPE_INTERFACIALVOLTAGE The chemical potentials for these
     * "species" refer to electrons in metal electrodes. They have the
     * following formula
     *
     *     m_feSpecies(I) = m_SSfeSpecies(I) - F z[I] / RT
     *
     * - `F` is Faraday's constant.
     * - `R` = gas constant
     * - `T` = temperature
     * - `V` = potential of the interface = phi_electrode - phi_solution
     *
     * For these species, the solution vector unknown, z[I], is V, the phase
     * voltage, in volts.
     *
     * @param ll     Determine which group of species gets updated
     *     - `ll = 0`: Calculate for all species
     *     - `ll < 0`: calculate for components and for major non-components
     *     - `ll = 1`: calculate for components and for minor non-components
     *
     * @param lbot    Restricts the calculation of the chemical potential
     *                to the species between LBOT <= i < LTOP. Usually
     *                 LBOT and LTOP will be equal to 0 and MR, respectively.
     * @param ltop    Top value of the loops
     *
     * @param stateCalc   Determines whether z is old or new or tentative:
     *            - 1: Use the tentative values for the total number of
     *                 moles in the phases, i.e., use TG1 instead of TG etc.
     *            - 0: Use the base values of the total number of
     *                 moles in each system.
     *
     *  Also needed:
     *     ff     : standard state chemical potentials. These are the
     *              chemical potentials of the standard states at
     *              the same T and P as the solution.
     *     tg     : Total Number of moles in the phase.
     */
    void vcs_dfe(const int stateCalc, const int ll, const size_t lbot, const size_t ltop);

    //! Print out a table of chemical potentials
    /*!
     *    @param stateCalc Determines where to get the mole numbers from.
     *                -  VCS_STATECALC_OLD -> from m_molNumSpecies_old
     *                -  VCS_STATECALC_NEW -> from m_molNumSpecies_new
     */
    void vcs_printSpeciesChemPot(const int stateCalc) const;

    //!  This routine uploads the state of the system into all of the
    //!  vcs_VolumePhase objects in the current problem.
    /*!
     *  @param stateCalc Determines where to get the mole numbers from.
     *                -  VCS_STATECALC_OLD -> from m_molNumSpecies_old
     *                -  VCS_STATECALC_NEW -> from m_molNumSpecies_new
     */
    void vcs_updateVP(const int stateCalc);

    //! Utility function that evaluates whether a phase can be popped
    //! into existence
    /*!
     * A phase can be popped iff the stoichiometric coefficients for the
     * component species, whose concentrations will be lowered during the
     * process, are positive by at least a small degree.
     *
     * If one of the phase species is a zeroed component, then the phase can
     * be popped if the component increases in mole number as the phase moles
     * are increased.
     *
     * @param iphasePop  id of the phase, which is currently zeroed,
     *
     * @return Returns true if the phase can come into existence
     *         and false otherwise.
     */
    bool vcs_popPhasePossible(const size_t iphasePop) const;

    //! Determine the list of problems that need to be checked to see if there are any phases pops
    /*!
     *  This routine evaluates and fills in #phasePopProblemLists_. Need to
     *  work in species that are zeroed by element constraints.
     *
     *  @return    Returns the number of problems that must be checked.
     */
    int vcs_phasePopDeterminePossibleList();

    //! Decision as to whether a phase pops back into existence
    /*!
     * @param  phasePopPhaseIDs Vector containing the phase ids of the phases
     *         that will be popped this step.
     *
     * @return returns the phase id of the phase that pops back into
     *         existence. Returns -1 if there are no phases
     */
    size_t vcs_popPhaseID(std::vector<size_t> &phasePopPhaseIDs);

    //! Calculates the deltas of the reactions due to phases popping
    //! into existence
    /*!
     * Updates #m_deltaMolNumSpecies[irxn] : reaction adjustments, where irxn
     * refers to the irxn'th species formation reaction. This  adjustment is
     * for species irxn + M, where M is the number of components.
     *
     * @param iphasePop  Phase id of the phase that will come into existence
     *
     * @return  Returns an int representing the status of the step
     *            -  0 : normal return
     *            -  1 : A single species phase species has been zeroed out
     *                   in this routine. The species is a noncomponent
     *            -  2 : Same as one but, the zeroed species is a component.
     *            -  3 : Nothing was done because the phase couldn't be birthed
     *                   because a needed component is zero.
     */
    int vcs_popPhaseRxnStepSizes(const size_t iphasePop);

    //! Calculates formation reaction step sizes.
    /*!
     *  This is equation 6.4-16, p. 143 in Smith and Missen.
     *
     * Output
     * -------
     * m_deltaMolNumSpecies(irxn) : reaction adjustments, where irxn refers to
     *                              the irxn'th species formation reaction.
     *                              This  adjustment is for species irxn + M,
     *                              where M is the number of components.
     *
     * Special branching occurs sometimes. This causes the component basis
     * to be reevaluated
     *
     * @param forceComponentCalc  integer flagging whether a component
     *                            recalculation needs to be carried out.
     * @param kSpecial            species number of phase being zeroed.
     *
     * @return  Returns an int representing which phase may need to be zeroed
     */
    size_t vcs_RxnStepSizes(int& forceComponentCalc, size_t& kSpecial);

    //! Calculates the total number of moles of species in all phases.
    /*!
     *  Also updates the variable m_totalMolNum and Reconciles Phase existence
     *  flags with total moles in each phase.
     */
    double vcs_tmoles();
#ifdef DEBUG_MODE
    void check_tmoles() const;
#endif

    //! This subroutine calculates reaction free energy changes for
    //! all noncomponent formation reactions.
    /*!
     *  Formation reactions are
     *  reactions which create each noncomponent species from the component
     *  species. m_stoichCoeffRxnMatrix(jcomp,irxn)  are the stoichiometric
     *  coefficients for these  reactions. A stoichiometric coefficient of
     *  one is assumed for species irxn in this reaction.
     *
     *  @param l
     *    - `L < 0`: Calculate reactions corresponding to major noncomponent
     *      and zeroed species only
     *    - `L = 0`: Do all noncomponent reactions, i, between
     *      0 <= i < irxnl
     *    - `L > 0`: Calculate reactions corresponding to minor noncomponent
     *      and zeroed species only
     *
     *  @param doDeleted   Do deleted species
     *  @param vcsState    Calculate deltaG corresponding to either old or new
     *                     free energies
     *  @param alterZeroedPhases boolean indicating whether we should
     *                           add in a special section for zeroed phases.
     *
     *  Note we special case one important issue. If the component has zero
     *  moles, then we do not allow deltaG < 0.0 for formation reactions which
     *  would lead to the loss of more of that same component. This dG < 0.0
     *  condition feeds back into the algorithm in several places, and leads
     *  to a infinite loop in at least one case.
     */
    void vcs_deltag(const int l, const bool doDeleted, const int vcsState,
                    const bool alterZeroedPhases = true);

    void vcs_printDeltaG(const int stateCalc);

    //! Calculate deltag of formation for all species in a single phase.
    /*!
     * Calculate deltag of formation for all species in a single phase. It is
     * assumed that the fe[] is up to date for all species. However, if the
     * phase is currently zeroed out, a subproblem is calculated to solve for
     * AC[i] and pseudo-X[i] for that phase.
     *
     * @param iphase       phase index of the phase to be calculated
     * @param doDeleted    boolean indicating whether to do deleted
     *                     species or not
     * @param stateCalc    integer describing which set of free energies
     *                     to use and where to stick the results.
     * @param alterZeroedPhases boolean indicating whether we should
     *                          add in a special section for zeroed phases.
     *
     *    NOTE: this is currently not used used anywhere.
     *          It may be in the future?
     */
    void vcs_deltag_Phase(const size_t iphase, const bool doDeleted,
                          const int stateCalc, const bool alterZeroedPhases = true);

    //!  Swaps the indices for all of the global data for two species, k1
    //!  and k2.
    /*!
     *  @param  ifunc:  If true, switch the species data and the noncomponent
     *                  reaction data. This must be called for a non-component
     *                  species only. If false, switch the species data only.
     *                  Typically, we use this option when determining the
     *                  component species and at the end of the calculation,
     *                  when we want to return unscrambled results. All rxn
     *                  data will be out-of-date.
     *
     *  @param k1        First species index
     *  @param k2        Second species index
     */
    void vcs_switch_pos(const bool ifunc, const size_t k1, const size_t k2);

    //! Birth guess returns the number of moles of a species
    //! that is coming back to life.
    /*!
     *  Birth guess returns the number of moles of a species that is coming
     *  back to life. Note, this routine is not applicable if the whole phase
     *  is coming back to life, not just one species in that phase.
     *
     *  Do a minor alt calculation. But, cap the mole numbers at 1.0E-15. For
     *  SS phases use VCS_DELETE_SPECIES_CUTOFF * 100.
     *
     *  The routine makes sure the guess doesn't reduce the concentration of a
     *  component by more than 1/3. Note this may mean that the vlaue coming
     *  back from this routine is zero or a very small number.
     *
     * @param kspec   Species number that is coming back to life
     * @return      Returns the number of kmol that the species should have.
     */
    double vcs_birthGuess(const int kspec);

    //! Routine that independently determines whether a phase should be popped
    //! under the current conditions.
    /*
     * This is the main routine that solves for equilibrium at constant T and
     * P using a variant of the VCS method. Nonideal phases can be
     * accommodated as well. Any number of single-species phases and multi-
     * species phases can be handled by the present version.
     *
     * @param print_lvl     1 -> Print results to standard output; -> don't
     *     report on anything
     * @param printDetails  1 -> Print intermediate results.
     * @param maxit         Maximum number of iterations for the algorithm
     *
     * @return
     * - 0 = Equilibrium Achieved
     * - 1 = Range space error encountered. The element abundance criteria are
     *   only partially satisfied. Specifically, the first NC= (number of
     *   components) conditions are satisfied. However, the full NE (number of
     *   elements) conditions are not satisfied. The equilibrium condition is
     *   returned.
     * - -1 = Maximum number of iterations is exceeded. Convergence was not
     *   found.
     */
    int vcs_solve_phaseStability(const int iphase, int ifunc, double& funcval, int print_lvl);

    //! Main program to test whether a deleted phase should be brought
    //! back into existence
    /*!
     * @param iph Phase id of the deleted phase
     */
    double vcs_phaseStabilityTest(const size_t iph);

    //! Solve an equilibrium problem at a particular fixed temperature
    //! and pressure
    /*!
     *  The actual problem statement is assumed to be in the structure
     *  already.  This is a wrapper around the solve_TP() function. In this
     *  wrapper, we nondimensionalize the system we calculate the standard
     *  state Gibbs free energies of the species, and we decide whether to we
     *  need to use the initial guess algorithm.
     *
     * @param ipr = 1 -> Print results to standard output;
     *              0 -> don't report on anything
     * @param ip1 = 1 -> Print intermediate results;
     *              0 -> Dont print any intermediate results
     * @param maxit  Maximum number of iterations for the algorithm
     * @param T    Value of the Temperature (Kelvin)
     * @param pres Value of the Pressure (units given by m_VCS_UnitsFormat variable
     *
     * @return Returns an integer representing the success of the algorithm
     * * 0 = Equilibrium Achieved
     * * 1 = Range space error encountered. The element abundance criteria are
     *   only partially satisfied. Specifically, the first NC= (number of
     *   components) conditions are satisfied. However, the full NE (number of
     *   elements) conditions are not satisfied. The equilibrium condition is
     *   returned.
     * * -1 = Maximum number of iterations is exceeded. Convergence was not
     *   found.
     */
    int vcs_TP(int ipr, int ip1, int maxit, double T, double pres);

    /*!
     * Evaluate the standard state free energies at the current temperature
     * and pressure. Ideal gas pressure contribution is added in here.
     *
     * @param  ipr   1 -> Print results to standard output;  0 -> don't report
     *     on anything
     * @param  ip1   1 -> Print intermediate results; 0 -> don't.
     * @param  Temp  Temperature (Kelvin)
     * @param  pres  Pressure (Pascal)
     */
    int vcs_evalSS_TP(int ipr, int ip1, double Temp, double pres);

    //! Initialize the chemical potential of single species phases
    /*!
     * For single species phases, initialize the chemical potential with the
     * value of the standard state chemical potential. This value doesn't
     * change during the calculation
     */
    void vcs_fePrep_TP();

    //! Calculation of the total volume and the partial molar volumes
    /*!
     *  This function calculates the partial molar volume for all species,
     *  kspec, in the thermo problem at the temperature TKelvin and pressure,
     *  Pres, pres is in atm. And, it calculates the total volume of the
     *  combined system.
     *
     * @param[in] tkelvin   Temperature in kelvin()
     * @param[in] pres      Pressure in Pascal
     * @param[in] w         w[] is the vector containing the current mole
     *                      numbers in units of kmol.
     * @param[out] volPM[]  For species in all phase, the entries are the
     *                      partial molar volumes units of M**3 / kmol.
     * @return              The return value is the total volume of
     *                      the entire system in units of m**3.
     */
    double vcs_VolTotal(const double tkelvin, const double pres,
                        const double w[], double volPM[]);

    //!  This routine is mostly concerned with changing the private data
    //!  to be consistent with what's needed for solution. It is called one
    //!  time for each new problem structure definition.
    /*!
     *  This routine is always followed by vcs_prep(). Therefore, tasks
     *  that need to be done for every call to vcsc() should be placed in
     *  vcs_prep() and not in this routine.
     *
     *  The problem structure refers to:
     *
     *  - the number and identity of the species.
     *  - the formula matrix and thus the number of components.
     *  - the number and identity of the phases.
     *  - the equation of state
     *  - the method and parameters for determining the standard state
     *  - The method and parameters for determining the activity coefficients.
     *
     * Tasks:
     *    1. Fill in the SSPhase[] array.
     *    2. Check to see if any multispecies phases actually have only one
     *       species in that phase. If true, reassign that phase and species
     *       to be a single-species phase.
     *    3. Determine the number of components in the problem if not already
     *       done so. During this process the order of the species is changed
     *       in the private data structure. All references to the species
     *       properties must employ the ind[] index vector.
     *
     *  @param printLvl Print level of the routine
     *  @return VCS_SUCCESS = everything went OK
     */
    int vcs_prep_oneTime(int printLvl);

    //! Prepare the object for solution
    /*!
     *  This routine is mostly concerned with changing the private data
     *  to be consistent with that needed for solution. It is called for
     *  every invocation of the vcs_solve() except for the cleanup invocation.
     *
     * Tasks:
     *   1. Initialization of arrays to zero.
     *
     * @return
     *     VCS_SUCCESS = everything went OK;
     *     VCS_PUB_BAD = There is an irreconcilable difference in the
     *                   public data structure from when the problem was
     *                   initially set up.
     */
    int vcs_prep();

    //! In this routine, we check for things that will cause the algorithm
    //! to fail.
    /*!
     *  We check to see if the problem is well posed. If it is not, we return
     *  false and print out error conditions.
     *
     *  Current there is one condition. If all the element abundances are
     *  zero, the algorithm will fail.
     *
     * @param vprob   VCS_PROB pointer to the definition of the equilibrium
     *                problem
     *
     * @return  If true, the problem is well-posed. If false, the problem
     *          is not well posed.
     */
    bool vcs_wellPosed(VCS_PROB* vprob);

    //! Rearrange the constraint equations represented by the Formula
    //! Matrix so that the operational ones are in the front
    /*!
     * This subroutine handles the rearrangement of the constraint equations
     * represented by the Formula Matrix. Rearrangement is only necessary when
     * the number of components is less than the number of elements. For this
     * case, some constraints can never be satisfied exactly, because the
     * range space represented by the Formula Matrix of the components can't
     * span the extra space. These constraints, which are out of the range
     * space of the component Formula matrix entries, are migrated to the back
     * of the Formula matrix.
     *
     * A prototypical example is an extra element column in FormulaMatrix[],
     * which is identically zero. For example, let's say that argon is has an
     * element column in FormulaMatrix[], but no species in the mechanism
     * actually contains argon. Then, nc < ne. Also, without perturbation of
     * FormulaMatrix[] vcs_basopt[] would produce a zero pivot because the
     * matrix would be singular (unless the argon element column was already
     * the last column of  FormulaMatrix[].
     *
     * This routine borrows heavily from vcs_basopt's algorithm. It finds nc
     * constraints which span the range space of the Component Formula matrix,
     * and assigns them as the first nc components in the formula matrix. This
     * guarantees that vcs_basopt[] has a nonsingular matrix to invert.
     *
     * Other Variables
     *  @param aw   Mole fraction work space        (ne in length)
     *  @param sa   Gram-Schmidt orthog work space (ne in length)
     *  @param sm   QR matrix work space (ne*ne in length)
     *  @param ss   Gram-Schmidt orthog work space (ne in length)
     */
    int vcs_elem_rearrange(double* const aw, double* const sa,
                           double* const sm, double* const ss);

    //!  Swaps the indices for all of the global data for two elements, ipos
    //!  and jpos.
    /*!
     *  This function knows all of the element information with VCS_SOLVE, and
     *  can therefore switch element positions
     *
     *  @param ipos  first global element index
     *  @param jpos  second global element index
     */
    void vcs_switch_elem_pos(size_t ipos, size_t jpos);

    //!  Calculates reaction adjustments using a full Hessian approximation
    /*!
     * This does what equation 6.4-16, p. 143 in Smith and Missen is supposed
     * to do. However, a full matrix is formed and then solved via a conjugate
     * gradient algorithm. No preconditioning is done.
     *
     * If special branching is warranted, then the program bails out.
     *
     * Output
     * -------
     * DS(I) : reaction adjustment, where I refers to the Ith species
     * Special branching occurs sometimes. This causes the component basis
     * to be reevaluated
     *     return = 0 : normal return
     *              1 : A single species phase species has been zeroed out
     *                  in this routine. The species is a noncomponent
     *              2 : Same as one but, the zeroed species is a component.
     *
     * Special attention is taken to flag cases where the direction of the
     * update is contrary to the steepest descent rule. This is an important
     * attribute of the regular vcs algorithm. We don't want to violate this.
     *
     *  NOTE: currently this routine is not used.
     */
    int  vcs_rxn_adj_cg(void);

    //!  Calculates the diagonal contribution to the Hessian due to
    //!  the dependence of the activity coefficients on the mole numbers.
    /*!
     *  (See framemaker notes, Eqn. 20 - VCS Equations document)
     *
     *  We allow the diagonal to be increased positively to any degree.
     *  We allow the diagonal to be decreased to 1/3 of the ideal solution
     *  value, but no more -> it must remain positive.
     *
     *  NOTE: currently this routine is not used
     */
    double vcs_Hessian_diag_adj(size_t irxn, double hessianDiag_Ideal);

    //! Calculates the diagonal contribution to the Hessian due to
    //!  the dependence of the activity coefficients on the mole numbers.
    /*!
     *  (See framemaker notes, Eqn. 20 - VCS Equations document)
     *
     *  NOTE: currently this routine is not used
     */
    double vcs_Hessian_actCoeff_diag(size_t irxn);

    //! Recalculate all of the activity coefficients in all of the phases
    //! based on input mole numbers
    /*
     * @param moleSpeciesVCS kmol of species to be used in the update.
     *
     * NOTE: This routine needs to be regulated.
     */
    void vcs_CalcLnActCoeffJac(const double* const moleSpeciesVCS);

    //! A line search algorithm is carried out on one reaction
    /*!
     *  In this routine we carry out a rough line search algorithm to make
     *  sure that the m_deltaGRxn_new doesn't switch signs prematurely.
     *
     *  @param irxn     Reaction number
     *  @param dx_orig  Original step length
     *
     *  @param ANOTE    Output character string stating the conclusions of the
     *                  line search
     *  @return         Returns the optimized step length found by the search
     */
    double vcs_line_search(const size_t irxn, const double dx_orig,
                           char* const ANOTE=0);

    //!   Print out a report on the state of the equilibrium problem to
    //!   standard output.
    /*!
     *  @param iconv Indicator of convergence, to be printed out in the report:
     *    -   0 converged
     *    -   1 range space error
     *    -  -1 not converged
     */
    int vcs_report(int iconv);

    //!  Switch all species data back to the original order.
    /*!
     *  This destroys the data based on reaction ordering.
     */
    int vcs_rearrange();

    //! Returns the multiplier for electric charge terms
    /*
     *   This is basically equal to F/RT
     *
     * @param mu_units integer representing the dimensional units system
     * @param TKelvin  double  Temperature in Kelvin
     *
     * @return Returns the value of F/RT
     */
    double vcs_nondim_Farad(int mu_units, double TKelvin) const;

    //! Returns the multiplier for the nondimensionalization of the equations
    /*!
     *   This is basically equal to RT
     *
     * @param mu_units integer representing the dimensional units system
     * @param TKelvin  double  Temperature in Kelvin
     *
     * @return Returns the value of RT
     */
    double vcs_nondimMult_TP(int mu_units, double TKelvin) const;

    //! Nondimensionalize the problem data
    /*!
     *   Nondimensionalize the free energies using the divisor, R * T
     *
     *  Essentially the internal data can either be in dimensional form
     *  or in nondimensional form. This routine switches the data from
     *  dimensional form into nondimensional form.
     *
     *  @todo Add a scale factor based on the total mole numbers.
     *        The algorithm contains hard coded numbers based on the
     *        total mole number. If we ever were faced with a problem
     *        with significantly different total kmol numbers than one
     *        the algorithm would have problems.
     */
    void   vcs_nondim_TP();

    //! Redimensionalize the problem data
    /*!
     *   Reddimensionalize the free energies using the multiplier R * T
     *
     *  Essentially the internal data can either be in dimensional form
     *  or in nondimensional form. This routine switches the data from
     *  nondimensional form into dimensional form.
     */
    void   vcs_redim_TP();

    //! Print the string representing the Chemical potential units
    /*!
     *  This gets printed using plogf()
     *
     * @param unitsFormat   Integer representing the units system
     */
    void   vcs_printChemPotUnits(int unitsFormat) const;

    //! Computes the current elemental abundances vector
    /*!
     *   Computes the elemental abundances vector, m_elemAbundances[], and stores it
     *   back into the global structure
     */
    void vcs_elab();

    /*!
     * Checks to see if the element abundances are in compliance. If they are,
     * then TRUE is returned. If not, FALSE is returned. Note the number of
     * constraints checked is usually equal to the number of components in the
     * problem. This routine can check satisfaction of all of the constraints
     * in the problem, which is equal to ne. However, the solver can't fix
     * breakage of constraints above nc, because that nc is the range space by
     * definition. Satisfaction of extra constraints would have had to occur
     * in the problem specification.
     *
     * The constraints should be broken up into 2  sections. If a constraint
     * involves a formula matrix with positive and negative signs, and eaSet =
     * 0.0, then you can't expect that the sum will be zero. There may be
     * roundoff that inhibits this. However, if the formula matrix is all of
     * one sign, then this requires that all species with nonzero entries in
     * the formula matrix be identically zero. We put this into the logic
     * below.
     *
     *  @param ibound  1: Checks constraints up to the number of elements;
     *                 0: Checks constraints up to the number of components.
     */
    bool vcs_elabcheck(int ibound);

    /*!
     * Computes the elemental abundances vector for a single phase,
     * elemAbundPhase[], and returns it through the argument list. The mole
     * numbers of species are taken from the current value in
     * m_molNumSpecies_old[].
     */
    void vcs_elabPhase(size_t iphase, double* const elemAbundPhase);

    /*!
     * This subroutine corrects for element abundances. At the end of the
     * subroutine, the total moles in all phases are recalculated again,
     * because we have changed the number of moles in this routine.
     *
     * @param aa  temporary work vector, length ne*ne
     * @param x   temporary work vector, length ne
     *
     * @returns
     * - 0 = Nothing of significance happened, Element abundances were and
     *   still are good.
     * - 1 = The solution changed significantly; The element abundances are
     *   now good.
     * - 2 = The solution changed significantly, The element abundances are
     *   still bad.
     * - 3 = The solution changed significantly, The element abundances are
     *   still bad and a component species got zeroed out.
     *
     *  Internal data to be worked on::
     *  - ga    Current element abundances
     *  - m_elemAbundancesGoal   Required elemental abundances
     *  - m_molNumSpecies_old     Current mole number of species.
     *  - m_formulaMatrix[][]  Formula matrix of the species
     *  - ne    Number of elements
     *  - nc    Number of components.
     *
     * NOTES:
     *  This routine is turning out to be very problematic. There are
     *  lots of special cases and problems with zeroing out species.
     *
     *  Still need to check out when we do loops over nc vs. ne.
     *
     */
    int vcs_elcorr(double aa[], double x[]);

    //!  Create an initial estimate of the solution to the thermodynamic
    //!  equilibrium problem.
    /*!
     *    @return  Return value indicates success:
     *      -    0: successful initial guess
     *      -   -1: Unsuccessful initial guess; the elemental abundances aren't
     *              satisfied.
     */
    int vcs_inest_TP();

    //! Estimate the initial mole numbers by constrained linear programming
    /*!
     * This is done by running each reaction as far forward or backward as
     * possible, subject to the constraint that all mole numbers remain non-
     * negative. Reactions for which \f$ \Delta \mu^0 \f$ are positive are run
     * in reverse, and ones for which it is negative are run in the forward
     * direction. The end result is equivalent to solving the linear
     * programming problem of minimizing the linear Gibbs function subject to
     * the element and non-negativity constraints.
     */
    int vcs_setMolesLinProg();

    //! Calculate the total dimensionless Gibbs free energy
    /*!
     *  Inert species are handled as if they had a standard free energy of
     *  zero. Note, for this algorithm this function should be monotonically
     *  decreasing.
     */
    double vcs_Total_Gibbs(double* w, double* fe, double* tPhMoles);

    //! Calculate the total dimensionless Gibbs free energy of a single phase
    /*!
     *  Inert species are handled as if they had a standard free energy of
     *  zero and if they obeyed ideal solution/gas theory.
     *
     * @param iphase   ID of the phase
     * @param w        Species mole number vector for all species
     * @param fe       vector of partial molar free energies of all of the
     *                 species
     */
    double vcs_GibbsPhase(size_t iphase, const double* const w,
                          const double* const fe);

    //! Transfer the results of the equilibrium calculation back to VCS_PROB
    /*!
     *   The VCS_PROB structure is returned to the user.
     *
     *  @param pub  Pointer to VCS_PROB object that will get the results of the
     *              equilibrium calculation transfered to it.
     */
    int vcs_prob_update(VCS_PROB* pub);

    //! Fully specify the problem to be solved using VCS_PROB
    /*!
     *  Use the contents of the VCS_PROB to specify the contents of the
     *  private data, VCS_SOLVE.
     *
     *  @param pub  Pointer to VCS_PROB that will be used to
     *              initialize the current equilibrium problem
     */
    int vcs_prob_specifyFully(const VCS_PROB* pub);

    //! Specify the problem to be solved using VCS_PROB, incrementally
    /*!
     *  Use the contents of the VCS_PROB to specify the contents of the
     *  private data, VCS_SOLVE.
     *
     *  It's assumed we are solving the same problem.
     *
     *  @param pub  Pointer to VCS_PROB that will be used to
     *              initialize the current equilibrium problem
     */
    int vcs_prob_specify(const VCS_PROB* pub);

private:

    //!  Zero out the concentration of a species.
    /*!
     *  Make sure to conserveelements and keep track of the total moles in all
     *  phases.
     *  - w[]
     *  - m_tPhaseMoles_old[]
     *
     *  @param kspec  Species index
     *
     *  @return:
     *      1: succeeded
     *      0: failed.
     */
    int vcs_zero_species(const size_t kspec);

    //! Change a single species from active to inactive status
    /*!
     * Rearrange data when species is added or removed. The Lth species is
     * moved to the back of the species vector. The back of the species
     * vector is indicated by the value of MR, the current number of
     * active species in the mechanism.
     *
     * @param kspec   Species Index
     * @return
     *     Returns 0 unless.
     *     The return is 1 when the current number of
     *     noncomponent species is equal to zero. A recheck of deleted species
     *     is carried out in the main code.
     */
    int vcs_delete_species(const size_t kspec);

    //! This routine handles the bookkeeping involved with the
    //!  deletion of multiphase phases from the problem.
    /*!
     *   When they are deleted, all of their species become active
     *   species, even though their mole numbers are set to zero.
     *   The routine does not make the decision to eliminate multiphases.
     *
     *   Note, species in phases with zero mole numbers are still
     *   considered active. Whether the phase pops back into
     *   existence or not is checked as part of the main iteration
     *   loop.
     *
     * @param iph Phase to be deleted
     *
     * @return Returns whether the operation was successful or not
     */
    bool vcs_delete_multiphase(const size_t iph);

    //!  Change the concentration of a species by delta moles.
    /*!
     *  Make sure to conserve elements and keep track of the total kmoles in
     *  all phases.
     *
     *  @param kspec The species index
     *  @param delta_ptr   pointer to the delta for the species. This may
     *                     change during the calculation
     *
     *  @return
     *      1: succeeded without change of dx
     *      0: Had to adjust dx, perhaps to zero, in order to do the delta.
     */
    int delta_species(const size_t kspec, double* const delta_ptr);

    //!  Provide an estimate for the deleted species in phases that
    //!  are not zeroed out
    /*!
     *  Try to add back in all deleted species. An estimate of the kmol numbers
     *  are obtained and the species is added back into the equation system,
     *  into the old state vector.
     *
     *  This routine is called at the end of the calculation, just before
     *  returning to the user.
     */
    size_t vcs_add_all_deleted();

    //! Recheck deleted species in multispecies phases.
    /*!
     *   We are checking the equation:
     *
     *         sum_u = sum_j_comp [ sigma_i_j * u_j ]
     *               = u_i_O + log((AC_i * W_i)/m_tPhaseMoles_old)
     *
     *   by first evaluating:
     *
     *          DG_i_O = u_i_O - sum_u.
     *
     *   Then, if TL is zero, the phase pops into existence if DG_i_O < 0.
     *   Also, if the phase exists, then we check to see if the species
     *   can have a mole number larger than  VCS_DELETE_SPECIES_CUTOFF
     *   (default value = 1.0E-32).
     *
     */
    int vcs_recheck_deleted();

    //! Recheck deletion condition for multispecies phases.
    /*!
     *  We assume here that DG_i_0 has been calculated for deleted species correctly
     *
     *      m_feSpecies(I) = m_SSfeSpecies(I)
     *                     + ln(ActCoeff[I])
     *                     - ln(Mnaught * m_units)
     *                     + m_chargeSpecies[I] * Faraday_dim * m_phasePhi[iphase];
     *
     *      sum_u = sum_j_comp [ sigma_i_j * u_j ]
     *            = u_i_O + log((AC_i * W_i)/m_tPhaseMoles_old)
     *
     *      DG_i_0 =  m_feSpecies(I) - sum_m{ a_i_m  DG_m }
     *
     *  by first evaluating:
     *
     *      DG_i_O = u_i_O - sum_u.
     *
     *  Then, the phase pops into existence iff
     *
     *      phaseDG = 1.0 - sum_i{exp(-DG_i_O)}  < 0.0
     *
     *  This formula works for both single species phases and for multispecies
     *  phases. It's an overkill for single species phases.
     *
     *  @param iphase Phase index number
     *
     *  @return   Returns true if the phase is currently deleted
     *            but should be reinstated. Returns false otherwise.
     *
     *  NOTE: this routine is currently not used in the code, and
     *       contains some basic changes that are incompatible.
     *
     *  assumptions:
     *    1. Vphase Existence is up to date
     *    2. Vphase->IndSpecies is up to date
     *    3. m_deltaGRxn_old[irxn] is up to date
     */
    bool recheck_deleted_phase(const int iphase);

    //! Minor species alternative calculation
    /*!
     *  This is based upon the following approximation: The mole fraction
     *  changes due to these reactions don't affect the mole numbers of the
     *  component species. Therefore the following approximation is valid for
     *  a small component of an ideal phase:
     *
     *       0 = m_deltaGRxn_old(I) + log(molNum_new(I)/molNum_old(I))
     *
     *  `m_deltaGRxn_old` contains the contribution from
     *
     *       m_feSpecies_old(I) =
     *              m_SSfeSpecies(I) +
     *              log(ActCoeff[i] * molNum_old(I) / m_tPhaseMoles_old(iph))
     *  Thus,
     *
     *       molNum_new(I)= molNum_old(I) * EXP(-m_deltaGRxn_old(I))
     *
     *  Most of this section is mainly restricting the update to reasonable
     *  values. We restrict the update a factor of 1.0E10 up and 1.0E-10 down
     *  because we run into trouble with the addition operator due to roundoff
     *  if we go larger than ~1.0E15. Roundoff will then sometimes produce
     *  zero mole fractions.
     *
     *  Note: This routine was generalized to incorporate nonideal phases and
     *  phases on the molality basis
     *
     *  @param[in] kspec   The current species and corresponding formation
     *                     reaction number.
     *  @param[in] irxn    The current species and corresponding formation
     *                     reaction number.
     *  @param[out] do_delete:  BOOLEAN which if true on return, then we
     *                          branch to the section that deletes a species
     *                          from the current set of active species.
     */
    double vcs_minor_alt_calc(size_t kspec, size_t irxn, bool* do_delete,
                              char* ANOTE=0) const;

    //! This routine optimizes the minimization of the total Gibbs free energy
    //! by making sure the slope of the following functional stays negative:
    /*!
     *  The slope of the following functional is equivalent to the slope
     *  of the total Gibbs free energy of the system:
     *
     *      d_Gibbs/ds = sum_k( m_deltaGRxn * m_deltaMolNumSpecies[k] )
     *
     *  along the current direction m_deltaMolNumSpecies[], by choosing a value, al: (0<al<1)
     *  such that the a parabola approximation to Gibbs(al) fit to the
     *  end points al = 0 and al = 1 is minimized.
     *  - s1 = slope of Gibbs function at al = 0, which is the previous
     *    solution = d(Gibbs)/d(al).
     *  - s2 = slope of Gibbs function at al = 1, which is the current
     *    solution = d(Gibbs)/d(al).
     *
     *  Only if there has been an inflection point (i.e., s1 < 0 and s2 > 0),
     *  does this code section kick in. It finds the point on the parabola
     *  where the slope is equal to zero.
     */
    bool vcs_globStepDamp();

    //! Calculate the norm of a deltaGibbs free energy vector
    /*!
     *   Positive DG for species which don't exist are ignored.
     *
     * @param dg Vector of local delta G's.
     */
    double l2normdg(double dg[]) const;

#ifdef DEBUG_MODE

    //! Print out and check the elemental abundance vector
    void prneav() const;
#endif

    void checkDelta1(double* const ds, double* const delTPhMoles, size_t kspec);

    //! Estimate equilibrium compositions
    /*!
     *  Algorithm covered in a section of Smith and Missen's Book.
     *
     *  Linear programming module is based on using dbolm.
     *
     *  @param aw   aw[i[  Mole fraction work space        (ne in length)
     *  @param sa   sa[j] = Gram-Schmidt orthog work space (ne in length)
     *  @param sm   sm[i+j*ne] = QR matrix work space (ne*ne in length)
     *  @param ss   ss[j] = Gram-Schmidt orthog work space (ne in length)
     *  @param test This is a small negative number.
     */
    void vcs_inest(double* const aw, double* const sa, double* const sm,
                   double* const ss, double test);

    //!  Calculate the status of single species phases.
    void vcs_SSPhase(void);

    //! This function recalculates the deltaG for reaction, irxn
    /*!
     * This function recalculates the deltaG for reaction irxn, given the mole
     * numbers in molNum. It uses the temporary space mu_i, to hold the
     * recalculated chemical potentials. It only recalculates the chemical
     * potentials for species in phases which participate in the irxn
     * reaction. This function is used by the vcs_line_search algorithm() and
     * should not be used widely due to the unknown state it leaves the
     * system.
     *
     * @param[in] irxn    Reaction number
     * @param[in] molNum  Current mole numbers of species to be used as input
     *         to the calculation (units = kmol), (length = totalNuMSpecies)
     *
     * @param[out] ac  Activity coefficients   (length = totalNumSpecies) Note
     *         this is only partially formed. Only species in phases that
     *         participate in the reaction will be updated
     * @param[out] mu_i  dimensionless chemical potentials (length
     *         totalNumSpecies) Note this is only partially formed. Only
     *         species in phases that participate in the reaction will be
     *         updated
     *
     * @return Returns the dimensionless deltaG of the reaction
     */
    double deltaG_Recalc_Rxn(const int stateCalc,
                             const size_t irxn, const double* const molNum,
                             double* const ac, double* const mu_i);

    //! Delete memory that isn't just resizable STL containers
    /*!
     * This gets called by the destructor or by InitSizes().
     */
    void vcs_delete_memory();

    //! Initialize the internal counters
    /*!
     * Initialize the internal counters containing the subroutine call
     * values and times spent in the subroutines.
     *
     *  ifunc = 0     Initialize only those counters appropriate for the top of
     *                vcs_solve_TP().
     *        = 1     Initialize all counters.
     */
    void vcs_counters_init(int ifunc);

    //! Create a report on the plog file containing timing and its information
    /*!
     *   @param timing_print_lvl If 0, just report the iteration count.
     *                If larger than zero, report the timing information
     */
    void vcs_TCounters_report(int timing_print_lvl = 1);

    void vcs_setFlagsVolPhases(const bool upToDate, const int stateCalc);

    void vcs_setFlagsVolPhase(const size_t iph, const bool upToDate, const int stateCalc);

    //! Update all underlying vcs_VolPhase objects
    /*!
     *  Update the mole numbers and the phase voltages of all phases in the
     *  vcs problem
     *
     *  @param stateCalc Location of the update (either VCS_STATECALC_NEW or
     *         VCS_STATECALC_OLD).
     */
    void vcs_updateMolNumVolPhases(const int stateCalc);

    // Helper functions used internally by vcs_solve_TP
    int solve_tp_component_calc(bool& allMinorZeroedSpecies);
    void solve_tp_inner(size_t& iti, size_t& it1, bool& uptodate_minors,
                        bool& allMinorZeroedSpecies, int& forceComponentCalc,
                        int& stage, bool printDetails, char* ANOTE);
    void solve_tp_equilib_check(bool& allMinorZeroedSpecies, bool& uptodate_minors,
                                bool& giveUpOnElemAbund, int& solveFail,
                                size_t& iti, size_t& it1, int maxit,
                                int& stage, bool& lec);
    void solve_tp_elem_abund_check(size_t& iti, int& stage, bool& lec,
                                   bool& giveUpOnElemAbund,
                                   int& finalElemAbundAttempts,
                                   int& rangeErrorFound);

    // data used by vcs_solve_TP and it's helper functions
    std::vector<double> m_sm;
    std::vector<double> m_ss;
    std::vector<double> m_sa;
    std::vector<double> m_aw;
    std::vector<double> m_wx;

public:
    //! Calculate the rank of a matrix and return the rows and columns that
    //! will generate an independent basis for that rank
    /*
     * Choose the optimum component species basis for the calculations,
     * finding the rank and set of linearly independent rows for that
     * calculation. Then find the set of linearly indepedent element columns
     * that can support that rank. This is done by taking the transpose of the
     * matrix and redoing the same calculation. (there may be a better way to
     * do this. I don't know.)
     *
     * @param[in] awtmp  Vector of mole numbers which will be used to
     *         construct a ranking for how to pick the basis species. This is
     *         largely ignored here.
     * @param[in] numSpecies Number of species. This is the number of rows in
     *         the matrix.
     * @param[in] matrix This is the formula matrix. Nominally, the rows are
     *         species, while the columns are element compositions. However,
     *         this routine is totally general, so that the rows and columns
     *         can be anything.
     * @param[in] numElemConstraints Number of element constraints
     *
     * @param[out] usedZeroedSpecies  If true, then a species with a zero
     *         concentration was used as a component.
     * @param[out] compRes  Vector of rows which are linearly independent.
     *         (these are the components)
     * @param[out] elemComp  Vector of columns which are linearly independent
     *         (These are the actionable element constraints).
     *
     * @return  Returns number of components. This is the rank of the matrix
     * @deprecated To be removed after Cantera 2.2.
     */
    int vcs_rank(const double* awtmp, size_t numSpecies, const double* matrix,  size_t numElemConstraints,
                 std::vector<size_t> &compRes, std::vector<size_t> &elemComp, int* const usedZeroedSpecies) const;

    //! value of the number of species  used to malloc data structures
    size_t NSPECIES0;

    //! value of the number of phases  used to malloc data structures
    size_t NPHASE0;

    //!  Total number of species in the problems
    size_t m_numSpeciesTot;

    //! Number of element constraints in the problem
    /*!
     * This is typically equal to the number of elements in the problem
     */
    size_t m_numElemConstraints;

    //! Number of components calculated for the problem
    size_t m_numComponents;

    //! Total number of non-component species in the problem
    size_t m_numRxnTot;

    //! Current number of species in the problems
    /*!
     * Species can be deleted if they aren't
     * stable under the current conditions
     */
    size_t m_numSpeciesRdc;

    //! Current number of non-component species in the problem
    /*!
     * Species can be deleted if they aren't
     * stable under the current conditions
     */
    size_t m_numRxnRdc;

    //!  Number of active species which are currently either treated as
    //!  minor species
    size_t m_numRxnMinorZeroed;

    //! Number of Phases in the problem
    size_t m_numPhases;

    //! Formula matrix for the problem
    /*!
     *  FormulaMatrix(kspec,j) =  Number of elements, j, in the kspec species
     *
     *  Both element and species indices are swapped.
     */
    Array2D m_formulaMatrix;

    //! Stoichiometric coefficient matrix for the reaction mechanism expressed in Reduced Canonical Form.
    /*!
     *   This is the stoichiometric coefficient matrix for the
     *   reaction which forms species kspec from the component species. A
     *   stoichiometric coefficient of one is assumed for the species kspec in this mechanism.
     *
     *   NOTE: kspec = irxn + m_numComponents
     *
     *   m_stoichCoeffRxnMatrix(j,irxn) :
     *     j refers to the component number, and irxn refers to the irxn_th non-component species.
     *     The stoichiometric coefficients multilplied by the Formula coefficients of the
     *     component species add up to the negative value of the number of elements in
     *     the species kspec.
     *
     *   size = nelements0 x nspecies0
     */
    Array2D m_stoichCoeffRxnMatrix;

    //! Absolute size of the stoichiometric coefficients
    /*!
     *  scSize[irxn] = abs(Size) of the stoichiometric
     *               coefficients. These are used to determine
     *               whether a given species should be
     *               handled by the alt_min treatment or
     *               should be handled as a major species.
     */
    std::vector<double> m_scSize;

    //! total size of the species
    /*!
     *  This is used as a multiplier to the mole number in figuring out which
     *  species should be components.
     */
    std::vector<double> m_spSize;

    //!  Standard state chemical potentials for species K at the current
    //!  temperature and pressure.
    /*!
     *  The first NC entries are for components. The following NR entries are
     *  for the current non-component species in the mechanism.
     */
    std::vector<double> m_SSfeSpecies;

    //! Free energy vector from the start of the current iteration
    /*!
     *  The free energies are saved at the start of the current iteration.
     *  Length = number of species
     */
    std::vector<double> m_feSpecies_old;

    //! Dimensionless new free energy for all the species in the mechanism
    //! at the new tentatite T, P, and mole numbers.
    /*!
     *   The first NC entries are for components. The following
     *   NR entries are for the current  non-component species in the mechanism.
     *  Length = number of species
     */
    std::vector<double> m_feSpecies_new;

    //! Setting for whether to do an initial estimate
    /*!
     *  Initial estimate:
     *      *  0 Do not estimate the solution at all. Use the
     *      *    supplied mole numbers as is.
     *      *  1 Only do an estimate if the element abundances
     *      *    aren't satisfied.
     *      * -1 Force an estimate of the soln. Throw out the input
     *      *    mole numbers.
     */
    int m_doEstimateEquil;

    //! Total moles of the species
    /*!
     *  Total number of moles of the kth species.
     *  Length = Total number of species = m
     */
    std::vector<double> m_molNumSpecies_old;

    //! Specifies the species unknown type
    /*!
     *  There are two types. One is the straightforward species, with the mole
     *  number w[k], as the unknown. The second is the an interfacial voltage
     *  where w[k] refers to the interfacial voltage in volts.
     *
     *  These species types correspond to metallic electrons corresponding to
     *  electrodes. The voltage and other interfacial conditions sets up an
     *  interfacial current, which is set to zero in this initial treatment.
     *  Later we may have non-zero interfacial currents.
     */
    std::vector<int> m_speciesUnknownType;

    //! Change in the number of moles of phase, iphase, due to the
    //! noncomponent formation reaction, irxn, for species, k:
    /*!
     *       m_deltaMolNumPhase(iphase,irxn) = k = nc + irxn
     */
    Array2D m_deltaMolNumPhase;

    //!  This is 1 if the phase, iphase,  participates in the formation reaction
    //!  irxn, and zero otherwise.  PhaseParticipation(iphase,irxn)
    Array2D m_phaseParticipation;

    //! electric potential of the iph phase
    std::vector<double> m_phasePhi;

    //! Tentative value of the mole number vector. It's also used to store the
    //! mole fraction vector.
    //std::vector<double> wt;
    std::vector<double> m_molNumSpecies_new;

    //! Delta G(irxn) for the noncomponent species in the mechanism.
    /*!
     *    Computed by the  subroutine  deltaG. m_deltaGRxn is the free
     *    energy change for the reaction which forms species K from the
     *    component species. This vector has length equal to the number
     *    of noncomponent species in the mechanism. It starts with
     *    the first current noncomponent species in the mechanism.
     */
    std::vector<double> m_deltaGRxn_new;

    //!  Last deltag[irxn] from the previous step
    std::vector<double> m_deltaGRxn_old;

    //! Last deltag[irxn] from the previous step with additions for
    //! possible births of zeroed phases.
    std::vector<double> m_deltaGRxn_Deficient;

    //! Temporary vector of Rxn DeltaG's
    /*!
     *  This is used from time to time, for printing purposes
     */
    std::vector<double> m_deltaGRxn_tmp;

    //! Reaction Adjustments for each species during the current step
    /*!
     *  delta Moles for each species during the current step.
     *  Length = number of species
     */
    std::vector<double> m_deltaMolNumSpecies;

    //!  Element abundances vector
    /*!
     *  Vector of moles of each element actually in the solution
     *  vector. Except for certain parts of the algorithm,
     *  this is a constant.
     *  Note other constraint conditions are added to this vector.
     *  This is input from the input file and
     *  is considered a constant from thereon.
     *   units = kmoles
     */
    std::vector<double> m_elemAbundances;

    //! Element abundances vector Goals
    /*!
     *  Vector of moles of each element that are the goals of the simulation.
     *  This is a constant in the problem. Note other constraint conditions
     *  are added to this vector. This is input from the input file and is
     *  considered a constant from thereon. units = kmoles
     */
    std::vector<double> m_elemAbundancesGoal;

    //! Total number of kmoles in all phases
    /*!
     * This number includes the inerts.
     *            -> Don't use this except for scaling purposes
     */
    double m_totalMolNum;

    //! Total kmols of species in each phase
    /*!
     *  This contains the total number of moles of species in each phase
     *
     *  Length = number of phases
     */
    std::vector<double> m_tPhaseMoles_old;

    //! total kmols of species in each phase in the tentative soln vector
    /*!
     *  This contains the total number of moles of species in each phase
     *  in the tentative solution vector
     *
     *  Length = number of phases
     */
    std::vector<double> m_tPhaseMoles_new;

    //! Temporary vector of length NPhase
    mutable std::vector<double> m_TmpPhase;

    //! Temporary vector of length NPhase
    mutable std::vector<double> m_TmpPhase2;

    //! Change in the total moles in each phase
    /*!
     *  Length number of phases.
     */
    std::vector<double> m_deltaPhaseMoles;

    //! Temperature (Kelvin)
    double   m_temperature;

    //! Pressure (units are determined by m_VCS_UnitsFormat
    /*!
     *  | Values | units |
     *  | ------ | -----
     *  |   -1:  | atm   |
     *  |    0:  | atm   |
     *  |    1:  | atm   |
     *  |    2:  | atm   |
     *  |    3:  | Pa    |
     *
     *  Units being changed to Pa
     */
    double m_pressurePA;

    //!  Total kmoles of inert to add to each phase
    /*!
     *  TPhInertMoles[iph] = Total kmoles of  inert to add to each phase
     *  length = number of phases
     */
    std::vector<double> TPhInertMoles;

    //! Tolerance requirement for major species
    double m_tolmaj;

    //! Tolerance requirements for minor species
    double m_tolmin;

    //! Below this, major species aren't refined  any more
    double m_tolmaj2;

    //! Below this, minor species aren't refined any more
    double m_tolmin2;

    //!  Index vector that keeps track of the species vector rearrangement
    /*!
     *  At the end of each run, the species vector and associated data gets put back
     *  in the original order.
     *
     * Example
     *
     *           k = m_speciesMapIndex[kspec]
     *
     *           kspec = current order in the vcs_solve object
     *           k     = original order in the vcs_prob object and in the MultiPhase object
     */
    std::vector<size_t> m_speciesMapIndex;

    //! Index that keeps track of the index of the species within the local
    //! phase
    /*!
     *  This returns the local index of the species within the phase. Its argument
     *  is the global species index within the VCS problem.
     *
     *  k = m_speciesLocalPhaseIndex[kspec]
     *
     *  k varies between 0 and the nSpecies in the phase
     *
     *  Length = number of species
     */
    std::vector<size_t> m_speciesLocalPhaseIndex;

    //! Index vector that keeps track of the rearrangement of the elements
    /*!
     *  At the end of each run, the element vector and associated data gets
     *  put back in the original order.
     *
     * Example
     *
     *     e    = m_elementMapIndex[eNum]
     *     eNum  = current order in the vcs_solve object
     *     e     = original order in the vcs_prob object and in the MultiPhase object
     */
    std::vector<size_t> m_elementMapIndex;

    //!  Mapping between the species index for noncomponent species and the
    //!  full species  index.
    /*!
     * ir[irxn]   = Mapping between the reaction index for noncomponent
     *              formation reaction of a species and the full species
     *              index.
     *
     * Initially set to a value of K = NC + I This vector has length equal to
     * number of noncomponent species in the mechanism. It starts with the
     * first current noncomponent species in the mechanism. kspec = ir[irxn]
     */
    std::vector<size_t> m_indexRxnToSpecies;

    //! Major -Minor status vector for the species in the problem
    /*!
     *  The index for this is species. The reaction that this is referring to
     *  is `kspec = irxn + m_numComponents`. For possible values and their
     *  meanings, see vcs_evaluate_speciesType().
     */
    std::vector<int> m_speciesStatus;

    //!  Mapping from the species number to the phase number
    std::vector<size_t> m_phaseID;

    //!  Boolean indicating whether a species belongs to a single-species phase
    // vector<bool> can't be used here because it doesn't work with std::swap
    std::vector<char> m_SSPhase;

    //! Species string name for the kth species
    std::vector<std::string> m_speciesName;

    //! Vector of strings containing the element names
    /*!
     *   ElName[j]  = String containing element names
     */
    std::vector<std::string> m_elementName;

    //! Type of the element constraint
    /*!
     *  * 0 - #VCS_ELEM_TYPE_ABSPOS Normal element that is positive or zero in
     *    all species.
     *  * 1 - #VCS_ELEM_TYPE_ELECTRONCHARGE element dof that corresponds to
     *    the electronic charge DOF.
     *  * 2 - #VCS_ELEM_TYPE_CHARGENEUTRALITY element dof that corresponds to
     *    a required charge neutrality constraint on the phase. The element
     *    abundance is always exactly zero.
     *  * 3 - #VCS_ELEM_TYPE_OTHERCONSTRAINT Other constraint which may mean
     *    that a species has neg 0 or pos value of that constraint (other than
     *    charge)
     */
    std::vector<int> m_elType;

    //! Specifies whether an element constraint is active
    /*!
     * The default is true. Length = nelements
     */
    std::vector<int> m_elementActive;

    //! Array of Phase Structures. Length = number of phases.
    std::vector<vcs_VolPhase*> m_VolPhaseList;

    //! String containing the title of the run
    std::string m_title;

    //! This specifies the current state of units for the Gibbs free energy
    //! properties in the program.
    /*!
     *  The default is to have this unitless
     */
    char  m_unitsState;

    //! Multiplier for the mole numbers within the nondimensionless formulation
    /*!
     *   All numbers within the main routine are on an absolute basis. This
     *   presents some problems wrt very large and very small mole numbers.
     *   We get around this by using a multiplier coming into and coming
     *   out of the equilibrium routines
     */
    double m_totalMoleScale;

    //! specifies the activity  convention of the phase containing the species
    /*!
     *  * 0 = molar based
     *  * 1 = molality based
     *
     *  length = number of species
     */
    std::vector<int> m_actConventionSpecies;

    //! specifies the activity convention of the phase.
    /*!
     *  * 0 = molar based
     *  * 1 = molality based
     *
     *  length = number of phases
     */
    std::vector<int> m_phaseActConvention;

    //!  specifies the ln(Mnaught) used to   calculate the chemical potentials
    /*!
     *  For molar based activity conventions this will be equal to 0.0.
     *  length = number of species.
     */
    std::vector<double> m_lnMnaughtSpecies;

    //! Molar-based Activity Coefficients for Species.
    //! Length = number of species
    std::vector<double> m_actCoeffSpecies_new;

    //!  Molar-based Activity Coefficients for Species based on old mole numbers
    /*!
     *  These activity coefficients are based on the m_molNumSpecies_old
     *  values Molar based activity coeffients. Length = number of species
     */
    std::vector<double> m_actCoeffSpecies_old;

    //! Change in the log of the activity coefficient with respect to the mole number
    //! multiplied by the phase mole number
    /*!
     *  size = nspecies x nspecies
     *
     *  This is a temporary array that gets regenerated every time it's
     *  needed. It is not swapped wrt species.
     */
    Array2D m_np_dLnActCoeffdMolNum;

    //! Molecular weight of each species
    /*!
     *  units = kg/kmol. length = number of species.
     *
     * note: this is a candidate for removal. I don't think we use it.
     */
    std::vector<double> m_wtSpecies;

    //! Charge of each species. Length = number of species.
    std::vector<double> m_chargeSpecies;

    std::vector<std::vector<size_t> > phasePopProblemLists_;

    //! Vector of pointers to thermostructures which identify the model
    //! and parameters for evaluating the  thermodynamic functions for that
    //! particular species.
    /*!
     * SpeciesThermo[k] pointer to the thermo information for the kth species
     */
    std::vector<VCS_SPECIES_THERMO*> m_speciesThermoList;

    //! Choice of Hessians
    /*!
     *  If this is true, then we will use a better approximation to the
     *  Hessian based on Jacobian of the  ln(ActCoeff) with respect to mole
     *  numbers
     */
    int m_useActCoeffJac;

    //! Total volume of all phases. Units are m^3
    double m_totalVol;

    //! Partial molar volumes of the species
    /*!
     *  units = mks (m^3/kmol) -determined by m_VCS_UnitsFormat
     *  Length = number of species
     */
    std::vector<double> m_PMVolumeSpecies;

    //! dimensionless value of Faraday's constant, F / RT  (1/volt)
    double m_Faraday_dim;

    //! Timing and iteration counters for the vcs object
    VCS_COUNTERS* m_VCount;

    //! Debug printing lvl
    /*!
     *  Levels correspond to the following guidlines
     *     * 0  No printing at all
     *     * 1  Serious warnings or fatal errors get one line
     *     * 2  one line per eacdh successful vcs package call
     *     * 3  one line per every successful solve_TP calculation
     *     * 4  one line for every successful operation -> solve_TP gets a summary report
     *     * 5  each iteration in solve_TP gets a report with one line per species
     *     * 6  Each decision in solve_TP gets a line per species in addition to 4
     *     * 10 Additionally Hessian matrix is printed out
     *
     *   Levels of printing above 4 are only accessible when DEBUG_MODE is turned on
     */
    int m_debug_print_lvl;

    //! printing level of timing information
    /*!
     *  * 1 allowing printing of timing
     *  * 0 do not allow printing of timing -> everything is printed as a NA.
     */
    int m_timing_print_lvl;

    //! Units for the chemical potential data
    /*!
     *  | Value | chemical potential units | pressure units |
     *  | ----- | ------------------------ | -------------- |
     *  | -1    |  kcal/mol                |       Pa       |
     *  |  0    |  MU/RT                   |       Pa       |
     *  |  1    |  kJ/mol                  |       Pa       |
     *  |  2    |  Kelvin                  |       Pa       |
     *  |  3    |  J / kmol                |       Pa       |
     */
    int m_VCS_UnitsFormat;

    friend class vcs_phaseStabilitySolve;
};

}
#endif