ReactionPath.cpp

Go to the documentation of this file.

/**
 *  @file ReactionPath.cpp
 *  Implementation file for classes used in reaction path analysis.
 */
 
// 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/base/ctexceptions.h"
#include "cantera/kinetics/ReactionPath.h"
#include "cantera/kinetics/Reaction.h"
#include "cantera/thermo/ThermoPhase.h"
 
#include <boost/algorithm/string.hpp>
 
namespace ba = boost::algorithm;
 
using namespace std;
 
namespace Cantera
{
 
void SpeciesNode::addPath(Path* path)
{
    m_paths.push_back(path);
    if (path->begin() == this) {
        m_out += path->flow();
    } else if (path->end() == this) {
        m_in += path->flow();
    } else {
        throw CanteraError("SpeciesNode::addPath", "path added to wrong node");
    }
}
 
void SpeciesNode::printPaths()
{
    for (size_t i = 0; i < m_paths.size(); i++) {
        cout << m_paths[i]->begin()->name << " -->  "
             << m_paths[i]->end()->name << ":   "
             << m_paths[i]->flow() << endl;
    }
}
 
Path::Path(SpeciesNode* begin, SpeciesNode* end)
    : m_a(begin), m_b(end)
{
    begin->addPath(this);
    end->addPath(this);
}
 
void Path::addReaction(size_t rxnNumber, double value, const string& label)
{
    m_rxn[rxnNumber] += value;
    m_total += value;
    if (label != "") {
        m_label[label] += value;
    }
}
 
void Path::writeLabel(ostream& s, double threshold)
{
    if (m_label.size() == 0) {
        return;
    }
    double v;
    for (const auto& [species, value] : m_label) {
        v = value / m_total;
        if (m_label.size() == 1) {
            s << species << "\\l";
        } else if (v > threshold) {
            s << species;
            int percent = int(100*v + 0.5);
            if (percent < 100) {
                s << " (" << percent << "%)\\l";
            } else {
                s << "\\l";
            }
        }
    }
}
 
ReactionPathDiagram::ReactionPathDiagram(
    shared_ptr<Kinetics> kin, const string& element_) : element(element_), m_kin(kin)
{
    if (!m_kin) {
        throw CanteraError("ReactionPathDiagram::ReactionPathDiagram",
                           "Kinetics object must not be empty.");
    }
    m_builder = make_shared<ReactionPathBuilder>();
    m_builder->init(m_log, *m_kin.get());
}
 
ReactionPathDiagram::~ReactionPathDiagram()
{
    // delete the nodes
    for (const auto& [k, node] : m_nodes) {
        delete node;
    }
 
    // delete the paths
    size_t nn = nPaths();
    for (size_t n = 0; n < nn; n++) {
        delete m_pathlist[n];
    }
}
 
vector<int> ReactionPathDiagram::reactions()
{
    double flmax = 0.0;
    for (size_t i = 0; i < nPaths(); i++) {
        Path* p = path(i);
        flmax = std::max(p->flow(), flmax);
    }
    m_rxns.clear();
    for (size_t i = 0; i < nPaths(); i++) {
        for (const auto& [iRxn, flux] : path(i)->reactionMap()) {
            double flxratio = flux / flmax;
            if (flxratio > threshold) {
                m_rxns.insert(iRxn);
            }
        }
    }
    vector<int> r;
    for (const auto& rxn : m_rxns) {
        r.push_back(int(rxn));
    }
    return r;
}
 
void ReactionPathDiagram::add(ReactionPathDiagram& d)
{
    for (size_t n = 0; n < nPaths(); n++) {
        Path* p = path(n);
        size_t k1 = p->begin()->number;
        size_t k2 = p->end()->number;
        p->setFlow(p->flow() + d.flow(k1,k2));
    }
}
 
void ReactionPathDiagram::add(shared_ptr<ReactionPathDiagram> d)
{
    add(*d.get());
}
 
void ReactionPathDiagram::findMajorPaths(double athreshold, size_t lda, span<double> a)
{
    double netmax = 0.0;
    for (size_t n = 0; n < nNodes(); n++) {
        for (size_t m = n+1; m < nNodes(); m++) {
            size_t k1 = m_speciesNumber[n];
            size_t k2 = m_speciesNumber[m];
            double fl = fabs(netFlow(k1,k2));
            netmax = std::max(fl, netmax);
        }
    }
    for (size_t n = 0; n < nNodes(); n++) {
        for (size_t m = n+1; m < nNodes(); m++) {
            size_t k1 = m_speciesNumber[n];
            size_t k2 = m_speciesNumber[m];
            double fl = fabs(netFlow(k1,k2));
            if (fl > athreshold*netmax) {
                a[lda*k1 + k2] = 1;
            }
        }
    }
}
 
const string ReactionPathDiagram::flowType() const
{
    if (flow_type == OneWayFlow) {
        return "OneWayFlow";
    }
    return "NetFlow";
}
 
void ReactionPathDiagram::setFlowType(const string& fType)
{
    if (fType == "OneWayFlow") {
        flow_type = OneWayFlow;
    } else if (fType == "NetFlow") {
        flow_type = NetFlow;
    } else {
        throw CanteraError("ReactionPathDiagram::setFlowType",
                           "Unknown flow type '{}'", fType);
    }
}
 
void ReactionPathDiagram::build()
{
    m_builder->build(*m_kin.get(), element, m_log, *this, true);
    m_isBuilt = true;
}
 
string ReactionPathDiagram::getDot()
{
    if (!m_isBuilt) {
        build();
    }
    std::stringstream out;
    exportToDot(out);
    return out.str();
}
 
string ReactionPathDiagram::getData()
{
    if (!m_isBuilt) {
        build();
    }
    std::stringstream out;
    writeData(out);
    return out.str();
}
 
string ReactionPathDiagram::getLog()
{
    return m_log.str();
}
 
void ReactionPathDiagram::writeData(ostream& s)
{
    s << title << endl;
    for (size_t i1 = 0; i1 < nNodes(); i1++) {
        size_t k1 = m_speciesNumber[i1];
        s << m_nodes[k1]->name << " ";
    }
    s << endl;
    for (size_t i1 = 0; i1 < nNodes(); i1++) {
        size_t k1 = m_speciesNumber[i1];
        for (size_t i2 = i1+1; i2 < nNodes(); i2++) {
            size_t k2 = m_speciesNumber[i2];
            double f1 = flow(k1, k2);
            double f2 = flow(k2, k1);
            s << m_nodes[k1]->name << " " << m_nodes[k2]->name
              << " " << f1 << " " << -f2 << endl;
        }
    }
}
 
void ReactionPathDiagram::exportToDot(ostream& s)
{
    double flmax = 0.0;
    s.precision(3);
 
    // a directed graph
    s << "digraph " << name << " {" << endl;
 
    // the graph will be no larger than x_size, y_size
    if (x_size > 0.0) {
        if (y_size < 0.0) {
            y_size = x_size;
        }
        s << "size = \""
          << x_size << ","
          << y_size << "\";"
          << endl;
    }
 
    if (dot_options != "") {
        s << dot_options << endl;
    }
 
    // draw paths representing net flows
    if (flow_type == NetFlow) {
        // if no scale was specified, normalize net flows by the maximum net
        // flow
        if (scale <= 0.0) {
            for (size_t i1 = 0; i1 < nNodes(); i1++) {
                size_t k1 = m_speciesNumber[i1];
                node(k1)->visible = false;
                for (size_t i2 = i1+1; i2 < nNodes(); i2++) {
                    size_t k2 = m_speciesNumber[i2];
                    double flx = netFlow(k1, k2);
                    if (flx < 0.0) {
                        flx = -flx;
                    }
                    flmax = std::max(flx, flmax);
                }
            }
        } else {
            flmax = scale;
        }
        flmax = std::max(flmax, 1e-10);
 
        // loop over all unique pairs of nodes
        for (size_t i1 = 0; i1 < nNodes(); i1++) {
            size_t k1 = m_speciesNumber[i1];
            for (size_t i2 = i1+1; i2 < nNodes(); i2++) {
                size_t k2 = m_speciesNumber[i2];
                double flx = netFlow(k1, k2);
                if (m_local != npos && k1 != m_local && k2 != m_local) {
                    flx = 0.0;
                }
                if (flx != 0.0) {
                    double flxratio;
                    size_t kbegin, kend;
                    // set beginning and end of the path based on the sign of
                    // the net flow
                    if (flx > 0.0) {
                        kbegin = k1;
                        kend = k2;
                        flxratio = flx/flmax;
                    } else {
                        kbegin = k2;
                        kend = k1;
                        flxratio = -flx/flmax;
                    }
 
                    // write out path specification if the net flow is greater
                    // than the threshold
                    if (flxratio >= threshold) {
                        // make nodes visible
                        node(kbegin)->visible = true;
                        node(kend)->visible = true;
 
                        s << "s" << kbegin << " -> s" << kend;
                        s <<  "[fontname=\""+m_font+"\", penwidth=";
 
                        if (arrow_width < 0) {
                            double lwidth = 1.0 - 4.0
                                     * log10(flxratio/threshold)/log10(threshold) + 1.0;
                            s << lwidth;
                            s << ", arrowsize="
                              <<  std::min(6.0, 0.5*lwidth);
                        } else {
                            s << arrow_width;
                            s << ", arrowsize=" << flxratio + 1;
                        }
 
                        double hue = 0.7;
                        double bright = 0.9;
                        s << ", color=" << "\"" << hue << ", "
                          << flxratio + 0.5
                          << ", " << bright << "\"" << endl;
 
                        if (flxratio > label_min) {
                            s << ", label=\" " << flxratio;
                            if (show_details) {
                                if (flow(kbegin, kend) > 0.0) {
                                    s << "\\l fwd: "
                                      << flow(kbegin, kend)/flmax << "\\l";
                                    path(kbegin, kend)->writeLabel(s);
                                }
                                if (flow(kend, kbegin) > 0.0) {
                                    s << " \\l rev: "
                                      << flow(kend,kbegin)/flmax << "\\l";
                                    path(kend, kbegin)->writeLabel(s);
                                }
                            }
                            s << "\"";
                        }
                        s << "];" << endl;
                    }
                }
            }
        }
    } else {
        if (scale < 0) {
            for (size_t i = 0; i < nPaths(); i++) {
                flmax = std::max(path(i)->flow(), flmax);
            }
        } else {
            flmax = scale;
        }
 
        for (size_t i = 0; i < nPaths(); i++) {
            Path* p = path(i);
            double flxratio = p->flow()/flmax;
            if (m_local != npos) {
                if (p->begin()->number != m_local
                        && p->end()->number != m_local) {
                    flxratio = 0.0;
                }
            }
            if (flxratio > threshold) {
                p->begin()->visible = true;
                p->end()->visible = true;
                s << "s" << p->begin()->number
                  << " -> s" << p->end()->number;
 
                if (arrow_width < 0) {
                    double lwidth = 1.0 - 4.0 * log10(flxratio/threshold)/log10(threshold)
                             + 1.0;
                    s <<  "[fontname=\""+m_font+"\", penwidth="
                      << lwidth;
                    s << ", arrowsize="
                      <<  std::min(6.0, 0.5*lwidth);
                } else {
                    s <<  ", penwidth="
                      <<  arrow_width;
                    s << ", arrowsize=" << flxratio + 1;
                }
                double hue = 0.7;
                double bright = 0.9;
                s << ", color=" << "\"" << hue << ", " << flxratio + 0.5
                  << ", " << bright << "\"" << endl;
 
                if (flxratio > label_min) {
                    s << ", label = \" " << flxratio;
                    if (show_details) {
                        s << "\\l";
                        p->writeLabel(s);
                    }
                    s << "\"";
                }
                s << "];" << endl;
            }
        }
    }
    s.precision(2);
    for (const auto& [kSpecies, node] : m_nodes) {
        if (node->visible) {
            s << "s" << kSpecies << " [ fontname=\""+m_font+"\", label=\"" << node->name
              << "\"];" << endl;
        }
    }
    s << " label = " << "\"" << "Scale = "
      << flmax << "\\l " << title << "\";" << endl;
    s  << " fontname = \""+m_font+"\";" << endl << "}" << endl;
}
 
 
void ReactionPathDiagram::addNode(size_t k, const string& nm, double x)
{
    if (!m_nodes[k]) {
        m_nodes[k] = new SpeciesNode;
        m_nodes[k]->number = k;
        m_nodes[k]->name = nm;
        m_nodes[k]->value = x;
        m_speciesNumber.push_back(k);
    }
}
 
void ReactionPathDiagram::linkNodes(size_t k1, size_t k2, size_t rxn,
                                    double value, string legend)
{
    Path* ff = m_paths[k1][k2];
    if (!ff) {
        ff= new Path(m_nodes[k1], m_nodes[k2]);
        m_paths[k1][k2] = ff;
        m_pathlist.push_back(ff);
    }
    ff->addReaction(rxn, value, legend);
    m_rxns.insert(rxn);
    m_flxmax = std::max(ff->flow(), m_flxmax);
}
 
vector<size_t> ReactionPathDiagram::species()
{
    return m_speciesNumber;
}
 
int ReactionPathBuilder::findGroups(ostream& logfile, Kinetics& s)
{
    m_groups.resize(m_nr);
    for (size_t i = 0; i < m_nr; i++) { // loop over reactions
        logfile << endl << "Reaction " << i+1 << ": "
                << s.reaction(i)->equation();
 
        if (m_determinate[i]) {
            logfile << " ... OK." << endl;
        } else if (m_reac[i].size() == 2 && m_prod[i].size() == 2) {
            // indices for the two reactants
            size_t kr0 = m_reac[i][0];
            size_t kr1 = m_reac[i][1];
 
            // indices for the two products
            size_t kp0 = m_prod[i][0];
            size_t kp1 = m_prod[i][1];
 
            // references to the Group objects representing the reactants
            const Group& r0 = m_sgroup[kr0];
            const Group& r1 = m_sgroup[kr1];
            const Group& p0 = m_sgroup[kp0];
            const Group& p1 = m_sgroup[kp1];
 
            const Group* group_a0=0, *group_b0=0, *group_c0=0,
                         *group_a1=0, *group_b1=0, *group_c1=0;
            Group b0 = p0 - r0;
            Group b1 = p1 - r0;
            if (b0.valid() && b1.valid()) {
                logfile << " ... ambiguous." << endl;
            } else if (!b0.valid() && !b1.valid()) {
                logfile << " ... cannot express as A + BC = AB + C" << endl;
            } else {
                logfile << endl;
            }
 
            if (b0.valid()) {
                if (b0.sign() > 0) {
                    group_a0 = &r0;
                    group_b0 = &b0;
                    group_c0 = &p1;
                    m_transfer[i][0][0] = r0;
                    m_transfer[i][1][0] = b0;
                    m_transfer[i][1][1] = p1;
                } else {
                    group_a0 = &r1;
                    group_c0 = &p0;
                    b0 *= -1;
                    group_b0 = &b0;
                    m_transfer[i][1][1] = r1;
                    m_transfer[i][0][1] = b0;
                    m_transfer[i][0][0] = p0;
                }
                logfile << "     ";
                group_a0->fmt(logfile, m_elementSymbols);
                logfile << " + ";
                group_b0->fmt(logfile,m_elementSymbols);
                group_c0->fmt(logfile, m_elementSymbols);
                logfile << " = ";
                group_a0->fmt(logfile, m_elementSymbols);
                group_b0->fmt(logfile, m_elementSymbols);
                logfile << " + ";
                group_c0->fmt(logfile, m_elementSymbols);
                if (b1.valid()) {
                    logfile << "   [<= default] " << endl;
                } else {
                    logfile << endl;
                }
            }
 
            if (b1.valid()) {
                if (b1.sign() > 0) {
                    group_a1 = &r0;
                    group_b1 = &b1;
                    group_c1 = &p0;
                    if (!b0.valid()) {
                        m_transfer[i][0][1] = r0;
                        m_transfer[i][1][1] = b0;
                        m_transfer[i][1][0] = p0;
                    }
                } else {
                    group_a1 = &r1;
                    group_c1 = &p1;
                    b1 *= -1;
                    group_b1 = &b1;
                    if (!b0.valid()) {
                        m_transfer[i][1][0] = r1;
                        m_transfer[i][0][0] = b0;
                        m_transfer[i][0][1] = p1;
                    }
                }
                logfile << "     ";
                group_a1->fmt(logfile, m_elementSymbols);
                logfile << " + ";
                group_b1->fmt(logfile, m_elementSymbols);
                group_c1->fmt(logfile, m_elementSymbols);
                logfile << " = ";
                group_a1->fmt(logfile, m_elementSymbols);
                group_b1->fmt(logfile, m_elementSymbols);
                logfile << " + ";
                group_c1->fmt(logfile, m_elementSymbols);
                logfile << endl;
            }
        } else {
            logfile << "... cannot parse. [ignored]" << endl;
        }
    }
    return 1;
}
 
void ReactionPathBuilder::findElements(Kinetics& kin)
{
    m_enamemap.clear();
    m_nel = 0;
    for (size_t i = 0; i < kin.nPhases(); i++) {
        ThermoPhase* p = &kin.thermo(i);
        // iterate over the elements in this phase
        for (size_t m = 0; m < p->nElements(); m++) {
            string ename = p->elementName(m);
 
            // if no entry is found for this element name, then it is a new
            // element. In this case, add the name to the list of names,
            // increment the element count, and add an entry to the
            // name->(index+1) map.
            if (m_enamemap.find(ename) == m_enamemap.end()) {
                m_enamemap[ename] = m_nel + 1;
                m_elementSymbols.push_back(ename);
                m_nel++;
            }
        }
    }
    m_atoms.resize(kin.nTotalSpecies(), m_nel, 0.0);
    // iterate over the elements
    for (size_t m = 0; m < m_nel; m++) {
        size_t k = 0;
        // iterate over the phases
        for (size_t ip = 0; ip < kin.nPhases(); ip++) {
            ThermoPhase* p = &kin.thermo(ip);
            size_t mlocal = p->elementIndex(m_elementSymbols[m], false);
            if (mlocal != npos) {
                for (size_t kp = 0; kp < p->nSpecies(); kp++) {
                    m_atoms(k, m) = p->nAtoms(kp, mlocal);
                    k++;
                }
            }
        }
    }
}
 
int ReactionPathBuilder::init(ostream& logfile, Kinetics& kin)
{
    m_transfer.clear();
    m_elementSymbols.clear();
    findElements(kin);
    m_ns = kin.nTotalSpecies();
    m_nr = kin.nReactions();
 
    // all reactants / products, even ones appearing on both sides of the
    // reaction
    vector<vector<size_t>> allProducts(m_nr);
    vector<vector<size_t>> allReactants(m_nr);
    for (size_t i = 0; i < m_nr; i++) {
        for (size_t k = 0; k < m_ns; k++) {
            for (int n = 0; n < kin.reactantStoichCoeff(k, i); n++) {
                allReactants[i].push_back(k);
            }
            for (int n = 0; n < kin.productStoichCoeff(k, i); n++) {
                allProducts[i].push_back(k);
            }
        }
    }
 
    // m_reac and m_prod exclude indices for species that appear on
    // both sides of the reaction, so that the diagram contains no loops.
    m_reac.resize(m_nr);
    m_prod.resize(m_nr);
    m_ropf.resize(m_nr);
    m_ropr.resize(m_nr);
    m_determinate.resize(m_nr);
    m_x.resize(m_ns); // not currently used ?
    m_elatoms.resize(m_nel, m_nr);
 
    for (size_t i = 0; i < m_nr; i++) {
        // construct the lists of reactant and product indices, not including
        // molecules that appear on both sides.
        m_reac[i].clear();
        m_prod[i].clear();
        map<size_t, int> net;
        size_t nr = allReactants[i].size();
        size_t np = allProducts[i].size();
        for (size_t ir = 0; ir < nr; ir++) {
            net[allReactants[i][ir]]--;
        }
        for (size_t ip = 0; ip < np; ip++) {
            net[allProducts[i][ip]]++;
        }
 
        for (size_t k = 0; k < m_ns; k++) {
            if (net[k] < 0) {
                size_t nmol = -net[k];
                for (size_t jr = 0; jr < nmol; jr++) {
                    m_reac[i].push_back(k);
                }
            } else if (net[k] > 0) {
                size_t nmol = net[k];
                for (size_t jp = 0; jp < nmol; jp++) {
                    m_prod[i].push_back(k);
                }
            }
        }
 
        size_t nrnet = m_reac[i].size();
 
        // compute number of atoms of each element in each reaction, excluding
        // molecules that appear on both sides of the reaction. We only need to
        // compute this for the reactants, since the elements are conserved.
        for (size_t n = 0; n < nrnet; n++) {
            size_t k = m_reac[i][n];
            for (size_t m = 0; m < m_nel; m++) {
                m_elatoms(m,i) += m_atoms(k,m);
            }
        }
    }
 
    // build species groups
    vector<int> comp(m_nel);
    m_sgroup.resize(m_ns);
    for (size_t j = 0; j < m_ns; j++) {
        for (size_t m = 0; m < m_nel; m++) {
            comp[m] = int(m_atoms(j,m));
        }
        m_sgroup[j] = Group(comp);
    }
 
    // determine whether or not the reaction is "determinate", meaning that
    // there is no ambiguity about which reactant is the source for any element
    // in any product. This is false if more than one reactant contains a given
    // element, *and* more than one product contains the element. In this case,
    // additional information is needed to determine the partitioning of the
    // reactant atoms of that element among the products.
    for (size_t i = 0; i < m_nr; i++) {
        size_t nr = m_reac[i].size();
        size_t np = m_prod[i].size();
        m_determinate[i] = true;
        for (size_t m = 0; m < m_nel; m++) {
            int nar = 0;
            int nap = 0;
            for (size_t j = 0; j < nr; j++) {
                if (m_atoms(m_reac[i][j],m) > 0) {
                    nar++;
                }
            }
            for (size_t j = 0; j < np; j++) {
                if (m_atoms(m_prod[i][j],m) > 0) {
                    nap++;
                }
            }
            if (nar > 1 && nap > 1) {
                m_determinate[i] = false;
                break;
            }
        }
    }
 
    findGroups(logfile, kin);
    return 1;
}
 
string reactionLabel(size_t i, size_t kr, size_t nr,
                     const vector<size_t>& slist, const Kinetics& s)
{
    string label = "";
    for (size_t j = 0; j < nr; j++) {
        if (j != kr) {
            label += " + "+ s.kineticsSpeciesName(slist[j]);
        }
    }
    if (ba::starts_with(s.reaction(i)->type(), "three-body")) {
        label += " + M ";
    } else if (ba::starts_with(s.reaction(i)->type(), "falloff")) {
        label += " (+ M)";
    }
    return label;
}
 
int ReactionPathBuilder::build(Kinetics& s, const string& element,
                               ostream& output, ReactionPathDiagram& r, bool quiet)
{
    map<size_t, int> warn;
    double threshold = 0.0;
    size_t m = m_enamemap[element]-1;
    r.element = element;
    if (m == npos) {
        return -1;
    }
 
    s.getFwdRatesOfProgress(m_ropf);
    s.getRevRatesOfProgress(m_ropr);
 
    // species explicitly included or excluded
    auto in_nodes = r.included();
    auto out_nodes = r.excluded();
 
    vector<int> status(s.nTotalSpecies(), 0);
    for (size_t ni = 0; ni < in_nodes.size(); ni++) {
        status[s.kineticsSpeciesIndex(in_nodes[ni])] = 1;
    }
    for (size_t ne = 0; ne < out_nodes.size(); ne++) {
        status[s.kineticsSpeciesIndex(out_nodes[ne])] = -1;
    }
 
    for (size_t i = 0; i < m_nr; i++) {
        double ropf = m_ropf[i];
        double ropr = m_ropr[i];
 
        // loop over reactions involving element m
        if (m_elatoms(m, i) > 0) {
            size_t nr = m_reac[i].size();
            size_t np = m_prod[i].size();
 
            for (size_t kr = 0; kr < nr; kr++) {
                size_t kkr = m_reac[i][kr];
                string fwdlabel = reactionLabel(i, kr, nr, m_reac[i], s);
 
                for (size_t kp = 0; kp < np; kp++) {
                    size_t kkp = m_prod[i][kp];
                    string revlabel = "";
                    for (size_t j = 0; j < np; j++) {
                        if (j != kp) {
                            revlabel += " + "+ s.kineticsSpeciesName(m_prod[i][j]);
                        }
                    }
                    if (ba::starts_with(s.reaction(i)->type(), "three-body")) {
                        revlabel += " + M ";
                    } else if (ba::starts_with(s.reaction(i)->type(), "falloff")) {
                        revlabel += " (+ M)";
                    }
 
                    // calculate the flow only for pairs that are not the same
                    // species, both contain atoms of element m, and both are
                    // allowed to appear in the diagram
                    if ((kkr != kkp) && (m_atoms(kkr,m) > 0
                                         && m_atoms(kkp,m) > 0)
                            && status[kkr] >= 0 && status[kkp] >= 0) {
                        // if neither species contains the full number of atoms
                        // of element m in the reaction, then we must consider
                        // the type of reaction to determine which reactant
                        // species was the source of a given m-atom in the
                        // product
                        double f;
                        if ((m_atoms(kkp,m) < m_elatoms(m, i)) &&
                                (m_atoms(kkr,m) < m_elatoms(m, i))) {
                            map<size_t, map<size_t, Group>>& g = m_transfer[i];
                            if (g.empty()) {
                                if (!warn[i] && !quiet) {
                                    output << endl;
                                    output << "*************** REACTION IGNORED ***************" << endl;
                                    output << "Warning: no rule to determine partitioning of " << element
                                           << endl << " in reaction " << s.reaction(i)->equation() << "." << endl
                                           << "*************** REACTION IGNORED **************" << endl;
                                    output << endl;
                                    warn[i] = 1;
                                }
                                f = 0.0;
                            } else {
                                if (!g[kr][kp]) {
                                    f = 0.0;
                                } else {
                                    f = g[kr][kp].nAtoms(m);
                                }
                            }
                        } else {
                            // no ambiguity about where the m-atoms come from or
                            // go to. Either all reactant m atoms end up in one
                            // product, or only one reactant contains all the
                            // m-atoms. In either case, the number of atoms
                            // transferred is given by the same expression.
                            f = m_atoms(kkp,m) * m_atoms(kkr,m) / m_elatoms(m, i);
                        }
 
                        double fwd = ropf*f;
                        double rev = ropr*f;
                        bool force_incl = ((status[kkr] == 1) || (status[kkp] == 1));
 
                        bool fwd_incl = ((fwd > threshold) ||
                                         (fwd > 0.0 && force_incl));
                        bool rev_incl = ((rev > threshold) ||
                                         (rev > 0.0 && force_incl));
                        if (fwd_incl || rev_incl) {
                            if (!r.hasNode(kkr)) {
                                r.addNode(kkr, s.kineticsSpeciesName(kkr), m_x[kkr]);
                            }
                            if (!r.hasNode(kkp)) {
                                r.addNode(kkp, s.kineticsSpeciesName(kkp), m_x[kkp]);
                            }
                        }
                        if (fwd_incl) {
                            r.linkNodes(kkr, kkp, int(i), fwd, fwdlabel);
                        }
                        if (rev_incl) {
                            r.linkNodes(kkp, kkr, -int(i), rev, revlabel);
                        }
                    }
                }
            }
        }
    }
    return 1;
}
 
shared_ptr<ReactionPathDiagram> newReactionPathDiagram(
    shared_ptr<Kinetics> kin, const string& element)
{
    return shared_ptr<ReactionPathDiagram>(
        new ReactionPathDiagram(kin, element));
}
 
}