LpInterface_tpl.h

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#include "LpInterface.h"

namespace gum {
  namespace credal {
    namespace lp {
      LpCol::LpCol(unsigned int id) : __id(id) { GUM_CONSTRUCTOR(LpCol); }

      LpCol::LpCol(const LpCol& col) : __id(col.__id) { GUM_CONS_CPY(LpCol); }

      LpCol::~LpCol() { GUM_DESTRUCTOR(LpCol); }

      unsigned int LpCol::id() const { return __id; }

      bool LpCol::operator<(const LpCol& col) const { return (__id < col.id()); }

      bool LpCol::operator==(const LpCol& col) const { return (__id == col.id()); }

      bool LpCol::operator!=(const LpCol& col) const { return (__id != col.id()); }

      LpCol& LpCol::operator=(const LpCol& col) {
        __id = col.__id;

        return *this;
      }

      std::ostream& operator<<(std::ostream& out, const LpCol& col) {
        out << col.toString();
        return out;
      }

      std::string LpCol::toString() const { return "V" + std::to_string(__id); }
    }   // namespace lp

  }   // namespace credal


  namespace credal {
    namespace lp {

      LpExpr::LpExpr() :
          __ileft(false), __imiddle(false), __iright(false), __lValue(0.),
          __mValue(0.), __rValue(0.), __lCoeffs(new HashTable< LpCol, double >()),
          __mCoeffs(new HashTable< LpCol, double >()),
          __rCoeffs(new HashTable< LpCol, double >()) {
        GUM_CONSTRUCTOR(LpExpr);
      }

      LpExpr::LpExpr(const LpExpr& expr) :
          __ileft(expr.__ileft), __imiddle(expr.__imiddle),
          __iright(expr.__iright), __lValue(expr.__lValue),
          __mValue(expr.__mValue), __rValue(expr.__rValue),
          __lCoeffs(new HashTable< LpCol, double >(*expr.__lCoeffs)),
          __mCoeffs(new HashTable< LpCol, double >(*expr.__mCoeffs)),
          __rCoeffs(new HashTable< LpCol, double >(*expr.__rCoeffs)) {
        GUM_CONS_CPY(LpExpr);
      }

      LpExpr::LpExpr(const LpExpr& expr,
                     bool          copyLeft,
                     bool          copyMiddle,
                     bool          copyRight) :
          __ileft(false),
          __imiddle(false), __iright(false), __lValue(0.), __mValue(0.),
          __rValue(0.), __lCoeffs(nullptr), __mCoeffs(nullptr),
          __rCoeffs(nullptr) {
        if (copyLeft) {
          __lCoeffs = new HashTable< LpCol, double >(*expr.__lCoeffs);
          __lValue = expr.__lValue;
          __ileft = true;
        } else
          __lCoeffs = new HashTable< LpCol, double >();

        if (copyMiddle) {
          __mCoeffs = new HashTable< LpCol, double >(*expr.__mCoeffs);
          __mValue = expr.__mValue;
          __imiddle = true;
        } else
          __mCoeffs = new HashTable< LpCol, double >();

        if (copyRight) {
          __rCoeffs = new HashTable< LpCol, double >(*expr.__rCoeffs);
          __rValue = expr.__rValue;
          __iright = true;
        } else
          __rCoeffs = new HashTable< LpCol, double >();

        GUM_CONS_CPY(LpExpr);
      }

      LpExpr::LpExpr(LpExpr&& expr) :
          __ileft(expr.__ileft), __imiddle(expr.__imiddle),
          __iright(expr.__iright), __lValue(expr.__lValue),
          __mValue(expr.__mValue), __rValue(expr.__rValue),
          __lCoeffs(expr.__lCoeffs), __mCoeffs(expr.__mCoeffs),
          __rCoeffs(expr.__rCoeffs) {
        expr.__lCoeffs = nullptr;
        expr.__mCoeffs = nullptr;
        expr.__rCoeffs = nullptr;

        GUM_CONS_CPY(LpExpr);
      }

      LpExpr::LpExpr(LpExpr&& expr,
                     bool     copyLeft,
                     bool     copyMiddle,
                     bool     copyRight) :
          __ileft(false),
          __imiddle(false), __iright(false), __lValue(0.), __mValue(0.),
          __rValue(0.), __lCoeffs(nullptr), __mCoeffs(nullptr),
          __rCoeffs(nullptr) {
        if (copyLeft) {
          swap(__lCoeffs, expr.__lCoeffs);
          __lValue = expr.__lValue;
          __ileft = true;
        } else
          __lCoeffs = new HashTable< LpCol, double >();

        if (copyMiddle) {
          swap(__mCoeffs, expr.__mCoeffs);
          __mValue = expr.__mValue;
          __imiddle = true;
        } else
          __mCoeffs = new HashTable< LpCol, double >();

        if (copyRight) {
          swap(__rCoeffs, expr.__rCoeffs);
          __rValue = expr.__rValue;
          __iright = true;
        } else
          __rCoeffs = new HashTable< LpCol, double >();

        GUM_CONS_CPY(LpExpr);
      }

      LpExpr::~LpExpr() {
        delete __lCoeffs;
        delete __mCoeffs;
        delete __rCoeffs;

        GUM_DESTRUCTOR(LpExpr);
      }

      LpExpr& LpExpr::operator=(const LpCol& rhs) {
        clear();

        __mCoeffs->insert(rhs, 1.);
        __imiddle = true;

        return *this;
      }

      LpExpr& LpExpr::operator=(const LpExpr& rhs) {
        if (this == &rhs) return *this;

        *__lCoeffs = *rhs.__lCoeffs;
        *__mCoeffs = *rhs.__mCoeffs;
        *__rCoeffs = *rhs.__rCoeffs;

        __lValue = rhs.__lValue;
        __mValue = rhs.__mValue;
        __rValue = rhs.__rValue;

        __ileft = rhs.__ileft;
        __imiddle = rhs.__imiddle;
        __iright = rhs.__iright;

        return *this;
      }

      LpExpr& LpExpr::operator=(LpExpr&& rhs) {
        if (this == &rhs) return *this;

        swap(__lCoeffs, rhs.__lCoeffs);
        swap(__mCoeffs, rhs.__mCoeffs);
        swap(__rCoeffs, rhs.__rCoeffs);

        __lValue = rhs.__lValue;
        __mValue = rhs.__mValue;
        __rValue = rhs.__rValue;

        __ileft = rhs.__ileft;
        __imiddle = rhs.__imiddle;
        __iright = rhs.__iright;

        return *this;
      }

      template < typename SCALAR >
      LpExpr& LpExpr::operator=(const SCALAR& rhs) {
        clear();

        __mValue = rhs;
        __imiddle = true;

        return *this;
      }

      LpExpr& LpExpr::operator+=(const LpCol& rhs) {
        if (__ileft || __iright)
          GUM_ERROR(OperationNotAllowed,
                    "expr::operator+= (expr) : <= present on one side of expr");

        if (!__imiddle) __imiddle = true;

        __mCoeffs->getWithDefault(rhs, 0.) += 1.;

        return *this;
      }

      LpExpr& LpExpr::operator+=(const LpExpr& rhs) {
        if (__ileft || __iright || rhs.__ileft || rhs.__iright)
          GUM_ERROR(OperationNotAllowed,
                    "expr::operator+= (rhs) : <= present "
                    "on one side of rhs and/or expr");

        if (!__imiddle) __imiddle = true;

        for (const auto& elt : *rhs.__mCoeffs)
          __mCoeffs->getWithDefault(elt.first, 0.) += elt.second;

        __mValue += rhs.__mValue;

        return *this;
      }

      LpExpr& LpExpr::operator+=(LpExpr&& rhs) {
        if (__ileft || __iright || rhs.__ileft || rhs.__iright)
          GUM_ERROR(OperationNotAllowed,
                    "expr::operator+= (rhs) : <= present "
                    "on one side of rhs and/or expr");

        if (!__imiddle) {
          __imiddle = true;

          __mValue = rhs.__mValue;

          swap(__mCoeffs, rhs.__mCoeffs);

          return *this;
        }

        for (const auto& elt : *rhs.__mCoeffs)
          __mCoeffs->getWithDefault(elt.first, 0.) += elt.second;

        __mValue += rhs.__mValue;

        return *this;
      }

      template < typename T >
      LpExpr& LpExpr::operator+=(const T& rhs) {
        if (__ileft || __iright)
          GUM_ERROR(OperationNotAllowed,
                    "expr::operator+= (expr) : <= present on one side of expr");

        if (!__imiddle) __imiddle = true;

        __mValue += rhs;

        return *this;
      }

      LpExpr& LpExpr::operator-=(const LpCol& rhs) {
        if (__ileft || __iright)
          GUM_ERROR(OperationNotAllowed,
                    "expr::operator-= (rhs) : <= present in one of expr");

        if (!__imiddle) __imiddle = true;

        __mCoeffs->getWithDefault(rhs, 0.) -= 1.;

        return *this;
      }

      LpExpr& LpExpr::operator-=(const LpExpr& rhs) {
        if (__ileft || __iright || rhs.__ileft || rhs.__iright)
          GUM_ERROR(
             OperationNotAllowed,
             "expr::operator-= (rhs) : <= present in one of rhs and/or expr");

        if (!__imiddle) __imiddle = true;

        for (const auto& elt : *rhs.__mCoeffs)
          __mCoeffs->getWithDefault(elt.first, 0.) -= elt.second;

        __mValue -= rhs.__mValue;

        return *this;
      }

      template < typename T >
      LpExpr& LpExpr::operator-=(const T& rhs) {
        if (__ileft || __iright)
          GUM_ERROR(OperationNotAllowed,
                    "expr::operator-= (rhs) : <= present in one of expr");

        if (!__imiddle) __imiddle = true;

        __mValue -= rhs;

        return *this;
      }

      std::ostream& operator<<(std::ostream& out, const LpExpr& expr) {
        out << expr.toString();
        return out;
      }

      void LpExpr::__addSide(const LpCol& from) {
        if (!__ileft) {
          __lCoeffs->insert(from, 1.);
          __ileft = true;
        } else if (!__imiddle) {
          __mCoeffs->insert(from, 1.);
          __imiddle = true;
        } else if (!__iright) {
          __rCoeffs->insert(from, 1.);
          __iright = true;
        } else
          GUM_ERROR(OperationNotAllowed,
                    "LpExpr::setSide ( const LpCol & from "
                    ") : too many <= ; no free side");
      }

      void LpExpr::__addSide(const LpExpr& from) {
        if (__ileft && __iright && from.__imiddle)
          GUM_ERROR(OperationNotAllowed,
                    "LpExpr::setSide ( const LpCol & from "
                    ") : too many <= ; no free side");

        if (!from.__imiddle) return;

        if (!from.__ileft && !from.__iright) {
          if (!__ileft) {
            *__lCoeffs = *from.__mCoeffs;
            __lValue = from.__mValue;
            __ileft = true;

            return;
          } else if (!__imiddle) {
            *__mCoeffs = *from.__mCoeffs;
            __mValue = from.__mValue;
            __imiddle = true;

            return;
          } else if (!__iright) {
            *__rCoeffs = *from.__mCoeffs;
            __rValue = from.__mValue;
            __iright = true;

            return;
          } else
            GUM_ERROR(OperationNotAllowed,
                      "LpExpr::setSide ( const LpCol & from ) "
                      ": too many <= ; no free side");
        }
        else if (from.__ileft && !from.__iright) {
          if (!__ileft) {
            *__lCoeffs = *from.__lCoeffs;
            __lValue = from.__lValue;
            __ileft = true;

            *__mCoeffs = *from.__mCoeffs;
            __mValue = from.__mValue;
            __imiddle = true;

            return;
          } else if (!__imiddle && !__iright) {
            *__mCoeffs = *from.__lCoeffs;
            __mValue = from.__lValue;
            __imiddle = true;

            *__rCoeffs = *from.__mCoeffs;
            __rValue = from.__mValue;
            __iright = true;

            return;
          } else
            GUM_ERROR(OperationNotAllowed,
                      "LpExpr::setSide ( const LpCol & from ) "
                      ": too many <= ; no free side");
        }
        else if (from.__ileft && from.__iright) {
          if (__ileft || __imiddle || __iright)
            GUM_ERROR(OperationNotAllowed,
                      "LpExpr::setSide ( const LpCol & from ) "
                      ": too many <= ; no free side");

          *this = from;

          return;
        } else
          GUM_ERROR(OperationNotAllowed,
                    "LpExpr::setSide ( const LpCol & from "
                    ") : too many <= ; no free side");
      }

      void LpExpr::__addSide(LpExpr&& from) {
        if (__ileft && __iright && from.__imiddle)
          GUM_ERROR(OperationNotAllowed,
                    "LpExpr::setSide ( const LpCol & from "
                    ") : too many <= ; no free side");

        if (!from.__imiddle) return;

        if (!from.__ileft && !from.__iright) {
          if (!__ileft) {
            swap(__lCoeffs, from.__mCoeffs);
            __lValue = from.__mValue;
            __ileft = true;

            return;
          } else if (!__imiddle) {
            swap(__mCoeffs, from.__mCoeffs);
            __mValue = from.__mValue;
            __imiddle = true;

            return;
          } else if (!__iright) {
            swap(__rCoeffs, from.__mCoeffs);
            __rValue = from.__mValue;
            __iright = true;

            return;
          } else
            GUM_ERROR(OperationNotAllowed,
                      "LpExpr::setSide ( const LpCol & from ) "
                      ": too many <= ; no free side");
        }
        else if (from.__ileft && !from.__iright) {
          if (!__ileft) {
            swap(__lCoeffs, from.__lCoeffs);
            __lValue = from.__lValue;
            __ileft = true;

            swap(__mCoeffs, from.__mCoeffs);
            __mValue = from.__mValue;
            __imiddle = true;

            return;
          } else if (!__imiddle && !__iright) {
            swap(__mCoeffs, from.__lCoeffs);
            __mValue = from.__lValue;
            __imiddle = true;

            swap(__rCoeffs, from.__mCoeffs);
            __rValue = from.__mValue;
            __iright = true;

            return;
          } else
            GUM_ERROR(OperationNotAllowed,
                      "LpExpr::setSide ( const LpCol & from ) "
                      ": too many <= ; no free side");
        }
        else if (from.__ileft && from.__iright) {
          if (__ileft || __imiddle || __iright)
            GUM_ERROR(OperationNotAllowed,
                      "LpExpr::setSide ( const LpCol & from ) "
                      ": too many <= ; no free side");

          *this = std::move(from);

          return;
        } else
          GUM_ERROR(OperationNotAllowed,
                    "LpExpr::setSide ( const LpCol & from "
                    ") : too many <= ; no free side");
      }

      template < typename SCALAR >
      void LpExpr::__addSide(const SCALAR& from) {
        if (!__ileft) {
          __lValue = from;
          __ileft = true;
        } else if (!__imiddle) {
          __mValue = from;
          __imiddle = true;
        } else if (!__iright) {
          __rValue = from;
          __iright = true;
        } else
          GUM_ERROR(OperationNotAllowed,
                    "LpExpr::setSide ( const LpCol & from "
                    ") : too many <= ; no free side");
      }

      void LpExpr::clear() {
        __lCoeffs->clear();
        __mCoeffs->clear();
        __rCoeffs->clear();

        __lValue = 0.;
        __mValue = 0.;
        __rValue = 0.;

        __ileft = false;
        __imiddle = false;
        __iright = false;
      }

      std::string LpExpr::toString() const {
        std::ostringstream s;

        s << std::endl << "left side : " << std::endl;

        if (__lCoeffs != nullptr)
          for (const auto& elt : *__lCoeffs)
            s << elt.first.toString() << " " << elt.second << " | ";

        s << std::endl << "middle side : " << std::endl;

        if (__mCoeffs != nullptr)
          for (const auto& elt : *__mCoeffs)
            s << elt.first.toString() << " " << elt.second << " | ";

        s << std::endl << "right side : " << std::endl;

        if (__rCoeffs != nullptr)
          for (const auto& elt : *__rCoeffs)
            s << elt.first.toString() << " " << elt.second << " | ";

        s << std::endl
          << "lvalue : " << __lValue << std::endl
          << "mvalue : " << __mValue << std::endl
          << "rvalue : " << __rValue << std::endl;

        s << std::endl;

        return s.str();
      }

      LpRow::LpRow(const LpExpr& expr, const std::vector< LpCol >& cols) :
          __coeffs(nullptr) {
        // we write 0 <= Ax + b from Ex + f <= Cx + d
        if (expr.__ileft && !expr.__iright) {
          __coeffs = new HashTable< LpCol, double >(*expr.__mCoeffs);

          for (const auto& col : cols) {
            double col_coeff = 0.;

            // from left side to middle side : 0 <= middle - left
            if (expr.__lCoeffs->exists(col))
              col_coeff = expr.__lCoeffs->operator[](col);

            __coeffs->getWithDefault(col, 0.) -= col_coeff;
          }

          __cste = expr.__mValue - expr.__lValue;
        } else if (expr.__iright && !expr.__ileft) {
          __coeffs = new HashTable< LpCol, double >(*expr.__rCoeffs);

          for (const auto& col : cols) {
            double col_coeff = 0;

            // from middle side to right side : 0 <= right - middle
            if (expr.__mCoeffs->exists(col))
              col_coeff = expr.__mCoeffs->operator[](col);

            __coeffs->getWithDefault(col, 0.) -= col_coeff;
          }

          __cste = expr.__rValue - expr.__mValue;
        } else
          GUM_ERROR(OperationNotAllowed,
                    "expr : " << expr.toString()
                              << "is not a valid inequality; no <= detected");

        if (__coeffs->size() == 0)
          GUM_ERROR(OperationNotAllowed,
                    "expr : " << expr.toString()
                              << "is not a valid inequality; "
                                 "no variable in inequality, "
                                 "only constants");

        GUM_CONSTRUCTOR(LpRow);
      }

      LpRow::LpRow(LpExpr&& expr, const std::vector< LpCol >& cols) :
          __coeffs(nullptr) {
        if (expr.__ileft && !expr.__iright) {
          swap(__coeffs, expr.__mCoeffs);

          for (const auto& col : cols) {
            double col_coeff = 0;

            if (expr.__lCoeffs->exists(col))
              col_coeff = expr.__lCoeffs->operator[](col);

            __coeffs->getWithDefault(col, 0.) -= col_coeff;
          }

          __cste = expr.__mValue - expr.__lValue;
        } else if (expr.__iright && !expr.__ileft) {
          swap(__coeffs, expr.__rCoeffs);

          for (const auto& col : cols) {
            double col_coeff = 0;

            if (expr.__mCoeffs->exists(col))
              col_coeff = expr.__mCoeffs->operator[](col);

            __coeffs->getWithDefault(col, 0.) -= col_coeff;
          }

          __cste = expr.__rValue - expr.__mValue;
        } else
          GUM_ERROR(OperationNotAllowed,
                    "expr : " << expr.toString()
                              << "is not a valid inequality; no <= detected");

        if (__coeffs->size() == 0)
          GUM_ERROR(OperationNotAllowed,
                    "expr : " << expr.toString()
                              << "is not a valid inequality; "
                                 "no variable in inequality, "
                                 "only constants");

        GUM_CONSTRUCTOR(LpRow);
      }

      LpRow::LpRow(const LpRow& row) :
          __cste(row.__cste),
          __coeffs(new HashTable< LpCol, double >(*row.__coeffs)) {
        GUM_CONS_CPY(LpRow);
      }

      LpRow::LpRow(LpRow&& row) : __cste(row.__cste), __coeffs(row.__coeffs) {
        row.__coeffs = nullptr;

        GUM_CONS_CPY(LpRow);
      }

      LpRow::~LpRow() {
        delete __coeffs;

        GUM_DESTRUCTOR(LpRow);
      }

      LpRow& LpRow::operator=(const LpRow& row) {
        __cste = row.__cste;
        *__coeffs = *row.__coeffs;
        return *this;
      }

      LpRow& LpRow::operator=(LpRow&& row) {
        __cste = row.__cste;
        swap(__coeffs, row.__coeffs);
        return *this;
      }

      std::ostream& operator<<(std::ostream& out, const LpRow& row) {
        out << row.toString();
        return out;
      }

      std::string LpRow::toString() const {
        std::ostringstream s;

        s << "0 <= " << __cste;

        if (__coeffs != nullptr) {
          for (const auto& elt : *__coeffs) {
            if (elt.second > 0) {
              if (elt.second != 1) {
                s << " +" << elt.second << "*" << elt.first.toString();
              } else {
                s << " +" << elt.first.toString();
              }
            } else {
              if (elt.second < 0) {
                if (elt.second != -1) {
                  s << " " << elt.second << "*" << elt.first.toString();
                } else {
                  s << " -" << elt.first.toString();
                }
              }
            }
          }
        }

        return s.str();
      }

      template < typename GUM_SCALAR >
      LpInterface< GUM_SCALAR >::LpInterface() {
        __positivity = false;
        __sumIsOne = false;
        GUM_CONSTRUCTOR(LpInterface);
      }

      template < typename GUM_SCALAR >
      LpInterface< GUM_SCALAR >::LpInterface(
         const LpInterface< GUM_SCALAR >& from) :
          __cols(from.__cols),
          __positivity(from.__positivity), __sumIsOne(from.__sumIsOne) {
        __rows.resize(from.__rows.size());

        for (unsigned int i = 0, end = from.__rows.size(); i < end; i++)
          __rows[i] = new LpRow(*from.__rows[i]);

        GUM_CONS_CPY(LpInterface);
      }

      template < typename GUM_SCALAR >
      LpInterface< GUM_SCALAR >::LpInterface(LpInterface< GUM_SCALAR >&& from) :
          __positivity(from.__positivity), __sumIsOne(from.__sumIsOne) {
        __rows.swap(from.__rows);
        __cols.swap(from.__cols);
        GUM_CONS_CPY(LpInterface);
      }

      template < typename GUM_SCALAR >
      LpInterface< GUM_SCALAR >::~LpInterface() {
        for (const auto row : __rows)
          delete row;

        GUM_DESTRUCTOR(LpInterface);
      }

      template < typename GUM_SCALAR >
      LpInterface< GUM_SCALAR >& LpInterface< GUM_SCALAR >::
                                 operator=(const LpInterface< GUM_SCALAR >& from) {
        for (const auto& row : __rows)
          delete row;

        __rows.clear();
        __rows.shrink_to_fit();

        __rows.resize(from.__rows.size());

        for (unsigned int i = 0, end = from.__rows.size(); i < end; i++)
          __rows[i] = new LpRow(*from.__rows[i]);

        __cols = from.__cols;
        __positivity = from.__positivity;
        __sumIsOne = from.__sumIsOne;

        return *this;
      }

      template < typename GUM_SCALAR >
      LpInterface< GUM_SCALAR >& LpInterface< GUM_SCALAR >::
                                 operator=(LpInterface< GUM_SCALAR >&& from) {
        __rows.swap(from.__rows);
        __cols.swap(from.__cols);

        __positivity = from.__positivity;
        __sumIsOne = from.__sumIsOne;

        return *this;
      }

      template < typename T >
      std::ostream& operator<<(std::ostream& out, const LpInterface< T >& lpi) {
        out << lpi.toString();
        return out;
      }

      template < typename GUM_SCALAR >
      LpCol LpInterface< GUM_SCALAR >::addCol() {
        LpCol col((unsigned int)__cols.size());

        __cols.push_back(col);

        return col;
      }

      template < typename GUM_SCALAR >
      std::vector< LpCol >
         LpInterface< GUM_SCALAR >::addCols(const unsigned int& cols) {
        if (cols < 1)
          GUM_ERROR(OperationNotAllowed,
                    "LpInterface::addCols ( cols ) : cols "
                    "needs must be equal or greater than 1 : "
                       << cols << " < 1");

        for (unsigned int i = 0; i < cols; i++) {
          __cols.push_back(LpCol((unsigned int)__cols.size()));
        }

        return __cols;
      }

      template < typename GUM_SCALAR >
      void LpInterface< GUM_SCALAR >::addRow(const LpExpr& expr) {
        if (!expr.__ileft && !expr.__iright)
          GUM_ERROR(OperationNotAllowed,
                    "addRow ( const LpExpr & expr ) : expr : "
                       << expr.toString() << "is not an inequality.");

        if ((expr.__ileft && !expr.__iright) || (!expr.__ileft && expr.__iright)) {
          __rows.push_back(new LpRow(expr, __cols));
        } else {
          LpExpr lexpr(expr, true, true, false);
          LpExpr rexpr(expr, false, true, true);

          __rows.push_back(
             new LpRow(std::move(lexpr),
                       __cols));   
          __rows.push_back(
             new LpRow(std::move(rexpr),
                       __cols));   
        }
      }

      template < typename GUM_SCALAR >
      void LpInterface< GUM_SCALAR >::addRow(LpExpr&& expr) {
        if (!expr.__ileft && !expr.__iright)
          GUM_ERROR(OperationNotAllowed,
                    "addRow ( const LpExpr & expr ) : expr : "
                       << expr.toString() << "is not an inequality.");

        if ((expr.__ileft && !expr.__iright) || (!expr.__ileft && expr.__iright)) {
          __rows.push_back(new LpRow(std::move(expr), __cols));
        } else {
          LpExpr lexpr(std::move(expr), true, true, false);

          LpExpr rexpr(std::move(expr), false, false, true);


          *rexpr.__mCoeffs = *lexpr.__mCoeffs;
          rexpr.__mValue = lexpr.__mValue;
          rexpr.__imiddle = true;

          __rows.push_back(
             new LpRow(std::move(lexpr),
                       __cols));   
          __rows.push_back(
             new LpRow(std::move(rexpr),
                       __cols));   
        }
      }

      template < typename GUM_SCALAR >
      void LpInterface< GUM_SCALAR >::addPositivity() {
        if (__positivity) return;

        for (const auto& col : __cols)
          addRow(0 <= col);

        __positivity = true;
      }

      template < typename GUM_SCALAR >
      void LpInterface< GUM_SCALAR >::addSumIsOne() {
        if (__sumIsOne) return;

        LpExpr expr;

        for (const auto& col : __cols)
          expr += col;

        addRow(1 <= std::move(expr) <= 1);

        __sumIsOne = true;
      }

      template < typename GUM_SCALAR >
      void LpInterface< GUM_SCALAR >::addProba() {
        if (__positivity && __sumIsOne) {
          return;
        } else if (__positivity && !__sumIsOne) {
          addSumIsOne();
          return;
        } else if (!__positivity && __sumIsOne) {
          addPositivity();
          return;
        }

        // we can do both with one loop, don't call the above functions.
        // addPositivity();
        // addSumIsOne();
        LpExpr expr;

        for (const auto& col : __cols) {
          addRow(0 <= col);
          expr += col;
        }

        addRow(1 <= std::move(expr) <= 1);

        __sumIsOne = true;
        __positivity = true;
      }

      template < typename GUM_SCALAR >
      std::vector< std::vector< GUM_SCALAR > > LpInterface< GUM_SCALAR >::solve() {
        LRSWrapper< GUM_SCALAR > lrs;

        lrs.setUpH((unsigned int)__cols.size());

        std::vector< std::vector< GUM_SCALAR > > lrsMatrix;

        for (const auto& row : __rows) {
          std::vector< GUM_SCALAR > expandedRow(__cols.size() + 1, 0);

          expandedRow[0] = row->__cste;

          for (const auto& elt : *row->__coeffs)
            expandedRow[elt.first.id() + 1] = elt.second;

          lrsMatrix.push_back(expandedRow);
        }

        lrs.fillMatrix(lrsMatrix);

        lrs.H2V();

        return lrs.getOutput();
      }

      template < typename GUM_SCALAR >
      std::vector< LpCol > LpInterface< GUM_SCALAR >::getCols() const {
        return __cols;
      }

      template < typename GUM_SCALAR >
      std::string LpInterface< GUM_SCALAR >::toString() const {
        std::ostringstream s;

        s << std::endl << std::endl << "Variables : " << std::endl;

        for (const auto& col : __cols)
          s << " " << col.toString();

        s << std::endl;

        for (const auto& row : __rows)
          s << std::endl << row->toString();

        s << std::endl << std::endl;

        return s.str();
      }

      template < typename GUM_SCALAR >
      void LpInterface< GUM_SCALAR >::clear() {
        for (const auto& row : __rows)
          delete row;

        __rows.clear();
        __rows.shrink_to_fit();   

        __cols.clear();
        __cols.shrink_to_fit();

        __positivity = false;
        __sumIsOne = false;
      }

      template < typename GUM_SCALAR >
      void LpInterface< GUM_SCALAR >::clearRows() {
        for (const auto& row : __rows)
          delete row;

        __rows.clear();
        __rows.shrink_to_fit();

        __positivity = false;
        __sumIsOne = false;
      }

      void swap(HashTable< LpCol, double >*& a, HashTable< LpCol, double >*& b) {
        HashTable< LpCol, double >* tmp(a);
        a = b;
        b = tmp;
      }

      template < typename T2 >
      LpExpr operator+(LpExpr&& lhs, const T2& rhs) {
        LpExpr expr = std::move(lhs);
        expr += rhs;

        return expr;
      }

      template < typename T2 >
      LpExpr operator+(const LpExpr& lhs, const T2& rhs) {
        LpExpr expr(lhs);
        expr += rhs;

        return expr;
      }

      template < typename T1, forbidden_type< T1, LpExpr > >
      LpExpr operator+(const T1& lhs, LpExpr&& rhs) {
        LpExpr expr = std::move(rhs);
        ;
        expr += lhs;

        return expr;
      }

      template < typename T1, forbidden_type< T1, LpExpr > >
      LpExpr operator+(const T1& lhs, LpExpr& rhs) {
        LpExpr expr(rhs);
        expr += lhs;

        return expr;
      }

      template < typename T2, forbidden_type< T2, LpExpr > >
      LpExpr operator+(const LpCol& lhs, const T2& rhs) {
        LpExpr expr;
        expr += lhs;
        expr += rhs;

        return expr;
      }

      template < typename T1,
                 forbidden_type< T1, LpExpr >,
                 forbidden_type< T1, LpCol > >
      LpExpr operator+(const T1& lhs, const LpCol& rhs) {
        LpExpr expr;
        expr += rhs;
        expr += lhs;

        return expr;
      }

      template < typename T2 >
      LpExpr operator-(LpExpr&& lhs, const T2& rhs) {
        LpExpr expr = std::move(lhs);
        expr -= rhs;

        return expr;
      }

      template < typename T2 >
      LpExpr operator-(const LpExpr& lhs, const T2& rhs) {
        LpExpr expr(lhs);
        expr -= rhs;

        return expr;
      }

      template < typename T1, forbidden_type< T1, LpExpr > >
      LpExpr operator-(const T1& lhs, LpExpr&& rhs) {
        LpExpr expr;
        expr += std::move(rhs);
        ;
        expr -= lhs;

        return expr;
      }

      template < typename T1, forbidden_type< T1, LpExpr > >
      LpExpr operator-(const T1& lhs, LpExpr& rhs) {
        LpExpr expr;
        expr += rhs;
        expr -= lhs;

        return expr;
      }

      template < typename T2, forbidden_type< T2, LpExpr > >
      LpExpr operator-(const LpCol& lhs, const T2& rhs) {
        LpExpr expr;
        expr += lhs;
        expr -= rhs;

        return expr;
      }

      template < typename T1,
                 forbidden_type< T1, LpExpr >,
                 forbidden_type< T1, LpCol > >
      LpExpr operator-(const T1& lhs, const LpCol& rhs) {
        LpExpr expr;
        expr += rhs;
        expr -= lhs;

        return expr;
      }

      template < typename SCALAR >
      INLINE LpExpr LpExpr::multiply(const SCALAR& lhs, const LpCol& rhs) {
        LpExpr expr;
        expr.__mCoeffs->insert(rhs, lhs);
        expr.__imiddle = true;
        return expr;
      }

      template < typename SCALAR >
      LpExpr operator*(const SCALAR& lhs, const LpCol& rhs) {
        return LpExpr::multiply(lhs, rhs);
      }

      template < typename SCALAR >
      LpExpr operator*(const LpCol& lhs, const SCALAR& rhs) {
        return LpExpr::multiply(rhs, lhs);
      }

      template < typename T1, typename T2 >
      INLINE LpExpr LpExpr::lessThan(T1&& lhs, T2&& rhs) {
        LpExpr expr;
        expr.__addSide(std::forward< T1 >(lhs));
        expr.__addSide(std::forward< T2 >(rhs));
        return expr;
      }

      // const lvalue
      template < typename T2 >
      LpExpr operator<=(const LpExpr& lhs, T2&& rhs) {
        return LpExpr::lessThan(lhs, std::forward< T2 >(rhs));
      }

      template < typename T2 >
      LpExpr operator<=(const LpCol& lhs, T2&& rhs) {
        return LpExpr::lessThan(lhs, std::forward< T2 >(rhs));
      }

      template < typename T1,
                 forbidden_type< T1, LpExpr& >,
                 forbidden_type< T1, LpCol& > >
      LpExpr operator<=(T1&& lhs, const LpExpr& rhs) {
        return LpExpr::lessThan(std::forward< T1 >(lhs), rhs);
      }

      template < typename T1,
                 forbidden_type< T1, LpExpr& >,
                 forbidden_type< T1, LpCol& > >
      LpExpr operator<=(T1&& lhs, const LpCol& rhs) {
        return LpExpr::lessThan(std::forward< T1 >(lhs), rhs);
      }

      // rvaue
      template < typename T2 >
      LpExpr operator<=(LpExpr&& lhs, T2&& rhs) {
        return LpExpr::lessThan(std::move(lhs), std::forward< T2 >(rhs));
      }

      template < typename T2 >
      LpExpr operator<=(LpCol&& lhs, T2&& rhs) {
        return LpExpr::lessThan(std::move(lhs), std::forward< T2 >(rhs));
      }

      template < typename T1,
                 forbidden_type< T1, LpExpr >,
                 forbidden_type< T1, LpCol > >
      LpExpr operator<=(T1&& lhs, LpExpr&& rhs) {
        return LpExpr::lessThan(std::forward< T1 >(lhs), std::move(rhs));
      }

      template < typename T1,
                 forbidden_type< T1, LpExpr >,
                 forbidden_type< T1, LpCol > >
      LpExpr operator<=(T1&& lhs, LpCol&& rhs) {
        return LpExpr::lessThan(std::forward< T1 >(lhs), std::move(rhs));
      }
    }   // namespace lp

  }   // namespace credal

}   // namespace gum