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 #ifndef RIVET_MATH_VECTOR3
 #define RIVET_MATH_VECTOR3
 
 #include "Rivet/Tools/TypeTraits.hh"
 #include "Rivet/Math/MathConstants.hh"
 #include "Rivet/Math/MathUtils.hh"
 #include "Rivet/Math/VectorN.hh"
 
 namespace Rivet {
 
 
   class Vector3;
   typedef Vector3 ThreeVector;
   typedef Vector3 V3;
   Vector3 multiply(const double, const Vector3&);
   Vector3 multiply(const Vector3&, const double);
   Vector3 add(const Vector3&, const Vector3&);
   Vector3 operator*(const double, const Vector3&);
   Vector3 operator*(const Vector3&, const double);
   Vector3 operator/(const Vector3&, const double);
   Vector3 operator+(const Vector3&, const Vector3&);
   Vector3 operator-(const Vector3&, const Vector3&);
 
   class ThreeMomentum;
   typedef ThreeMomentum P3;
   ThreeMomentum multiply(const double, const ThreeMomentum&);
   ThreeMomentum multiply(const ThreeMomentum&, const double);
   ThreeMomentum add(const ThreeMomentum&, const ThreeMomentum&);
   ThreeMomentum operator*(const double, const ThreeMomentum&);
   ThreeMomentum operator*(const ThreeMomentum&, const double);
   ThreeMomentum operator/(const ThreeMomentum&, const double);
   ThreeMomentum operator+(const ThreeMomentum&, const ThreeMomentum&);
   ThreeMomentum operator-(const ThreeMomentum&, const ThreeMomentum&);
 
   class Matrix3;
 
 
 
   /// @brief Three-dimensional specialisation of Vector.
   class Vector3 : public Vector<3> {
 
     friend class Matrix3;
     friend Vector3 multiply(const double, const Vector3&);
     friend Vector3 multiply(const Vector3&, const double);
     friend Vector3 add(const Vector3&, const Vector3&);
     friend Vector3 subtract(const Vector3&, const Vector3&);
 
   public:
     Vector3() : Vector<3>() { }
 
     template<typename V3TYPE>
     Vector3(const V3TYPE& other) {
       this->setX(other.x());
       this->setY(other.y());
       this->setZ(other.z());
     }
 
     Vector3(const Vector<3>& other) {
       this->setX(other.get(0));
       this->setY(other.get(1));
       this->setZ(other.get(2));
     }
 
     Vector3(double x, double y, double z) {
       this->setX(x);
       this->setY(y);
       this->setZ(z);
     }
 
     ~Vector3() { }
 
 
   public:
 
     static Vector3 mkX() { return Vector3(1,0,0); }
     static Vector3 mkY() { return Vector3(0,1,0); }
     static Vector3 mkZ() { return Vector3(0,0,1); }
 
 
   public:
 
     double x() const { return get(0); }
     double x2() const { return sqr(x()); }
     Vector3& setX(double x) { set(0, x); return *this; }
 
     double y() const { return get(1); }
     double y2() const { return sqr(y()); }
     Vector3& setY(double y) { set(1, y); return *this; }
 
     double z() const { return get(2); }
     double z2() const { return sqr(z()); }
     Vector3& setZ(double z) { set(2, z); return *this; }
 
 
     /// Dot-product with another vector
     double dot(const Vector3& v) const {
       return _vec.dot(v._vec);
     }
 
     /// Cross-product with another vector
     Vector3 cross(const Vector3& v) const {
       Vector3 result;
       result._vec = _vec.cross(v._vec);
       return result;
     }
 
     /// Angle in radians to another vector
     double angle(const Vector3& v) const {
       const double localDotOther = unit().dot(v.unit());
       if (localDotOther > 1.0) return 0.0;
       if (localDotOther < -1.0) return M_PI;
       return acos(localDotOther);
     }
 
 
     /// Unit-normalized version of this vector.
     Vector3 unitVec() const {
       double md = mod();
       if ( fuzzyLessEquals(md, 0.0) ) return Vector3();
       else return *this * 1.0/md;
     }
 
     /// Synonym for unitVec
     Vector3 unit() const {
       return unitVec();
     }
 
     /// Polar projection of this vector into the x-y plane
     Vector3 polarVec() const {
       Vector3 rtn = *this;
       rtn.setZ(0.);
       return rtn;
     }
     /// Synonym for polarVec
     Vector3 perpVec() const {
       return polarVec();
     }
     /// Synonym for polarVec
     Vector3 rhoVec() const {
       return polarVec();
     }
 
     /// Square of the polar radius (
     double polarRadius2() const {
       return x()*x() + y()*y();
     }
     /// Synonym for polarRadius2
     double perp2() const {
       return polarRadius2();
     }
     /// Synonym for polarRadius2
     double rho2() const {
       return polarRadius2();
     }
 
     /// Polar radius
     double polarRadius() const {
       return sqrt(polarRadius2());
     }
     /// Synonym for polarRadius
     double perp() const {
       return polarRadius();
     }
     /// Synonym for polarRadius
     double rho() const {
       return polarRadius();
     }
 
     /// @brief Angle subtended by the vector's projection in x-y and the x-axis.
     ///
     /// @note Returns zero in the case of a vector with null x and y components.
     /// @todo Would it be better to return NaN in the null-perp case? Or throw?!
     double azimuthalAngle(const PhiMapping mapping = ZERO_2PI) const {
       // If this has a null perp-vector, return zero rather than let atan2 set an error state
       // This isn't necessary if the implementation supports IEEE floating-point arithmetic (IEC 60559)... are we sure?
       if (x() == 0 && y() == 0) return 0.0; //< Or return nan / throw an exception?
       // Calculate the arctan and return in the requested range
       const double value = atan2( y(), x() );
       return mapAngle(value, mapping);
     }
     /// Synonym for azimuthalAngle.
     double phi(const PhiMapping mapping = ZERO_2PI) const {
       return azimuthalAngle(mapping);
     }
 
     /// Tangent of the polar angle
     double tanTheta() const {
       return polarRadius()/z();
     }
 
     /// Sine of the polar angle
     double sinTheta() const {
       return sqrt(polarRadius2()/mod2());
     }
 
     /// Cosine of the polar angle
     double cosTheta() const {
       return z()/mod2();
     }
 
     /// Angle subtended by the vector and the z-axis.
     double polarAngle() const {
       // Get number beween [0,PI]
       const double polarangle = atan2(polarRadius(), z());
       return mapAngle0ToPi(polarangle);
     }
 
     /// Synonym for polarAngle
     double theta() const {
       return polarAngle();
     }
 
     /// @brief Purely geometric approximation to rapidity
     ///
     /// eta = -ln[ tan(theta/2) ]
     ///
     /// Also invariant under z-boosts, equal to y for massless particles.
     ///
     /// Implemented using the tan half-angle formula
     /// tan(theta/2) = sin(theta) / [1 + cos(theta)] = pT / (p + pz)
     double pseudorapidity() const {
       if (mod() == 0.0) return 0.0; ///< @todo Add [[ unlikely ]] with C++20
       if (mod() == fabs(z()) ) return std::copysign(INF, z()); ///< @todo Add [[ unlikely ]] with C++20
       const double eta = std::log((mod() + fabs(z())) / perp());
       return std::copysign(eta, z());
     }
 
     /// Synonym for pseudorapidity
     double eta() const {
       return pseudorapidity();
     }
 
     /// Convenience shortcut for fabs(eta())
     double abseta() const {
       return fabs(eta());
     }
 
 
   public:
 
     /// In-place scalar multiplication operator
     Vector3& operator *= (const double a) {
       _vec = multiply(a, *this)._vec;
       return *this;
     }
 
     /// In-place scalar division operator
     Vector3& operator /= (const double a) {
       _vec = multiply(1.0/a, *this)._vec;
       return *this;
     }
 
     /// In-place addition operator
     Vector3& operator += (const Vector3& v) {
       _vec = add(*this, v)._vec;
       return *this;
     }
 
     /// In-place subtraction operator
     Vector3& operator -= (const Vector3& v) {
       _vec = subtract(*this, v)._vec;
       return *this;
     }
 
     /// In-place negation operator
     Vector3 operator - () const {
       Vector3 rtn;
       rtn._vec = -_vec;
       return rtn;
     }
 
   };
 
 
 
   /// Unbound dot-product function
   inline double dot(const Vector3& a, const Vector3& b) {
     return a.dot(b);
   }
 
   /// Unbound cross-product function
   inline Vector3 cross(const Vector3& a, const Vector3& b) {
     return a.cross(b);
   }
 
   /// Unbound scalar-product function
   inline Vector3 multiply(const double a, const Vector3& v) {
     Vector3 result;
     result._vec = a * v._vec;
     return result;
   }
 
   /// Unbound scalar-product function
   inline Vector3 multiply(const Vector3& v, const double a) {
     return multiply(a, v);
   }
 
   /// Unbound scalar multiplication operator
   inline Vector3 operator * (const double a, const Vector3& v) {
     return multiply(a, v);
   }
 
   /// Unbound scalar multiplication operator
   inline Vector3 operator * (const Vector3& v, const double a) {
     return multiply(a, v);
   }
 
   /// Unbound scalar division operator
   inline Vector3 operator / (const Vector3& v, const double a) {
     return multiply(1.0/a, v);
   }
 
   /// Unbound vector addition function
   inline Vector3 add(const Vector3& a, const Vector3& b) {
     Vector3 result;
     result._vec = a._vec + b._vec;
     return result;
   }
 
   /// Unbound vector subtraction function
   inline Vector3 subtract(const Vector3& a, const Vector3& b) {
     Vector3 result;
     result._vec = a._vec - b._vec;
     return result;
   }
 
   /// Unbound vector addition operator
   inline Vector3 operator + (const Vector3& a, const Vector3& b) {
     return add(a, b);
   }
 
   /// Unbound vector subtraction operator
   inline Vector3 operator - (const Vector3& a, const Vector3& b) {
     return subtract(a, b);
   }
 
   // More physicsy coordinates etc.
 
   /// Angle (in radians) between two 3-vectors.
   inline double angle(const Vector3& a, const Vector3& b) {
     return a.angle(b);
   }
 
 
   /////////////////////////////////////////////////////
 
 
   /// Specialized version of the ThreeVector with momentum functionality.
   class ThreeMomentum : public ThreeVector {
   public:
     ThreeMomentum() { }
 
     template<typename V3TYPE, typename std::enable_if<HasXYZ<V3TYPE>::value, int>::type DUMMY=0>
     ThreeMomentum(const V3TYPE& other) {
       this->setPx(other.x());
       this->setPy(other.y());
       this->setPz(other.z());
     }
 
     ThreeMomentum(const Vector<3>& other)
       : ThreeVector(other) { }
 
     ThreeMomentum(const double px, const double py, const double pz) {
       this->setPx(px);
       this->setPy(py);
       this->setPz(pz);
     }
 
     ~ThreeMomentum() {}
 
   public:
 
 
     /// @name Coordinate setters
     /// @{
 
     /// Set x-component of momentum \f$ p_x \f$.
     ThreeMomentum& setPx(double px) {
       setX(px);
       return *this;
     }
 
     /// Set y-component of momentum \f$ p_y \f$.
     ThreeMomentum& setPy(double py) {
       setY(py);
       return *this;
     }
 
     /// Set z-component of momentum \f$ p_z \f$.
     ThreeMomentum& setPz(double pz) {
       setZ(pz);
       return *this;
     }
 
     /// @}
 
 
     /// @name Accessors
     /// @{
 
     /// Get x-component of momentum \f$ p_x \f$.
     double px() const { return x(); }
     /// Get x-squared \f$ p_x^2 \f$.
     double px2() const { return x2(); }
 
     /// Get y-component of momentum \f$ p_y \f$.
     double py() const { return y(); }
     /// Get y-squared \f$ p_y^2 \f$.
     double py2() const { return y2(); }
 
     /// Get z-component of momentum \f$ p_z \f$.
     double pz() const { return z(); }
     /// Get z-squared \f$ p_z^2 \f$.
     double pz2() const { return z2(); }
 
 
     /// Get the modulus of the 3-momentum
     double p() const { return mod(); }
     /// Get the modulus-squared of the 3-momentum
     double p2() const { return mod2(); }
 
 
     /// Calculate the transverse momentum vector \f$ \vec{p}_T \f$.
     ThreeMomentum pTvec() const {
       return polarVec();
     }
     /// Synonym for pTvec
     ThreeMomentum ptvec() const {
       return pTvec();
     }
 
     /// Calculate the squared transverse momentum \f$ p_T^2 \f$.
     double pT2() const {
       return polarRadius2();
     }
     /// Calculate the squared transverse momentum \f$ p_T^2 \f$.
     double pt2() const {
       return polarRadius2();
     }
 
     /// Calculate the transverse momentum \f$ p_T \f$.
     double pT() const {
       return sqrt(pT2());
     }
     /// Calculate the transverse momentum \f$ p_T \f$.
     double pt() const {
       return sqrt(pT2());
     }
 
     /// @}
 
 
     ////////////////////////////////////////
 
 
     /// @name Arithmetic operators (needed again for covariant returns)
     /// @{
 
     /// Multiply by a scalar
     ThreeMomentum& operator *= (double a) {
       _vec = multiply(a, *this)._vec;
       return *this;
     }
 
     /// Divide by a scalar
     ThreeMomentum& operator /= (double a) {
       _vec = multiply(1.0/a, *this)._vec;
       return *this;
     }
 
     /// Add two 3-momenta
     ThreeMomentum& operator += (const ThreeMomentum& v) {
       _vec = add(*this, v)._vec;
       return *this;
     }
 
     /// Subtract two 3-momenta
     ThreeMomentum& operator -= (const ThreeMomentum& v) {
       _vec = add(*this, -v)._vec;
       return *this;
     }
 
     /// Multiply all components by -1.
     ThreeMomentum operator - () const {
       ThreeMomentum result;
       result._vec = -_vec;
       return result;
     }
 
     // /// Multiply space (i.e. all!) components by -1.
     // ThreeMomentum reverse() const {
     //   return -*this;
     // }
 
     /// @}
 
   };
 
 
   inline ThreeMomentum multiply(const double a, const ThreeMomentum& v) {
     ThreeMomentum result;
     result._vec = a * v._vec;
     return result;
   }
 
   inline ThreeMomentum multiply(const ThreeMomentum& v, const double a) {
     return multiply(a, v);
   }
 
   inline ThreeMomentum operator*(const double a, const ThreeMomentum& v) {
     return multiply(a, v);
   }
 
   inline ThreeMomentum operator*(const ThreeMomentum& v, const double a) {
     return multiply(a, v);
   }
 
   inline ThreeMomentum operator/(const ThreeMomentum& v, const double a) {
     return multiply(1.0/a, v);
   }
 
   inline ThreeMomentum add(const ThreeMomentum& a, const ThreeMomentum& b) {
     ThreeMomentum result;
     result._vec = a._vec + b._vec;
     return result;
   }
 
   inline ThreeMomentum operator+(const ThreeMomentum& a, const ThreeMomentum& b) {
     return add(a, b);
   }
 
   inline ThreeMomentum operator-(const ThreeMomentum& a, const ThreeMomentum& b) {
     return add(a, -b);
   }
 
 
   /// @todo Mixed-arg operators: better via SFINAE??
   /// @note Why *does* this actually cause compiler trouble, given (V3, V3) is a correct sig-match for (V3,P3) and (P3, P3) is not?
   inline Vector3 operator+(const ThreeMomentum& a, const Vector3& b) {
     return add(static_cast<const Vector3&>(a), b);
   }
   inline Vector3 operator+(const Vector3& a, const ThreeMomentum& b) {
     return add(a, static_cast<const Vector3&>(b));
   }
 
   inline Vector3 operator-(const ThreeMomentum& a, const Vector3& b) {
     return add(static_cast<const Vector3&>(a), -b);
   }
   inline Vector3 operator-(const Vector3& a, const ThreeMomentum& b) {
     return add(a, -static_cast<const Vector3&>(b));
   }
 
 
 
   /////////////////////////////////////////////////////
 
 
   /// @defgroup momutils_vec3_deta \f$ |\Delta eta| \f$ calculations from 3-vectors
   /// @{
 
   /// Calculate the difference in pseudorapidity between two spatial vectors.
   inline double deltaEta(const Vector3& a, const Vector3& b, bool sign=false) {
     return deltaEta(a.pseudorapidity(), b.pseudorapidity(), sign);
   }
 
   /// Calculate the difference in pseudorapidity between two spatial vectors.
   inline double deltaEta(const Vector3& v, double eta2, bool sign=false) {
     return deltaEta(v.pseudorapidity(), eta2, sign);
   }
 
   /// Calculate the difference in pseudorapidity between two spatial vectors.
   inline double deltaEta(double eta1, const Vector3& v, bool sign=false) {
     return deltaEta(eta1, v.pseudorapidity(), sign);
   }
 
   /// @}
 
 
   /// @defgroup momutils_vec3_dphi \f$ \Delta phi \f$ calculations from 3-vectors
   /// @{
 
   /// Calculate the difference in azimuthal angle between two spatial vectors.
   inline double deltaPhi(const Vector3& a, const Vector3& b, bool sign=false) {
     return deltaPhi(a.azimuthalAngle(), b.azimuthalAngle(), sign);
   }
 
   /// Calculate the difference in azimuthal angle between two spatial vectors.
   inline double deltaPhi(const Vector3& v, double phi2, bool sign=false) {
     return deltaPhi(v.azimuthalAngle(), phi2, sign);
   }
 
   /// Calculate the difference in azimuthal angle between two spatial vectors.
   inline double deltaPhi(double phi1, const Vector3& v, bool sign=false) {
     return deltaPhi(phi1, v.azimuthalAngle(), sign);
   }
 
   /// @}
 
 
   /// @defgroup momutils_vec3_dr \f$ \Delta R \f$ calculations from 3-vectors
   /// @{
 
   /// Calculate the 2D rapidity-azimuthal ("eta-phi") distance between two spatial vectors.
   inline double deltaR2(const Vector3& a, const Vector3& b) {
     return deltaR2(a.pseudorapidity(), a.azimuthalAngle(),
                    b.pseudorapidity(), b.azimuthalAngle());
   }
 
   /// Calculate the 2D rapidity-azimuthal ("eta-phi") distance between two spatial vectors.
   inline double deltaR(const Vector3& a, const Vector3& b) {
     return sqrt(deltaR2(a,b));
   }
 
   /// Calculate the 2D rapidity-azimuthal ("eta-phi") distance between two spatial vectors.
   inline double deltaR2(const Vector3& v, double eta2, double phi2) {
     return deltaR2(v.pseudorapidity(), v.azimuthalAngle(), eta2, phi2);
   }
 
   /// Calculate the 2D rapidity-azimuthal ("eta-phi") distance between two spatial vectors.
   inline double deltaR(const Vector3& v, double eta2, double phi2) {
     return sqrt(deltaR2(v, eta2, phi2));
   }
 
   /// Calculate the 2D rapidity-azimuthal ("eta-phi") distance between two spatial vectors.
   inline double deltaR2(double eta1, double phi1, const Vector3& v) {
     return deltaR2(eta1, phi1, v.pseudorapidity(), v.azimuthalAngle());
   }
 
   /// Calculate the 2D rapidity-azimuthal ("eta-phi") distance between two spatial vectors.
   inline double deltaR(double eta1, double phi1, const Vector3& v) {
     return sqrt(deltaR2(eta1, phi1, v));
   }
 
   /// @}
 
 
   /// @defgroup momutils_vec3_mt MT calculation
   /// @{
 
   /// Calculate transverse mass of a visible and an invisible 3-vector
   ///
   /// @note Note assumption of zero-mass particles
   inline double mT(const Vector3& vis, const Vector3& invis) {
     // return sqrt(2*vis.perp()*invis.perp() * (1 - cos(deltaPhi(vis, invis))) );
     return mT(vis.perp(), invis.perp(), deltaPhi(vis, invis));
   }
 
   /// Calculate transverse momentum of pair of 3-vectors
   inline double pT(const Vector3& a, const Vector3& b) {
     return (a+b).perp();
   }
 
   /// @}
 
 
 }
 
 #endif

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