FourVector Class Reference

Specialisation of VectorN to a general (non-momentum) Lorentz 4-vector. More...

#include <Vector4.hh>

List of all members.

Public Member Functions
	FourVector ()
template<typename V4 >
	FourVector (const V4 &other)
	FourVector (const Vector< 4 > &other)
	FourVector (const double t, const double x, const double y, const double z)
virtual	~FourVector ()
double	t () const
double	t2 () const
FourVector &	setT (const double t)
double	x () const
double	x2 () const
FourVector &	setX (const double x)
double	y () const
double	y2 () const
FourVector &	setY (const double y)
double	z () const
double	z2 () const
FourVector &	setZ (const double z)
double	invariant () const
bool	isNull () const
double	angle (const FourVector &v) const
	Angle between this vector and another.
double	angle (const Vector3 &v3) const
	Angle between this vector and another (3-vector)
double	polarRadius2 () const
	Square of the projection of the 3-vector on to the plane This is a more efficient function than polarRadius, as it avoids the square root. Use it if you only need the squared value, or e.g. an ordering by magnitude.
double	perp2 () const
	Synonym for polarRadius2.
double	rho2 () const
	Synonym for polarRadius2.
double	polarRadius () const
	Projection of 3-vector on to the plane.
double	perp () const
	Synonym for polarRadius.
double	rho () const
	Synonym for polarRadius.
double	azimuthalAngle (const PhiMapping mapping=ZERO_2PI) const
	Angle subtended by the 3-vector's projection in x-y and the x-axis.
double	phi (const PhiMapping mapping=ZERO_2PI) const
	Synonym for azimuthalAngle.
double	polarAngle () const
	Angle subtended by the 3-vector and the z-axis.
double	theta () const
	Synonym for polarAngle.
double	pseudorapidity () const
	Pseudorapidity (defined purely by the 3-vector components)
double	eta () const
	Synonym for pseudorapidity.
double	abspseudorapidity () const
	Get the directly.
double	abseta () const
	Get the directly (alias).
Vector3	vector3 () const
	Get the spatial part of the 4-vector as a 3-vector.
double	contract (const FourVector &v) const
	Contract two 4-vectors, with metric signature (+ - - -).
double	dot (const FourVector &v) const
	Contract two 4-vectors, with metric signature (+ - - -).
double	operator* (const FourVector &v) const
	Contract two 4-vectors, with metric signature (+ - - -).
FourVector &	operator*= (double a)
	Multiply by a scalar.
FourVector &	operator/= (double a)
	Divide by a scalar.
FourVector &	operator+= (const FourVector &v)
	Add to this 4-vector.
FourVector &	operator-= (const FourVector &v)
	Subtract from this 4-vector. NB time as well as space components are subtracted.
FourVector	operator- () const
	Multiply all components (space and time) by -1.
FourVector	reverse () const
	Multiply space components only by -1.
const double &	get (const size_t index) const
double &	get (const size_t index)
const double &	operator[] (const size_t index) const
	Direct access to vector elements by index.
double &	operator[] (const size_t index)
	Direct access to vector elements by index.
Vector< N > &	set (const size_t index, const double value)
	Set indexed value.
size_t	size () const
	Vector dimensionality.
bool	isZero (double tolerance=1E-5) const
	Check for nullness, allowing for numerical precision.
double	mod2 () const
	Calculate the modulus-squared of a vector. .
double	mod () const
	Calculate the modulus of a vector. .
bool	operator== (const Vector< N > &a) const
bool	operator!= (const Vector< N > &a) const
bool	operator< (const Vector< N > &a) const
bool	operator<= (const Vector< N > &a) const
bool	operator> (const Vector< N > &a) const
bool	operator>= (const Vector< N > &a) const
Public Attributes
Eigen::Vector< double, N >	_vec
	Vector.
Friends
FourVector	multiply (const double a, const FourVector &v)
FourVector	multiply (const FourVector &v, const double a)
FourVector	add (const FourVector &a, const FourVector &b)
FourVector	transform (const LorentzTransform &lt, const FourVector &v4)

---

Detailed Description

Specialisation of VectorN to a general (non-momentum) Lorentz 4-vector.

Todo:

Add composite set/mk methods from different coord systems

Definition at line 22 of file Vector4.hh.

---

Constructor & Destructor Documentation

FourVector

(

)

[inline]

Definition at line 30 of file Vector4.hh.

: Vector<4>() { }

FourVector

(

const V4 &

other

)

[inline]

Definition at line 33 of file Vector4.hh.

                                {
      this->setT(other.t());
      this->setX(other.x());
      this->setY(other.y());
      this->setZ(other.z());
    }

FourVector

(

const Vector< 4 > &

other

)

[inline]

Definition at line 40 of file Vector4.hh.

      : Vector<4>(other) { }

FourVector	(	const double	t,
		const double	x,
		const double	y,
		const double	z
	)		[inline]

Definition at line 43 of file Vector4.hh.

                                                                               {
      this->setT(t);
      this->setX(x);
      this->setY(y);
      this->setZ(z);
    }

virtual ~FourVector

(

)

[inline, virtual]

Definition at line 50 of file Vector4.hh.

{ }

---

Member Function Documentation

double abseta

(

)

const [inline]

Get the directly (alias).

Definition at line 146 of file Vector4.hh.

{ return fabs(eta()); }

double abspseudorapidity

(

)

const [inline]

Get the directly.

Definition at line 144 of file Vector4.hh.

{ return fabs(eta()); }

double angle

(

const FourVector &

v

)

const [inline]

Angle between this vector and another.

Definition at line 80 of file Vector4.hh.

                                            {
      return vector3().angle( v.vector3() );
    }

double angle

(

const Vector3 &

v3

)

const [inline]

Angle between this vector and another (3-vector)

Definition at line 84 of file Vector4.hh.

                                          {
      return vector3().angle(v3);
    }

double azimuthalAngle

(

const PhiMapping

mapping = ZERO_2PI

)

const [inline]

Angle subtended by the 3-vector's projection in x-y and the x-axis.

Definition at line 117 of file Vector4.hh.

                                                                   {
      return vector3().azimuthalAngle(mapping);
    }

double contract

(

const FourVector &

v

)

const [inline]

Contract two 4-vectors, with metric signature (+ - - -).

Definition at line 157 of file Vector4.hh.

                                               {
      const double result = t()*v.t() - x()*v.x() - y()*v.y() - z()*v.z();
      return result;
    }

double dot

(

const FourVector &

v

)

const [inline]

Contract two 4-vectors, with metric signature (+ - - -).

Definition at line 163 of file Vector4.hh.

                                          {
      return contract(v);
    }

double eta

(

)

const [inline]

Synonym for pseudorapidity.

Definition at line 139 of file Vector4.hh.

                       {
      return vector3().eta();
    }

const double& get

(

const size_t

index

)

const [inline, inherited]

Definition at line 33 of file VectorN.hh.

                                                {
      if (index >= N) {
        throw std::runtime_error("Tried to access an invalid vector index.");
      } else {
        return _vec(index);
      }
    }

double& get

(

const size_t

index

)

[inline, inherited]

Definition at line 41 of file VectorN.hh.

                                    {
      if (index >= N) {
        throw std::runtime_error("Tried to access an invalid vector index.");
      } else {
        return _vec(index);
      }
    }

double invariant

(

)

const [inline]

Definition at line 70 of file Vector4.hh.

                             {
      // Done this way for numerical precision
      return (t() + z())*(t() - z()) - x()*x() - y()*y();
    }

bool isNull

(

)

const [inline]

Definition at line 75 of file Vector4.hh.

                        {
      return Rivet::isZero(invariant());
    }

bool isZero

(

double

tolerance = 1E-5

)

const [inline, inherited]

Check for nullness, allowing for numerical precision.

Definition at line 75 of file VectorN.hh.

                                             {
      for (size_t i=0; i < N; ++i) {
        if (! Rivet::isZero(_vec[i], tolerance) ) return false;
      }
      return true;
    }

double mod

(

)

const [inline, inherited]

Calculate the modulus of a vector. .

Definition at line 95 of file VectorN.hh.

                       {
      const double norm = mod2();
      assert(norm >= 0);
      return sqrt(norm);
    }

double mod2

(

)

const [inline, inherited]

Calculate the modulus-squared of a vector. .

Definition at line 84 of file VectorN.hh.

                        {
      double mod2 = 0.0;
      for (size_t i = 0; i < size(); ++i) {
        const double element = get(i);
        mod2 += element*element;
      }
      return mod2;
    }

bool operator!=

(

const Vector< N > &

a

)

const [inline, inherited]

Definition at line 112 of file VectorN.hh.

                                              {
      return _vec != a._vec;
    }

double operator*

(

const FourVector &

v

)

const [inline]

Contract two 4-vectors, with metric signature (+ - - -).

Definition at line 168 of file Vector4.hh.

                                                {
      return contract(v);
    }

FourVector& operator*=

(

double

a

)

[inline]

Multiply by a scalar.

Reimplemented in FourMomentum.

Definition at line 173 of file Vector4.hh.

                                     {
      _vec = multiply(a, *this)._vec;
      return *this;
    }

FourVector& operator+=

(

const FourVector &

v

)

[inline]

Add to this 4-vector.

Definition at line 185 of file Vector4.hh.

                                                {
      _vec = add(*this, v)._vec;
      return *this;
    }

FourVector operator-

(

)

const [inline]

Multiply all components (space and time) by -1.

Reimplemented from Vector< 4 >.

Reimplemented in FourMomentum.

Definition at line 197 of file Vector4.hh.

                                 {
      FourVector result;
      result._vec = -_vec;
      return result;
    }

FourVector& operator-=

(

const FourVector &

v

)

[inline]

Subtract from this 4-vector. NB time as well as space components are subtracted.

Definition at line 191 of file Vector4.hh.

                                                {
      _vec = add(*this, -v)._vec;
      return *this;
    }

FourVector& operator/=

(

double

a

)

[inline]

Divide by a scalar.

Reimplemented in FourMomentum.

Definition at line 179 of file Vector4.hh.

                                     {
      _vec = multiply(1.0/a, *this)._vec;
      return *this;
    }

bool operator<

(

const Vector< N > &

a

)

const [inline, inherited]

Definition at line 116 of file VectorN.hh.

                                             {
      return _vec < a._vec;
    }

bool operator<=

(

const Vector< N > &

a

)

const [inline, inherited]

Definition at line 120 of file VectorN.hh.

                                              {
      return _vec <= a._vec;
    }

bool operator==

(

const Vector< N > &

a

)

const [inline, inherited]

Definition at line 108 of file VectorN.hh.

                                              {
      return _vec == a._vec;
    }

bool operator>

(

const Vector< N > &

a

)

const [inline, inherited]

Definition at line 124 of file VectorN.hh.

                                             {
      return _vec > a._vec;
    }

bool operator>=

(

const Vector< N > &

a

)

const [inline, inherited]

Definition at line 128 of file VectorN.hh.

                                              {
      return _vec >= a._vec;
    }

const double& operator[]

(

const size_t

index

)

const [inline, inherited]

Direct access to vector elements by index.

Definition at line 50 of file VectorN.hh.

                                                       {
      return get(index);
    }

double& operator[]

(

const size_t

index

)

[inline, inherited]

Direct access to vector elements by index.

Definition at line 55 of file VectorN.hh.

                                           {
      return get(index);
    }

double perp

(

)

const [inline]

Synonym for polarRadius.

Definition at line 108 of file Vector4.hh.

                        {
      return vector3().perp();
    }

double perp2

(

)

const [inline]

Synonym for polarRadius2.

Definition at line 95 of file Vector4.hh.

                         {
      return vector3().perp2();
    }

double phi

(

const PhiMapping

mapping = ZERO_2PI

)

const [inline]

Synonym for azimuthalAngle.

Definition at line 121 of file Vector4.hh.

                                                        {
      return vector3().phi(mapping);
    }

double polarAngle

(

)

const [inline]

Angle subtended by the 3-vector and the z-axis.

Definition at line 126 of file Vector4.hh.

                              {
      return vector3().polarAngle();
    }

double polarRadius

(

)

const [inline]

Projection of 3-vector on to the plane.

Definition at line 104 of file Vector4.hh.

                               {
      return vector3().polarRadius();
    }

double polarRadius2

(

)

const [inline]

Square of the projection of the 3-vector on to the plane This is a more efficient function than polarRadius, as it avoids the square root. Use it if you only need the squared value, or e.g. an ordering by magnitude.

Definition at line 91 of file Vector4.hh.

                                {
      return vector3().polarRadius2();
    }

double pseudorapidity

(

)

const [inline]

Pseudorapidity (defined purely by the 3-vector components)

Definition at line 135 of file Vector4.hh.

                                  {
      return vector3().pseudorapidity();
    }

FourVector reverse

(

)

const [inline]

Multiply space components only by -1.

Reimplemented in FourMomentum.

Definition at line 204 of file Vector4.hh.

                               {
      FourVector result = -*this;
      result.setT(-result.t());
      return result;
    }

double rho

(

)

const [inline]

Synonym for polarRadius.

Definition at line 112 of file Vector4.hh.

                       {
      return vector3().rho();
    }

double rho2

(

)

const [inline]

Synonym for polarRadius2.

Definition at line 99 of file Vector4.hh.

                        {
      return vector3().rho2();
    }

Vector<N>& set	(	const size_t	index,
		const double	value
	)		[inline, inherited]

Set indexed value.

Definition at line 60 of file VectorN.hh.

                                                           {
      if (index >= N) {
        throw std::runtime_error("Tried to access an invalid vector index.");
      } else {
        _vec[index] = value;
      }
      return *this;
    }

FourVector& setT

(

const double

t

)

[inline]

Definition at line 56 of file Vector4.hh.

{ set(0, t); return *this; }

FourVector& setX

(

const double

x

)

[inline]

Definition at line 60 of file Vector4.hh.

{ set(1, x); return *this; }

FourVector& setY

(

const double

y

)

[inline]

Definition at line 64 of file Vector4.hh.

{ set(2, y); return *this; }

FourVector& setZ

(

const double

z

)

[inline]

Definition at line 68 of file Vector4.hh.

{ set(3, z); return *this; }

size_t size

(

)

const [inline, inherited]

Vector dimensionality.

Definition at line 70 of file VectorN.hh.

                        {
      return N;
    }

double t

(

)

const [inline]

Definition at line 54 of file Vector4.hh.

{ return get(0); }

double t2

(

)

const [inline]

Definition at line 55 of file Vector4.hh.

{ return sqr(t()); }

double theta

(

)

const [inline]

Synonym for polarAngle.

Definition at line 130 of file Vector4.hh.

                         {
      return vector3().theta();
    }

Vector3 vector3

(

)

const [inline]

Get the spatial part of the 4-vector as a 3-vector.

Definition at line 149 of file Vector4.hh.

                            {
      return Vector3(get(1), get(2), get(3));
    }

double x

(

)

const [inline]

Definition at line 58 of file Vector4.hh.

{ return get(1); }

double x2

(

)

const [inline]

Definition at line 59 of file Vector4.hh.

{ return sqr(x()); }

double y

(

)

const [inline]

Definition at line 62 of file Vector4.hh.

{ return get(2); }

double y2

(

)

const [inline]

Definition at line 63 of file Vector4.hh.

{ return sqr(y()); }

double z

(

)

const [inline]

Definition at line 66 of file Vector4.hh.

{ return get(3); }

double z2

(

)

const [inline]

Definition at line 67 of file Vector4.hh.

{ return sqr(z()); }

---

Friends And Related Function Documentation

FourVector add	(	const FourVector &	a,
		const FourVector &	b
	)		[friend]

Definition at line 245 of file Vector4.hh.

                                                                  {
    FourVector result;
    result._vec = a._vec + b._vec;
    return result;
  }

FourVector multiply	(	const double	a,
		const FourVector &	v
	)		[friend]

Definition at line 223 of file Vector4.hh.

                                                                  {
    FourVector result;
    result._vec = a * v._vec;
    return result;
  }

FourVector multiply	(	const FourVector &	v,
		const double	a
	)		[friend]

Definition at line 229 of file Vector4.hh.

                                                                  {
    return multiply(a, v);
  }

FourVector transform	(	const LorentzTransform &	lt,
		const FourVector &	v4
	)		[friend]

Definition at line 250 of file LorentzTrans.hh.

                                                                                {
      return lt.transform(v4);
  }

---

Member Data Documentation

Eigen::Vector<double,N> _vec [inherited]

Vector.

Definition at line 133 of file VectorN.hh.

---

The documentation for this class was generated from the following file:

• Vector4.hh