smash::FourVector Class Reference

#include <fourvector.h>

The FourVector class holds relevant values in Minkowski spacetime with (+, −, −, −) metric signature.

The overloaded operators are built according to Andrew Koenig recommendations where the compound assignment operators is used as a base for their non-compound counterparts. This means that the operator + is implemented in terms of +=. The operator+ returns a copy of its result. + and friends are non-members, while the compound assignment counterparts, changing the left argument, are a member of the FourVector class.

Definition at line 33 of file fourvector.h.

Inheritance diagram for smash::FourVector:

Public Types
using	iterator = std::array< double, 4 >::iterator
	iterates over the components More...
using	const_iterator = std::array< double, 4 >::const_iterator
	iterates over the components More...

Public Member Functions
	FourVector ()
	default constructor nulls the fourvector components More...
	FourVector (double y0, double y1, double y2, double y3)
	copy constructor More...
	FourVector (double y0, ThreeVector vec)
	construct from time-like component and a ThreeVector. More...
double &	operator[] (std::size_t i)
	access the component at offset i. More...
double	operator[] (std::size_t i) const
	const overload of the [] operator More...
double	x0 () const
void	set_x0 (double t)
double	x1 () const
void	set_x1 (double x)
double	x2 () const
void	set_x2 (double y)
double	x3 () const
void	set_x3 (double z)
ThreeVector	threevec () const
void	reset ()
	Set all the 4-vector components to 0. More...
ThreeVector	velocity () const
	Get the velocity (3-vector divided by zero component). More...
double	Dot (const FourVector &a) const
	calculate the scalar product with another four-vector More...
double	sqr () const
	calculate the square of the vector (which is a scalar) More...
double	abs () const
	calculate the lorentz invariant absolute value More...
double	sqr3 () const
	calculate the square of the spatial three-vector More...
double	abs3 () const
	calculate the absolute value of the spatial three-vector More...
double	tau () const
	calculate the proper time from the given four vector More...
double	eta () const
	calculate the space-time rapidity from the given four vector More...
FourVector	lorentz_boost (const ThreeVector &v) const
	Returns the FourVector boosted with velocity v. More...
bool	operator== (const FourVector &a) const
	Check if all four vector components are almost equal (accuracy \(10^{-4}\)). More...
bool	operator!= (const FourVector &a) const
	checks inequality (logical complement to FourVector::operator==(const FourVector&) const) More...
bool	operator< (const FourVector &a) const
	checks if \(x^\mu < a^\mu\) for all \(\mu\) (all four vector components are below comparison vector) More...
bool	operator> (const FourVector &a) const
	checks if \(x^\mu > a^\mu\) for all \(\mu\) (all four vector components are above comparison vector) More...
bool	operator<= (const FourVector &a) const
	logical complement to FourVector::operator>(const FourVector&) const More...
bool	operator>= (const FourVector &a) const
	logical complement to FourVector::operator<(const FourVector&) const More...
FourVector	operator+= (const FourVector &a)
	adds \(a_\mu: x_\mu^\prime = x_\mu + a_\mu\) More...
FourVector	operator-= (const FourVector &a)
	subtracts \(a_\mu: x_\mu^\prime = x_\mu - a_\mu\) More...
FourVector	operator*= (const double &a)
	multiplies by \(a: x_\mu^\prime = a \cdot x_\mu\) More...
FourVector	operator/= (const double &a)
	divides by \(a: x_\mu^\prime = \frac{1}{a} \cdot x_\mu\) More...
iterator	begin ()
iterator	end ()
const_iterator	begin () const
const_iterator	end () const
const_iterator	cbegin () const
const_iterator	cend () const

Private Attributes
std::array< double, 4 >	x_
	internal storage of this vector's components More...

Member Typedef Documentation

iterator

using smash::FourVector::iterator = std::array<double, 4>::iterator

iterates over the components

Definition at line 281 of file fourvector.h.

const_iterator

using smash::FourVector::const_iterator = std::array<double, 4>::const_iterator

iterates over the components

Definition at line 283 of file fourvector.h.

Constructor & Destructor Documentation

FourVector() [1/3]

smash::FourVector::FourVector ( )

inline

default constructor nulls the fourvector components

Definition at line 36 of file fourvector.h.

: x_({0., 0., 0., 0.}) {}

FourVector() [2/3]

smash::FourVector::FourVector ( double  y0, double  y1, double  y2, double  y3  )

inline

copy constructor

Parameters

[in]	y0	The time component to be copied
[in]	y1	The x component to be copied
[in]	y2	The y component to be copied
[in]	y3	the z component to be copied

Definition at line 46 of file fourvector.h.

      : x_({y0, y1, y2, y3}) {}

FourVector() [3/3]

smash::FourVector::FourVector ( double  y0, ThreeVector  vec  )

inline

construct from time-like component and a ThreeVector.

Parameters

[in]	y0	The time component to be used
[in]	vec	A ThreeVector (x,y,z) to be used

Definition at line 55 of file fourvector.h.

      : x_({y0, vec.x1(), vec.x2(), vec.x3()}) {}

Member Function Documentation

operator[]() [1/2]

double& smash::FourVector::operator[] ( std::size_t  i )

inline

access the component at offset i.

This operator results in the same as using the x0()...x3() functions

Parameters

[in]

i

the index of the component to access (has to be 0,1,2 or 3)

Returns

the component at index i

Definition at line 65 of file fourvector.h.

{ return x_[i]; }

operator[]() [2/2]

double smash::FourVector::operator[] ( std::size_t  i ) const

inline

const overload of the [] operator

Definition at line 67 of file fourvector.h.

{ return x_[i]; }

x0()

double smash::FourVector::x0 ( void  ) const

inline

Returns

the time-like component

Definition at line 313 of file fourvector.h.

{ return x_[0]; }

set_x0()

void smash::FourVector::set_x0 ( double  t )

inline

Parameters

[in]

t

set time-like component

Definition at line 315 of file fourvector.h.

{ x_[0] = t; }

x1()

double smash::FourVector::x1 ( ) const

inline

Returns

the first space-like component

Definition at line 317 of file fourvector.h.

{ return x_[1]; }

set_x1()

void smash::FourVector::set_x1 ( double  x )

inline

Parameters

[in]

x

set first space-like component

Definition at line 319 of file fourvector.h.

{ x_[1] = x; }

x2()

double smash::FourVector::x2 ( ) const

inline

Returns

the second space-like component

Definition at line 321 of file fourvector.h.

{ return x_[2]; }

set_x2()

void smash::FourVector::set_x2 ( double  y )

inline

Parameters

[in]

y

set second space-like component

Definition at line 323 of file fourvector.h.

{ x_[2] = y; }

x3()

double smash::FourVector::x3 ( ) const

inline

Returns

the third space-like component

Definition at line 325 of file fourvector.h.

{ return x_[3]; }

set_x3()

void smash::FourVector::set_x3 ( double  z )

inline

Parameters

[in]

z

set third space-like component

Definition at line 327 of file fourvector.h.

{ x_[3] = z; }

threevec()

ThreeVector smash::FourVector::threevec ( ) const

inline

Returns

the space-like three-vector (x,y,z components)

Definition at line 329 of file fourvector.h.

                                              {
  return ThreeVector(x_[1], x_[2], x_[3]);
}

reset()

void smash::FourVector::reset ( )

inline

Set all the 4-vector components to 0.

Definition at line 486 of file fourvector.h.

                              {
  this->x_[0] = 0.;
  this->x_[1] = 0.;
  this->x_[2] = 0.;
  this->x_[3] = 0.;
}

velocity()

ThreeVector smash::FourVector::velocity ( ) const

inline

Get the velocity (3-vector divided by zero component).

Should only be used with momentum 4-vectors (not with space-time ones).

Returns

the ThreeVector velocity

Definition at line 333 of file fourvector.h.

{ return threevec() / x0(); }

Dot()

double smash::FourVector::Dot ( const FourVector &  a ) const

inline

calculate the scalar product with another four-vector

Parameters

[in]

a

the FourVector to dot product with *this

Returns

\(x^\mu a_\mu\)

Definition at line 456 of file fourvector.h.

                                                       {
  return x_[0] * a.x_[0] - x_[1] * a.x_[1] - x_[2] * a.x_[2] - x_[3] * a.x_[3];
}

sqr()

double smash::FourVector::sqr ( ) const

inline

calculate the square of the vector (which is a scalar)

Returns

\(x^\mu x_\mu\)

Definition at line 460 of file fourvector.h.

                                    {
  return x_[0] * x_[0] - x_[1] * x_[1] - x_[2] * x_[2] - x_[3] * x_[3];
}

abs()

double smash::FourVector::abs ( ) const

inline

calculate the lorentz invariant absolute value

Returns

\(\sqrt{x^\mu x_\mu}\)

Note that this will fail for space-like vectors.

Definition at line 464 of file fourvector.h.

                                    {
  if (this->sqr() > -really_small) {
    return std::sqrt(std::abs(this->sqr()));
  } else {
    throw std::runtime_error(
        "Absolute value of 4-vector could not be "
        "determined, taking sqrt of negative value.");
  }
}

sqr3()

double smash::FourVector::sqr3 ( ) const

inline

calculate the square of the spatial three-vector

Returns

\(\mathbf{x} \cdot \mathbf{x}\)

Definition at line 474 of file fourvector.h.

{ return this->threevec().sqr(); }

abs3()

double smash::FourVector::abs3 ( ) const

inline

calculate the absolute value of the spatial three-vector

Returns

\(\sqrt{\mathbf{x} \cdot \mathbf{x}}\)

Definition at line 476 of file fourvector.h.

{ return this->threevec().abs(); }

tau()

double smash::FourVector::tau ( ) const

inline

calculate the proper time from the given four vector

Returns

\(\sqrt{t^2 - z^2}\)

Definition at line 478 of file fourvector.h.

                                    {
  return std::sqrt(this->x0() * this->x0() - this->x3() * this->x3());
}

eta()

double smash::FourVector::eta ( ) const

inline

calculate the space-time rapidity from the given four vector

Returns

\(atanh(z/t)\)

Definition at line 482 of file fourvector.h.

                                    {
  return std::atanh(this->x3() / this->x0());
}

lorentz_boost()

FourVector smash::FourVector::lorentz_boost

(

const ThreeVector &

v

)

const

Returns the FourVector boosted with velocity v.

The current FourVector is not changed.

Parameters

[in]

v

( \(\mathbf{v}\) in the explanation below) is a ThreeVector representing the boost velocity

Algorithmic

Notation:

• \(\mathbf{a}\) is a Three-Vector,
• \(a^\mu\) is a Four-Vector.

The gamma factor is \(\gamma = 1/\sqrt{1-\mathbf{v}^2}\).

The time-like component of a Lorentz-boosted FourVector \(x^\mu = (x_0, x_1, x_2, x_3) = (x_0, \mathbf{r})\) with velocity \(\mathbf{v}\) is

\begin{eqnarray*} x^\prime_0 = \gamma \cdot (x_0 - \mathbf{r}\cdot\mathbf{v})\;, \end{eqnarray*}

and the space-like components i = 1, 2, 3 are:

\begin{eqnarray*} x^\prime_i &=& x_i + v_i \cdot \Bigl(\frac{\gamma - 1}{\mathbf{v}^2} \cdot \mathbf{r}\cdot\mathbf{v} - \gamma \cdot x_0\Bigr)\\ &=& x_i + v_i \cdot \Bigl(\frac{\gamma^2}{\gamma + 1} \cdot \mathbf{r}\cdot\mathbf{v} - \gamma \cdot x_0\Bigr)\\ &=& x_i - v_i \cdot \frac{\gamma}{\gamma + 1} \cdot \bigl[\gamma\,(x_0 - \mathbf{r}\cdot\mathbf{v})+x_0\bigr]\\ &=& x_i - v_i \cdot \frac{\gamma}{\gamma + 1} \cdot (x^\prime_0 + x^{\vphantom{\prime}}_0) \end{eqnarray*}

Note: This function is equivalent to -velocity Boost from ROOT

Definition at line 17 of file fourvector.cc.

                                                               {
  const double velocity_squared = v.sqr();
 
  const double gamma =
      velocity_squared < 1. ? 1. / std::sqrt(1. - velocity_squared) : 0;
 
  // this is used four times in the Vector:
  const double xprime_0 = gamma * (this->x0() - this->threevec() * v);
  // this is the part of the space-like components that is always the same:
  const double constantpart = gamma / (gamma + 1) * (xprime_0 + this->x0());
  return FourVector(xprime_0, this->threevec() - v * constantpart);
}

operator==()

bool smash::FourVector::operator==

(

const FourVector &

a

)

const

Check if all four vector components are almost equal (accuracy \(10^{-4}\)).

Parameters

[in]

a

The FourVector to compare to

Returns

Whether *this and a are almost equal

Definition at line 30 of file fourvector.cc.

                                                     {
  return almost_equal_physics(x_[0], a.x_[0]) &&
         almost_equal_physics(x_[1], a.x_[1]) &&
         almost_equal_physics(x_[2], a.x_[2]) &&
         almost_equal_physics(x_[3], a.x_[3]);
}

operator!=()

bool smash::FourVector::operator!= ( const FourVector &  a ) const

inline

checks inequality (logical complement to FourVector::operator==(const FourVector&) const)

Parameters

[in]

a

The FourVector to compare to

Returns

Whether *this and a are not almost equal

Definition at line 336 of file fourvector.h.

                                                            {
  return !(*this == a);
}

operator<()

bool smash::FourVector::operator< ( const FourVector &  a ) const

inline

checks if \(x^\mu < a^\mu\) for all \(\mu\) (all four vector components are below comparison vector)

Parameters

[in]

a

The FourVector to compare to

Returns

Whether all components of *this are strictly below the corresponding components of a

Definition at line 340 of file fourvector.h.

                                                           {
  return (x_[0] < a.x_[0]) && (x_[1] < a.x_[1]) && (x_[2] < a.x_[2]) &&
         (x_[3] < a.x_[3]);
}

operator>()

bool smash::FourVector::operator> ( const FourVector &  a ) const

inline

checks if \(x^\mu > a^\mu\) for all \(\mu\) (all four vector components are above comparison vector)

Parameters

[in]

a

The FourVector to compare to

Returns

Whether all components of *this are strictly above the corresponding components of a

Definition at line 346 of file fourvector.h.

                                                           {
  return a < *this;
}

operator<=()

bool smash::FourVector::operator<= ( const FourVector &  a ) const

inline

logical complement to FourVector::operator>(const FourVector&) const

Parameters

[in]

a

The FourVector to compare to

Returns

Whether all components of *this are below or equal to the corresponding components of a

Definition at line 351 of file fourvector.h.

                                                            {
  return !(*this > a);
}

operator>=()

bool smash::FourVector::operator>= ( const FourVector &  a ) const

inline

logical complement to FourVector::operator<(const FourVector&) const

Parameters

[in]

a

The FourVector to compare to

Returns

Whether all components of *this are above or equal to the corresponding components of a

Definition at line 356 of file fourvector.h.

                                                            {
  return !(*this < a);
}

operator+=()

FourVector smash::FourVector::operator+= ( const FourVector &  a )

inline

adds \(a_\mu: x_\mu^\prime = x_\mu + a_\mu\)

Parameters

[in]

a

The FourVector to add

Returns

FourVector that consists of the added components of *this and a

Definition at line 360 of file fourvector.h.

                                                            {
  this->x_[0] += a.x_[0];
  this->x_[1] += a.x_[1];
  this->x_[2] += a.x_[2];
  this->x_[3] += a.x_[3];
  return *this;
}

operator-=()

FourVector smash::FourVector::operator-= ( const FourVector &  a )

inline

subtracts \(a_\mu: x_\mu^\prime = x_\mu - a_\mu\)

Parameters

[in]

a

The FourVector to subtract

Returns

FourVector consisting of the components of a subtracted from *this

Definition at line 381 of file fourvector.h.

                                                            {
  this->x_[0] -= a.x_[0];
  this->x_[1] -= a.x_[1];
  this->x_[2] -= a.x_[2];
  this->x_[3] -= a.x_[3];
  return *this;
}

operator*=()

FourVector smash::FourVector::operator*= ( const double &  a )

inline

multiplies by \(a: x_\mu^\prime = a \cdot x_\mu\)

Parameters

[in]

a

The value with which to multiply

Returns

FourVector where each component of *this has been multiplied by a

Definition at line 402 of file fourvector.h.

                                                        {
  this->x_[0] *= a;
  this->x_[1] *= a;
  this->x_[2] *= a;
  this->x_[3] *= a;
  return *this;
}

operator/=()

FourVector smash::FourVector::operator/= ( const double &  a )

inline

divides by \(a: x_\mu^\prime = \frac{1}{a} \cdot x_\mu\)

Parameters

[in]

a

The value by which to divide

Returns

FourVector where each component of *this has been divided by a

Definition at line 434 of file fourvector.h.

                                                        {
  const double a_inv = 1.0 / a;
  this->x_[0] *= a_inv;
  this->x_[1] *= a_inv;
  this->x_[2] *= a_inv;
  this->x_[3] *= a_inv;
  return *this;
}

begin() [1/2]

iterator smash::FourVector::begin ( )

inline

Returns

An iterator starting at the 0th component.

The iterator implements the randomIterator concept. Thus, you can simply write begin() + 1 to get an iterator that points to the 1st component.

Definition at line 291 of file fourvector.h.

{ return x_.begin(); }

end() [1/2]

iterator smash::FourVector::end ( )

inline

Returns

An iterator pointing after the 4th component.

Definition at line 294 of file fourvector.h.

{ return x_.end(); }

begin() [2/2]

const_iterator smash::FourVector::begin ( ) const

inline

Returns

A const_iterator pointing at the 0th component.

Definition at line 297 of file fourvector.h.

{ return x_.begin(); }

end() [2/2]

const_iterator smash::FourVector::end ( ) const

inline

Returns

A const_iterator pointing after the 4th component.

Definition at line 299 of file fourvector.h.

{ return x_.end(); }

cbegin()

const_iterator smash::FourVector::cbegin ( ) const

inline

See also

begin

Definition at line 302 of file fourvector.h.

{ return x_.cbegin(); }

cend()

const_iterator smash::FourVector::cend ( ) const

inline

See also

end

Definition at line 304 of file fourvector.h.

{ return x_.cend(); }

Member Data Documentation

x_

std::array<double, 4> smash::FourVector::x_

private

internal storage of this vector's components

Definition at line 308 of file fourvector.h.

---

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

• src/include/smash/fourvector.h
• src/fourvector.cc