ROOT   Reference Guide
ROOT::Math::VectorUtil Namespace Reference

Global Helper functions for generic Vector classes. More...

## Functions

template<class Vector1 , class Vector2 >
double Angle (const Vector1 &v1, const Vector2 &v2)
Find Angle between two vectors. More...

template<class LVector , class BoostVector >
LVector boost (const LVector &v, const BoostVector &b)
Boost a generic Lorentz Vector class using a generic 3D Vector class describing the boost The only requirement on the vector is that implements the X(), Y(), Z(), T() and SetXYZT methods. More...

template<class LVector , class T >
LVector boostX (const LVector &v, T beta)
Boost a generic Lorentz Vector class along the X direction with a factor beta The only requirement on the vector is that implements the X(), Y(), Z(), T() and SetXYZT methods. More...

template<class LVector >
LVector boostY (const LVector &v, double beta)
Boost a generic Lorentz Vector class along the Y direction with a factor beta The only requirement on the vector is that implements the X(), Y(), Z(), T() methods and be constructed from x,y,z,t values The beta of the boost must be <= 1 or a nul Lorentz Vector will be returned. More...

template<class LVector >
LVector boostZ (const LVector &v, double beta)
Boost a generic Lorentz Vector class along the Z direction with a factor beta The only requirement on the vector is that implements the X(), Y(), Z(), T() methods and be constructed from x,y,z,t values The beta of the boost must be <= 1 or a nul Lorentz Vector will be returned. More...

template<class Vector1 , class Vector2 >
double CosTheta (const Vector1 &v1, const Vector2 &v2)
Find CosTheta Angle between two generic 3D vectors pre-requisite: vectors implement the X(), Y() and Z() More...

template<class Vector1 , class Vector2 >
Vector1::Scalar DeltaPhi (const Vector1 &v1, const Vector2 &v2)
Find aximutal Angle difference between two generic vectors ( v2.Phi() - v1.Phi() ) The only requirements on the Vector classes is that they implement the Phi() method. More...

template<class Vector1 , class Vector2 >
Vector1::Scalar DeltaR (const Vector1 &v1, const Vector2 &v2)
Find difference in pseudorapidity (Eta) and Phi betwen two generic vectors The only requirements on the Vector classes is that they implement the Phi() and Eta() method. More...

template<class Vector1 , class Vector2 >
Vector1::Scalar DeltaR2 (const Vector1 &v1, const Vector2 &v2)
Find square of the difference in pseudorapidity (Eta) and Phi betwen two generic vectors The only requirements on the Vector classes is that they implement the Phi() and Eta() method. More...

template<class Vector1 , class Vector2 >
Vector1::Scalar DeltaR2RapidityPhi (const Vector1 &v1, const Vector2 &v2)
Find square of the difference in true rapidity (y) and Phi betwen two generic vectors The only requirements on the Vector classes is that they implement the Phi() and Rapidity() method. More...

template<class Vector1 , class Vector2 >
Vector1::Scalar DeltaRapidityPhi (const Vector1 &v1, const Vector2 &v2)
Find difference in Rapidity (y) and Phi betwen two generic vectors The only requirements on the Vector classes is that they implement the Phi() and Rapidity() method. More...

template<class Vector1 , class Vector2 >
Vector1::Scalar InvariantMass (const Vector1 &v1, const Vector2 &v2)
return the invariant mass of two LorentzVector The only requirement on the LorentzVector is that they need to implement the X() , Y(), Z() and E() methods. More...

template<class Vector1 , class Vector2 >
Vector1::Scalar InvariantMass2 (const Vector1 &v1, const Vector2 &v2)

template<class Matrix , class CoordSystem , class U >
DisplacementVector3D< CoordSystem, U > Mult (const Matrix &m, const DisplacementVector3D< CoordSystem, U > &v)
Multiplications of a generic matrices with a DisplacementVector3D of any coordinate system. More...

template<class CoordSystem , class Matrix >
LorentzVector< CoordSystem > Mult (const Matrix &m, const LorentzVector< CoordSystem > &v)
Multiplications of a generic matrices with a LorentzVector described in any coordinate system. More...

template<class Matrix , class CoordSystem , class U >
PositionVector3D< CoordSystem, U > Mult (const Matrix &m, const PositionVector3D< CoordSystem, U > &p)
Multiplications of a generic matrices with a generic PositionVector Assume that the matrix implements the operator( i,j) and that it has at least 3 columns and 3 rows. More...

template<class Vector1 , class Vector2 >
double Perp (const Vector1 &v, const Vector2 &u)
Find the magnitude of the vector component of v perpendicular to the given direction of u. More...

template<class Vector1 , class Vector2 >
double Perp2 (const Vector1 &v, const Vector2 &u)
Find the magnitude square of the vector component of v perpendicular to the given direction of u. More...

template<class Vector1 , class Vector2 >
Vector1 PerpVector (const Vector1 &v, const Vector2 &u)
Find the vector component of v perpendicular to the given direction of u. More...

double Phi_0_2pi (double phi)
Return a phi angle in the interval (0,2*PI]. More...

double Phi_mpi_pi (double phi)
Returns phi angle in the interval (-PI,PI]. More...

template<class Vector1 , class Vector2 >
Vector1 ProjVector (const Vector1 &v, const Vector2 &u)
Find the projection of v along the given direction u. More...

template<class Vector , class RotationMatrix >
Vector Rotate (const Vector &v, const RotationMatrix &rot)
rotation on a generic vector using a generic rotation class. More...

template<class Vector >
Vector RotateX (const Vector &v, double alpha)
rotation along X axis for a generic vector by an Angle alpha returning a new vector. More...

template<class Vector >
Vector RotateY (const Vector &v, double alpha)
rotation along Y axis for a generic vector by an Angle alpha returning a new vector. More...

template<class Vector >
Vector RotateZ (const Vector &v, double alpha)
rotation along Z axis for a generic vector by an Angle alpha returning a new vector. More...

## Detailed Description

Global Helper functions for generic Vector classes.

Any Vector classes implementing some defined member functions, like Phi() or Eta() or mag() can use these functions. The functions returning a scalar value, returns always double precision number even if the vector are based on another precision type

Overview of the physics vector library

## ◆ Angle()

template<class Vector1 , class Vector2 >
 double ROOT::Math::VectorUtil::Angle ( const Vector1 & v1, const Vector2 & v2 )
inline

Find Angle between two vectors.

Use the CosTheta() function

Parameters
 v1 Vector v1 v2 Vector v2
Returns
Angle between the two vectors

$\theta = \cos ^{-1} \frac { \vec{v1} \cdot \vec{v2} }{ | \vec{v1} | | \vec{v2} | }$

Definition at line 169 of file VectorUtil.h.

## ◆ boost()

template<class LVector , class BoostVector >
 LVector ROOT::Math::VectorUtil::boost ( const LVector & v, const BoostVector & b )

Boost a generic Lorentz Vector class using a generic 3D Vector class describing the boost The only requirement on the vector is that implements the X(), Y(), Z(), T() and SetXYZT methods.

The requirement on the boost vector is that needs to implement the X(), Y() , Z() retorning the vector elements describing the boost The beta of the boost must be <= 1 or a nul Lorentz Vector will be returned

Definition at line 367 of file VectorUtil.h.

## ◆ boostX()

template<class LVector , class T >
 LVector ROOT::Math::VectorUtil::boostX ( const LVector & v, T beta )

Boost a generic Lorentz Vector class along the X direction with a factor beta The only requirement on the vector is that implements the X(), Y(), Z(), T() and SetXYZT methods.

The beta of the boost must be <= 1 or a nul Lorentz Vector will be returned

Definition at line 397 of file VectorUtil.h.

## ◆ boostY()

template<class LVector >
 LVector ROOT::Math::VectorUtil::boostY ( const LVector & v, double beta )

Boost a generic Lorentz Vector class along the Y direction with a factor beta The only requirement on the vector is that implements the X(), Y(), Z(), T() methods and be constructed from x,y,z,t values The beta of the boost must be <= 1 or a nul Lorentz Vector will be returned.

Definition at line 419 of file VectorUtil.h.

## ◆ boostZ()

template<class LVector >
 LVector ROOT::Math::VectorUtil::boostZ ( const LVector & v, double beta )

Boost a generic Lorentz Vector class along the Z direction with a factor beta The only requirement on the vector is that implements the X(), Y(), Z(), T() methods and be constructed from x,y,z,t values The beta of the boost must be <= 1 or a nul Lorentz Vector will be returned.

Definition at line 440 of file VectorUtil.h.

## ◆ CosTheta()

template<class Vector1 , class Vector2 >
 double ROOT::Math::VectorUtil::CosTheta ( const Vector1 & v1, const Vector2 & v2 )

Find CosTheta Angle between two generic 3D vectors pre-requisite: vectors implement the X(), Y() and Z()

Parameters
 v1 Vector v1 v2 Vector v2
Returns
cosine of Angle between the two vectors

$\cos \theta = \frac { \vec{v1} \cdot \vec{v2} }{ | \vec{v1} | | \vec{v2} | }$

Definition at line 142 of file VectorUtil.h.

## ◆ DeltaPhi()

template<class Vector1 , class Vector2 >
 Vector1::Scalar ROOT::Math::VectorUtil::DeltaPhi ( const Vector1 & v1, const Vector2 & v2 )
inline

Find aximutal Angle difference between two generic vectors ( v2.Phi() - v1.Phi() ) The only requirements on the Vector classes is that they implement the Phi() method.

Parameters
 v1 Vector of any type implementing the Phi() operator v2 Vector of any type implementing the Phi() operator
Returns
Phi difference

$\Delta \phi = \phi_2 - \phi_1$

Definition at line 61 of file VectorUtil.h.

## ◆ DeltaR()

template<class Vector1 , class Vector2 >
 Vector1::Scalar ROOT::Math::VectorUtil::DeltaR ( const Vector1 & v1, const Vector2 & v2 )
inline

Find difference in pseudorapidity (Eta) and Phi betwen two generic vectors The only requirements on the Vector classes is that they implement the Phi() and Eta() method.

Parameters
 v1 Vector 1 v2 Vector 2
Returns
Angle between the two vectors

$\Delta R = \sqrt{ ( \Delta \phi )^2 + ( \Delta \eta )^2 }$

Definition at line 112 of file VectorUtil.h.

## ◆ DeltaR2()

template<class Vector1 , class Vector2 >
 Vector1::Scalar ROOT::Math::VectorUtil::DeltaR2 ( const Vector1 & v1, const Vector2 & v2 )
inline

Find square of the difference in pseudorapidity (Eta) and Phi betwen two generic vectors The only requirements on the Vector classes is that they implement the Phi() and Eta() method.

Parameters
 v1 Vector 1 v2 Vector 2
Returns
Angle between the two vectors

$\Delta R2 = ( \Delta \phi )^2 + ( \Delta \eta )^2$

Definition at line 82 of file VectorUtil.h.

## ◆ DeltaR2RapidityPhi()

template<class Vector1 , class Vector2 >
 Vector1::Scalar ROOT::Math::VectorUtil::DeltaR2RapidityPhi ( const Vector1 & v1, const Vector2 & v2 )
inline

Find square of the difference in true rapidity (y) and Phi betwen two generic vectors The only requirements on the Vector classes is that they implement the Phi() and Rapidity() method.

Parameters
 v1 Vector 1 v2 Vector 2
Returns
Angle between the two vectors

$\Delta R2 = ( \Delta \phi )^2 + ( \Delta \y )^2$

Definition at line 97 of file VectorUtil.h.

## ◆ DeltaRapidityPhi()

template<class Vector1 , class Vector2 >
 Vector1::Scalar ROOT::Math::VectorUtil::DeltaRapidityPhi ( const Vector1 & v1, const Vector2 & v2 )
inline

Find difference in Rapidity (y) and Phi betwen two generic vectors The only requirements on the Vector classes is that they implement the Phi() and Rapidity() method.

Parameters
 v1 Vector 1 v2 Vector 2
Returns
Angle between the two vectors

$\Delta R = \sqrt{ ( \Delta \phi )^2 + ( \Delta y )^2 }$

,

Definition at line 126 of file VectorUtil.h.

## ◆ InvariantMass()

template<class Vector1 , class Vector2 >
 Vector1::Scalar ROOT::Math::VectorUtil::InvariantMass ( const Vector1 & v1, const Vector2 & v2 )
inline

return the invariant mass of two LorentzVector The only requirement on the LorentzVector is that they need to implement the X() , Y(), Z() and E() methods.

Parameters
 v1 LorenzVector 1 v2 LorenzVector 2
Returns
invariant mass M

$M_{12} = \sqrt{ (\vec{v1} + \vec{v2} ) \cdot (\vec{v1} + \vec{v2} ) }$

Definition at line 248 of file VectorUtil.h.

## ◆ InvariantMass2()

template<class Vector1 , class Vector2 >
 Vector1::Scalar ROOT::Math::VectorUtil::InvariantMass2 ( const Vector1 & v1, const Vector2 & v2 )
inline

Definition at line 263 of file VectorUtil.h.

## ◆ Mult() [1/3]

template<class Matrix , class CoordSystem , class U >
 DisplacementVector3D< CoordSystem, U > ROOT::Math::VectorUtil::Mult ( const Matrix & m, const DisplacementVector3D< CoordSystem, U > & v )
inline

Multiplications of a generic matrices with a DisplacementVector3D of any coordinate system.

Assume that the matrix implements the operator( i,j) and that it has at least 3 columns and 3 rows. There is no check on the matrix size !!

Definition at line 469 of file VectorUtil.h.

## ◆ Mult() [2/3]

template<class CoordSystem , class Matrix >
 LorentzVector< CoordSystem > ROOT::Math::VectorUtil::Mult ( const Matrix & m, const LorentzVector< CoordSystem > & v )
inline

Multiplications of a generic matrices with a LorentzVector described in any coordinate system.

Assume that the matrix implements the operator( i,j) and that it has at least 4 columns and 4 rows. There is no check on the matrix size !!

Definition at line 501 of file VectorUtil.h.

## ◆ Mult() [3/3]

template<class Matrix , class CoordSystem , class U >
 PositionVector3D< CoordSystem, U > ROOT::Math::VectorUtil::Mult ( const Matrix & m, const PositionVector3D< CoordSystem, U > & p )
inline

Multiplications of a generic matrices with a generic PositionVector Assume that the matrix implements the operator( i,j) and that it has at least 3 columns and 3 rows.

There is no check on the matrix size !!

Definition at line 484 of file VectorUtil.h.

## ◆ Perp()

template<class Vector1 , class Vector2 >
 double ROOT::Math::VectorUtil::Perp ( const Vector1 & v, const Vector2 & u )
inline

Find the magnitude of the vector component of v perpendicular to the given direction of u.

Parameters
 v Vector v for which the perpendicular component is to be found u Vector specifying the direction
Returns
value of the component of v which is perpendicular to u

$perp = | \vec{v} - \frac{ \vec{v} \cdot \vec{u} }{|\vec{u}|}\vec{u} |$

Precondition is that Vector1 implements Dot function and Vector2 implements X(),Y() and Z()

Definition at line 228 of file VectorUtil.h.

## ◆ Perp2()

template<class Vector1 , class Vector2 >
 double ROOT::Math::VectorUtil::Perp2 ( const Vector1 & v, const Vector2 & u )
inline

Find the magnitude square of the vector component of v perpendicular to the given direction of u.

Parameters
 v Vector v for which the perpendicular component is to be found u Vector specifying the direction
Returns
square value of the component of v which is perpendicular to u

$perp = | \vec{v} - \frac{ \vec{v} \cdot \vec{u} }{|\vec{u}|}\vec{u} |^2$

Precondition is that Vector1 implements Dot function and Vector2 implements X(),Y() and Z()

Definition at line 212 of file VectorUtil.h.

## ◆ PerpVector()

template<class Vector1 , class Vector2 >
 Vector1 ROOT::Math::VectorUtil::PerpVector ( const Vector1 & v, const Vector2 & u )
inline

Find the vector component of v perpendicular to the given direction of u.

Parameters
 v Vector v for which the perpendicular component is to be found u Vector specifying the direction
Returns
Vector component of v which is perpendicular to u

$\vec{perp} = \vec{v} - \frac{ \vec{v} \cdot \vec{u} }{|\vec{u}|}\vec{u}$

Precondition is that Vector1 implements Dot function and Vector2 implements X(),Y() and Z()

Definition at line 199 of file VectorUtil.h.

## ◆ Phi_0_2pi()

 double ROOT::Math::VectorUtil::Phi_0_2pi ( double phi )

Return a phi angle in the interval (0,2*PI].

Definition at line 22 of file VectorUtil.cxx.

## ◆ Phi_mpi_pi()

 double ROOT::Math::VectorUtil::Phi_mpi_pi ( double phi )

Returns phi angle in the interval (-PI,PI].

Definition at line 36 of file VectorUtil.cxx.

## ◆ ProjVector()

template<class Vector1 , class Vector2 >
 Vector1 ROOT::Math::VectorUtil::ProjVector ( const Vector1 & v, const Vector2 & u )

Find the projection of v along the given direction u.

Parameters
 v Vector v for which the propjection is to be found u Vector specifying the direction
Returns
Vector projection (same type of v)

$\vec{proj} = \frac{ \vec{v} \cdot \vec{u} }{|\vec{u}|}\vec{u}$

Precondition is that Vector1 implements Dot function and Vector2 implements X(),Y() and Z()

Definition at line 183 of file VectorUtil.h.

## ◆ Rotate()

template<class Vector , class RotationMatrix >
 Vector ROOT::Math::VectorUtil::Rotate ( const Vector & v, const RotationMatrix & rot )

rotation on a generic vector using a generic rotation class.

The only requirement on the vector is that implements the X(), Y(), Z() and SetXYZ methods. The requirement on the rotation matrix is that need to implement the (i,j) operator returning the matrix element with R(0,0) = xx element

Definition at line 346 of file VectorUtil.h.

## ◆ RotateX()

template<class Vector >
 Vector ROOT::Math::VectorUtil::RotateX ( const Vector & v, double alpha )

rotation along X axis for a generic vector by an Angle alpha returning a new vector.

The only pre requisite on the Vector is that it has to implement the X() , Y() and Z() and SetXYZ methods.

Definition at line 287 of file VectorUtil.h.

## ◆ RotateY()

template<class Vector >
 Vector ROOT::Math::VectorUtil::RotateY ( const Vector & v, double alpha )

rotation along Y axis for a generic vector by an Angle alpha returning a new vector.

The only pre requisite on the Vector is that it has to implement the X() , Y() and Z() and SetXYZ methods.

Definition at line 306 of file VectorUtil.h.

## ◆ RotateZ()

template<class Vector >
 Vector ROOT::Math::VectorUtil::RotateZ ( const Vector & v, double alpha )

rotation along Z axis for a generic vector by an Angle alpha returning a new vector.

The only pre requisite on the Vector is that it has to implement the X() , Y() and Z() and SetXYZ methods.

Definition at line 325 of file VectorUtil.h.