Class for sphericity tensor calculations. More...

#include <JEventShapeVariables.hh>

Inheritance diagram for JSIRENE::JSphericityTensor:

Public Types
typedef JMatrix3S::eigen_values	eigen_values

Public Member Functions
	JSphericityTensor ()
	Default constructor. More...

	JSphericityTensor (std::vector< Trk >::const_iterator __begin, std::vector< Trk >::const_iterator __end, const double r=2.0)
	Constructor. More...

	JSphericityTensor (const Evt &event, const double r=2.0)
	Constructor. More...

const eigen_values &	getEigenValues () const
	Get eigenvalues. More...

double	getSphericity () const
	Get sphericity. More...

double	getAplanarity () const
	Get aplanarity. More...

double	getCircularity () const
	Get circularity. More...

double	getPlanarFlow () const
	Get planar flow. More...

double	getC () const
	Get C-variable. More...

double	getD () const
	Get D-variable. More...

void	invert ()
	Invert matrix. More...

eigen_values	getEigenValues (const double epsilon=1e-6) const
	Get eigen values. More...

JMatrix3D &	setIdentity ()
	Set to identity matrix. More...

void	set (const JMatrix3D &A)
	Set matrix. More...

JMatrix3D &	reset ()
	Set matrix to the null matrix. More...

JMatrix3D &	transpose ()
	Transpose. More...

JMatrix3D &	negate ()
	Negate matrix. More...

JMatrix3D &	add (const JMatrix3D &A)
	Matrix addition. More...

JMatrix3D &	sub (const JMatrix3D &A)
	Matrix subtraction. More...

JMatrix3D &	mul (const double factor)
	Scale matrix. More...

JMatrix3D &	mul (const JMatrix3D &A, const JMatrix3D &B)
	Matrix multiplication. More...

JMatrix3D &	mul (const JNullType &object)
	Multiply with object. More...

JMatrix3D &	div (const double factor)
	Scale matrix. More...

bool	equals (const JMatrix3D &A, const double eps=std::numeric_limits< double >::min()) const
	Equality. More...

bool	isIdentity (const double eps=std::numeric_limits< double >::min()) const
	Test identity. More...

double	getDeterminant () const
	Get determinant of matrix. More...

void	transform (double &__x, double &__y, double &__z) const
	Transform. More...

Static Public Member Functions
static const JMatrix3D &	getInstance ()
	Get reference to unique instance of this class object. More...

static const JMatrix3D &	getIdentity ()
	Get reference to unique instance of this class object. More...

Public Attributes
double	a00

double	a01

double	a02

double	a10

double	a11

double	a12

double	a20

double	a21

double	a22

Private Attributes
eigen_values	lambda
	sorted eigenvalues More...

Detailed Description

Class for sphericity tensor calculations.

The tensor is constructed following the definition in section 15.2.1 of arXiv:hep-ph/0603175v2.

Definition at line 234 of file JEventShapeVariables.hh.

Member Typedef Documentation

typedef JMatrix3S::eigen_values JSIRENE::JSphericityTensor::eigen_values

Definition at line 237 of file JEventShapeVariables.hh.

Constructor & Destructor Documentation

JSIRENE::JSphericityTensor::JSphericityTensor ( )

inline

Default constructor.

Definition at line 243 of file JEventShapeVariables.hh.

244 {}

JSIRENE::JSphericityTensor::JSphericityTensor	(	std::vector< Trk >::const_iterator	__begin,
		std::vector< Trk >::const_iterator	__end,
		const double	r = `2.0`
	)

inline

Constructor.

Parameters

__begin	beginning of track data
__end	end of track data
r	the power of the momentum-dependence

Definition at line 254 of file JEventShapeVariables.hh.

     {
       using namespace std;
       using namespace JPP;
       
       double norm = 0.0;
 
       for (vector<Trk>::const_iterator i = __begin; i != __end; ++i) {
       
         if (is_finalstate(*i)) {
 
           const Vec p = getKineticEnergy(*i) * i->dir;
           
           const double c = pow(p.len(), r-2);
 
           a00 += c * p.x * p.x;
           a01 += c * p.x * p.y;
           a02 += c * p.x * p.z;
 
           a10 += c * p.y * p.x;
           a11 += c * p.y * p.y;
           a12 += c * p.y * p.z;
 
           a20 += c * p.z * p.x;
           a21 += c * p.z * p.y;
           a22 += c * p.z * p.z;
       
           norm += c * p.dot(p);
         }
       }
 
       this->div(norm);
       
       lambda = JMatrix3S::getEigenValues();
     }

JSIRENE::JSphericityTensor::JSphericityTensor	(	const Evt &	event,
		const double	r = `2.0`
	)

inline

Constructor.

Parameters

event	event
r	the power of the momentum dependence

Definition at line 299 of file JEventShapeVariables.hh.

                                             :
       JSphericityTensor(event.mc_trks.begin(), event.mc_trks.end(), r)
     {}

Member Function Documentation

const eigen_values& JSIRENE::JSphericityTensor::getEigenValues ( ) const

inline

Get eigenvalues.

Returns: eigenvalues

Definition at line 310 of file JEventShapeVariables.hh.

     {
       return lambda;
     }

double JSIRENE::JSphericityTensor::getSphericity ( ) const

inline

Get sphericity.

Returns: sphericity

Definition at line 321 of file JEventShapeVariables.hh.

     {
       return 3 * (lambda[1] + lambda[2]) / 2.0;
     }

double JSIRENE::JSphericityTensor::getAplanarity ( ) const

inline

Get aplanarity.

Returns: aplanarity

Definition at line 332 of file JEventShapeVariables.hh.

     {
       return 3 * lambda[2] / 2.0;
     }

double JSIRENE::JSphericityTensor::getCircularity ( ) const

inline

Get circularity.

Returns: circularity

Definition at line 343 of file JEventShapeVariables.hh.

     {
       return (fabs(lambda[0] + lambda[1]) > 0.0 ?
               2 * lambda[1] / (lambda[0] + lambda[1]) : 0.0);
     }

double JSIRENE::JSphericityTensor::getPlanarFlow ( ) const

inline

Get planar flow.

Returns: planar flow

Definition at line 355 of file JEventShapeVariables.hh.

     {
       return 4 * lambda[0] * lambda[1] / (lambda[0] + lambda[1]) / (lambda[0] + lambda[1]);
     }

double JSIRENE::JSphericityTensor::getC ( ) const

inline

Get C-variable.

Returns: C

Definition at line 366 of file JEventShapeVariables.hh.

     {
       return 3 * (lambda[0]*lambda[1] + lambda[0]*lambda[2] + lambda[1]*lambda[2]);
     }

double JSIRENE::JSphericityTensor::getD ( ) const

inline

Get D-variable.

Returns: D

Definition at line 377 of file JEventShapeVariables.hh.

     {
       return 27 * lambda[0] * lambda[1] * lambda[2];
     }

void JMATH::JMatrix3S::invert ( )

inlineinherited

Invert matrix.

Definition at line 80 of file JMatrix3S.hh.

     {
       using std::swap;
 
       // LDU decomposition
 
       int    p0 = 0; // permute row 0
       int    p1 = 0; // permute row 1
 
       double val;
 
       val = a00;
 
       if (fabs(a10) > fabs(val)) {
         p0  = 1;
         val = a10;
       }
 
       if (fabs(a20) > fabs(val)) {
         p0  = 2;
         val = a20;
       }
 
       switch (p0) {
 
       case 1:
         swap(a00,a10);
         swap(a01,a11);
         swap(a02,a12);
         break;
 
       case 2:
         swap(a00,a20);
         swap(a01,a21);
         swap(a02,a22);
         break;
       }
 
       if (val == 0) {
         throw JDivisionByZero("LDU decomposition zero pivot");  
       }
 
       a10 /= val;
       a11 -= a10 * a01;
       a12 -= a10 * a02;
 
       a20 /= val;
       a21 -= a20 * a01;
       a22 -= a20 * a02;
 
       val = a11;
 
       if (fabs(a21) > fabs(val)) {
         p1  = 2;
         val = a21;
       }
 
       switch (p1) {
 
       case 2:
         swap(a10,a20);
         swap(a11,a21);
         swap(a12,a22);
         break;
       }
 
       if (val == 0) {
         throw JDivisionByZero("LDU decomposition zero pivot");
       }
 
       a21 /= val;
       a22 -= a21 * a12;
 
       // invert D
 
       if (a22 == 0) {
         throw JDivisionByZero("D matrix not invertable");
       }
 
       a00  = 1.0 / a00;
       a11  = 1.0 / a11;
       a22  = 1.0 / a22;
 
       // invert U
 
       a01 *= -a00;
       a01 *=  a11;
 
       a02 *= -a00;
       a02 -=  a01 * a12;
       a02 *=  a22;
 
       a12 *= -a11;
       a12 *=  a22;
 
       // invert L
 
       a21  = -a21;
       a20  = -a20;
       a20 -=  a21 * a10;
       a10  = -a10;
 
       // U^-1 x L^-1
 
       a00 += a01 * a10  +  a02 * a20;
       a01 += a02 * a21;
       a10 *= a11;
       a10 += a12 * a20;
       a11 += a12 * a21;
       a20 *= a22;
       a21 *= a22;
 
       switch (p1) {
 
       case 2:
         swap(a01,a02);
         swap(a11,a12);
         swap(a21,a22);
         break;
       }
 
       switch (p0) {
 
       case 1:
         swap(a00,a01);
         swap(a10,a11);
         swap(a20,a21);
         break;
 
       case 2:
         swap(a00,a02);
         swap(a10,a12);
         swap(a20,a22);
         break;
       }
     }

eigen_values JMATH::JMatrix3S::getEigenValues ( const double epsilon = 1e-6 ) const

inlineinherited

Get eigen values.

The eigen values sorted in decreasing order of absolute values.
Algorithm taken from "Eigenvalues of a symmetric 3x3 matrix"
by Oliver K. Smith; see reference.

Parameters

epsilon precision

Returns: eigen values

Definition at line 227 of file JMatrix3S.hh.

     {
       using namespace std;
 
       eigen_values eigenvalues;
 
       const double p1 = a01*a01 + a02*a02 + a12*a12;
 
       if (fabs(p1 - 1.0) > epsilon) {
       
         const double q  = (a00 + a11 + a22) / 3.0;
         const double p2 = (a00 - q)*(a00 - q) + (a11 - q)*(a11 - q) + (a22 - q)*(a22 - q) + 2*p1;
         const double p  = sqrt(p2 / 6.0);
 
         JMatrix3S B(*this);
 
         B.sub(q * JMatrix3D::getIdentity());
         B.div(p);
 
         const double r   = B.getDeterminant() / 2.0;
         const double phi = (r < -1.0 ? PI / 3.0 : (r >  1.0 ? 0.0 : acos(r) / 3.0));
 
         eigenvalues[0] = q + 2*p*cos(phi);
         eigenvalues[2] = q + 2*p*cos(phi + 2*PI/3.0);
         eigenvalues[1] = 3 * q - eigenvalues[0] - eigenvalues[2];
 
       } else {
 
         eigenvalues = eigen_values{ a00, a11, a12 };
       }
 
       // sort absolute values in descending order
 
       if (fabs(eigenvalues[0]) < fabs(eigenvalues[1])) {
         swap(eigenvalues[0], eigenvalues[1]);
       }
 
       if (fabs(eigenvalues[1]) < fabs(eigenvalues[2])) {
 
         swap(eigenvalues[1], eigenvalues[2]);
 
         if (fabs(eigenvalues[0]) < fabs(eigenvalues[1])) {
           swap(eigenvalues[0], eigenvalues[1]);
         }
       }
 
       return eigenvalues;
     }

static const JMatrix3D& JMATH::JMatrix3D::getInstance ( )

inlinestaticinherited

Get reference to unique instance of this class object.

Returns: zero matrix

Definition at line 78 of file JMath/JMatrix3D.hh.

     {
       static JMatrix3D matrix;
 
       return matrix;
     }

JMatrix3D& JMATH::JMatrix3D::setIdentity ( )

inlineinherited

Set to identity matrix.

Returns: this matrix

Definition at line 91 of file JMath/JMatrix3D.hh.

     {
       a00 = 1.0;  a01 = 0.0;  a02 = 0.0;
       a10 = 0.0;  a11 = 1.0;  a12 = 0.0;
       a20 = 0.0;  a21 = 0.0;  a22 = 1.0;
 
       return *this;
     }

static const JMatrix3D& JMATH::JMatrix3D::getIdentity ( )

inlinestaticinherited

Get reference to unique instance of this class object.

Returns: identity matrix

Definition at line 106 of file JMath/JMatrix3D.hh.

     {
       static JMatrix3D matrix(JMatrix3D().setIdentity());
 
       return matrix;
     }

void JMATH::JMatrix3D::set ( const JMatrix3D & A )

inlineinherited

Set matrix.

Parameters

A matrix

Definition at line 119 of file JMath/JMatrix3D.hh.

     {
       static_cast<JMatrix3D&>(*this) = A;
     }

JMatrix3D& JMATH::JMatrix3D::reset ( )

inlineinherited

Set matrix to the null matrix.

Returns: this matrix

Definition at line 130 of file JMath/JMatrix3D.hh.

     {
       *this = JMatrix3D();
 
       return *this;
     }

JMatrix3D& JMATH::JMatrix3D::transpose ( )

inlineinherited

Transpose.

Returns: this matrix

Definition at line 143 of file JMath/JMatrix3D.hh.

     {
       using std::swap;
 
       swap(a10, a01);
       swap(a20, a02);
       swap(a21, a12);
 
       return *this;
     }

JMatrix3D& JMATH::JMatrix3D::negate ( )

inlineinherited

Negate matrix.

Returns: -this matrix

Definition at line 160 of file JMath/JMatrix3D.hh.

     {
       a00 = -a00;  a01 = -a01;  a02 = -a02;
       a10 = -a10;  a11 = -a11;  a12 = -a12;
       a20 = -a20;  a21 = -a21;  a22 = -a22;
 
       return *this;
     }

JMatrix3D& JMATH::JMatrix3D::add ( const JMatrix3D & A )

inlineinherited

Matrix addition.

Parameters

A matrix

Returns: this matrix + A

Definition at line 176 of file JMath/JMatrix3D.hh.

     {
       a00 += A.a00;  a01 += A.a01;  a02 += A.a02;
       a10 += A.a10;  a11 += A.a11;  a12 += A.a12;
       a20 += A.a20;  a21 += A.a21;  a22 += A.a22;
   
       return *this;
     }

JMatrix3D& JMATH::JMatrix3D::sub ( const JMatrix3D & A )

inlineinherited

Matrix subtraction.

Parameters

A matrix

Returns: this matrix - A

Definition at line 192 of file JMath/JMatrix3D.hh.

     {
       a00 -= A.a00;  a01 -= A.a01;  a02 -= A.a02;
       a10 -= A.a10;  a11 -= A.a11;  a12 -= A.a12;
       a20 -= A.a20;  a21 -= A.a21;  a22 -= A.a22;
   
       return *this;
     }

JMatrix3D& JMATH::JMatrix3D::mul ( const double factor )

inlineinherited

Scale matrix.

Parameters

factor factor

Returns: this matrix * factor

Definition at line 208 of file JMath/JMatrix3D.hh.

     {
       a00 *= factor; a01 *= factor; a02 *= factor;
       a10 *= factor; a11 *= factor; a12 *= factor;
       a20 *= factor; a21 *= factor; a22 *= factor;
 
       return *this;
     }

JMatrix3D& JMATH::JMatrix3D::mul	(	const JMatrix3D &	A,
		const JMatrix3D &	B
	)

inlineinherited

Matrix multiplication.

Parameters

A	matrix
B	matrix

Returns: this matrix

Definition at line 241 of file JMath/JMatrix3D.hh.

     {
       a00 = A.a00 * B.a00  +  A.a01 * B.a10  +  A.a02 * B.a20;
       a01 = A.a00 * B.a01  +  A.a01 * B.a11  +  A.a02 * B.a21;
       a02 = A.a00 * B.a02  +  A.a01 * B.a12  +  A.a02 * B.a22;
       
       a10 = A.a10 * B.a00  +  A.a11 * B.a10  +  A.a12 * B.a20;
       a11 = A.a10 * B.a01  +  A.a11 * B.a11  +  A.a12 * B.a21;
       a12 = A.a10 * B.a02  +  A.a11 * B.a12  +  A.a12 * B.a22;
       
       a20 = A.a20 * B.a00  +  A.a21 * B.a10  +  A.a22 * B.a20;
       a21 = A.a20 * B.a01  +  A.a21 * B.a11  +  A.a22 * B.a21;
       a22 = A.a20 * B.a02  +  A.a21 * B.a12  +  A.a22 * B.a22;
       
       return *this;
     }

JMatrix3D & JMATH::JMath< JMatrix3D , JNullType >::mul ( const JNullType & object )

inlineinherited

Multiply with object.

Parameters

object object

Returns: result object

Definition at line 354 of file JMath.hh.

     {
       return static_cast<JFirst_t&>(*this) = JFirst_t().mul(static_cast<const JFirst_t&>(*this), object);
     }

JMatrix3D& JMATH::JMatrix3D::div ( const double factor )

inlineinherited

Scale matrix.

Parameters

factor factor

Returns: this matrix / factor

Definition at line 224 of file JMath/JMatrix3D.hh.

     {
       a00 /= factor; a01 /= factor; a02 /= factor;
       a10 /= factor; a11 /= factor; a12 /= factor;
       a20 /= factor; a21 /= factor; a22 /= factor;
 
       return *this;
     }

bool JMATH::JMatrix3D::equals	(	const JMatrix3D &	A,
		const double	eps = `std::numeric_limits<double>::min()`
	)		const

inlineinherited

Equality.

Parameters

A	matrix
eps	numerical precision

Returns: true if matrices identical; else false

Definition at line 267 of file JMath/JMatrix3D.hh.

     {
       return (fabs(a00 - A.a00) <= eps  &&
               fabs(a01 - A.a01) <= eps  &&
               fabs(a02 - A.a02) <= eps  &&
               fabs(a10 - A.a10) <= eps  &&
               fabs(a11 - A.a11) <= eps  &&
               fabs(a12 - A.a12) <= eps  &&
               fabs(a20 - A.a20) <= eps  &&
               fabs(a21 - A.a21) <= eps  &&
               fabs(a22 - A.a22) <= eps);
     }

bool JMATH::JMatrix3D::isIdentity ( const double eps = std::numeric_limits<double>::min() ) const

inlineinherited

Test identity.

Parameters

eps	numerical precision

Returns: true if identity matrix; else false

Definition at line 288 of file JMath/JMatrix3D.hh.

     {
       return equals(getIdentity(), eps);
     }

double JMATH::JMatrix3D::getDeterminant ( ) const

inlineinherited

Get determinant of matrix.

Returns: determinant of matrix

Definition at line 299 of file JMath/JMatrix3D.hh.

     {
       double det = 0.0;
 
       det += a00 * (a11 * a22 - a21 * a12);
       det -= a01 * (a10 * a22 - a20 * a12);
       det += a02 * (a10 * a21 - a20 * a11);
 
       return det;
     }

void JMATH::JMatrix3D::transform	(	double &	__x,
		double &	__y,
		double &	__z
	)		const

inlineinherited

Transform.

Parameters

__x	x value
__y	y value
__z	z value

Definition at line 318 of file JMath/JMatrix3D.hh.

     {
       const double x = a00 * __x  +  a01 * __y  +  a02 * __z;
       const double y = a10 * __x  +  a11 * __y  +  a12 * __z;
       const double z = a20 * __x  +  a21 * __y  +  a22 * __z;
 
       __x = x;
       __y = y;
       __z = z;
     }

Member Data Documentation

eigen_values JSIRENE::JSphericityTensor::lambda

private

sorted eigenvalues

Definition at line 385 of file JEventShapeVariables.hh.

double JMATH::JMatrix3D::a00

inherited

Definition at line 385 of file JMath/JMatrix3D.hh.

double JMATH::JMatrix3D::a01

inherited

Definition at line 385 of file JMath/JMatrix3D.hh.

double JMATH::JMatrix3D::a02

inherited

Definition at line 385 of file JMath/JMatrix3D.hh.

double JMATH::JMatrix3D::a10

inherited

Definition at line 386 of file JMath/JMatrix3D.hh.

double JMATH::JMatrix3D::a11

inherited

Definition at line 386 of file JMath/JMatrix3D.hh.

double JMATH::JMatrix3D::a12

inherited

Definition at line 386 of file JMath/JMatrix3D.hh.

double JMATH::JMatrix3D::a20

inherited

Definition at line 387 of file JMath/JMatrix3D.hh.

double JMATH::JMatrix3D::a21

inherited

Definition at line 387 of file JMath/JMatrix3D.hh.

double JMATH::JMatrix3D::a22

inherited

Definition at line 387 of file JMath/JMatrix3D.hh.

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

JEventShapeVariables.hh

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Private Attributes

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation