utl::MuonArrivalTime Class Reference

all time delays are relative to arrival time of shower front plane More...

#include <MuonArrivalTime.h>

Classes
struct	ApproxMomentArg
struct	SuperArg
struct	TimeCDFArg
struct	TimePDFArg

Public Member Functions
return *	erf (z/kSqrt2))
	for (int i=fStart;i< lnt;++i)
	for (int i=fStart;i< 20;++i)
return fTimePDF	GetIntegral (0, t)
	MuonArrivalTime ()
void	SetCoordinates (const double r, const double delta)
void	SetTheta (const double theta)
	setup of model for given zenith angle More...
void	SetThetaAndDistance (const double theta, const double distance)
	setup model for given zenith angle and mean production distance More...
return nmuons *	std::pow (1.0-TimeCDF(t), nmuons-1)*TimePDF(t)
return nmuons *	std::pow (1.0-ApproximateTimeCDF(t), nmuons-1)*ApproximateTimePDF(t)

Public Attributes
double	const
	PDF of arrival time of muons. More...
return utl::NormalPDF(std::log(t), fMean, fSigma)/std double	const
	CDF of arrival time of muons using normal approximation in log(t) More...
void	const
fTimePDFArg	fT = t
const double	lnt = std::log(t)
	mean = result[0]
double	result = 0
return	result
	stdev = std::sqrt(result[1] - mean*mean)
const double	z = (std::log(t)-fMean)/fSigma - fSigma

Private Member Functions
	for (int i=1;i< n;++i)
	if (z<=0) return 0.0
return	PDF_dNdE (energy, x, fR)*dEdt
return	std::exp (f1+f2)*erfc(f3+f4)/(2.0 *fLogLambda)

Private Attributes
const double	c = utl::kSpeedOfLight
*std::pow(r/x, lamb)*std double	const
const double	cosaDa = std::sqrt(1.0-r*r/(z0*z0 + r*r))
const double	dEdt = 0.5*pk*x*1.0/std::sqrt(1.0+2.0*m2/(pk*pk*x*c*t))*m2/(pk*pk*x*c*t*t)
const double	dNdz = 1.0/(z*utl::kLn10)*PDF_dNdlgZ(lgZ)
const double	dzdt = 0.5*(r*r/(c*t*t)+c)
return cosaDa *dNdz *	dzdt
const double	energy = 0.5*pk*x*(1.0+std::sqrt(1.0+2.0*m2/(pk*pk*x*c*t)))
const double	f2 = 0.5*(fLogSigma*fLogSigma)/(fLogLambda*fLogLambda)
const double	f3 = (logz-fLogMean)/(utl::kSqrt2*fLogSigma)
const double	f4 = fLogSigma/(utl::kSqrt2*fLogLambda)
utl::VectorIntegrator < ApproxMomentArg, 2 >	fApproxMoment
ApproxMomentArg	fApproxMomentArg
double	fDelta
double	fLogLambda
double	fLogMean
double	fLogSigma
double	fMean
double	fNorm
double	fR
double	fSigma
double	fStart
utl::VectorIntegrator < SuperArg, 4 >	fSuper
SuperArg	fSuperArg
double	fTheta
utl::Integrator< TimeCDFArg >	fTimeCDF
TimeCDFArg	fTimeCDFArg
utl::Integrator< TimePDFArg >	fTimePDF
TimePDFArg	fTimePDFArg
const double	gam =2.6
const double	kappa =0.8
const double	lamb =1
const double	lgZ = std::log10(z)
const double	m2 = 0.011
const double	pk = 0.0002
const double	ptc =0.17
const double	r = fR
const double	x = std::sqrt(z0*z0 + fR*fR)
const double	z0 = 0.5*(r*r/(c*t)-c*t)
const double	zMean = std::pow(10, fLogMean)

Detailed Description

all time delays are relative to arrival time of shower front plane

Definition at line 23 of file MuonArrivalTime.h.

Constructor & Destructor Documentation

utl::MuonArrivalTime::MuonArrivalTime ( )

inline

Definition at line 26 of file MuonArrivalTime.h.

References fApproxMoment, fSuper, fTimeCDF, and fTimePDF.

Member Function Documentation

return* utl::MuonArrivalTime::erf

(

z/

kSqrt2

)

utl::MuonArrivalTime::for ( )

inline

Definition at line 125 of file MuonArrivalTime.h.

References fTimeCDF.

utl::MuonArrivalTime::for ( )

inline

Definition at line 178 of file MuonArrivalTime.h.

References fApproxMoment.

utl::MuonArrivalTime::for ( )

inlineprivate

Definition at line 275 of file MuonArrivalTime.h.

References x.

return fTimePDF utl::MuonArrivalTime::GetIntegral	(	0	,
		t
	)

utl::MuonArrivalTime::if ( z<=  0 )

private

return utl::MuonArrivalTime::PDF_dNdE ( energy  , x  , fR    )

private

void utl::MuonArrivalTime::SetCoordinates ( const double  r, const double  delta  )

inline

set coordinates of detector (shower front plane coordinate system) r = radial distance to shower axis, delta = distance to shower front plane

Definition at line 81 of file MuonArrivalTime.h.

References fDelta, fMean, fNorm, fR, fSigma, fStart, fSuper, r, result, and sqrt().

Referenced by SdHorizontalReconstructionNS::ShowerFrontFunction::Predict().

void utl::MuonArrivalTime::SetTheta ( const double  theta )

inline

setup of model for given zenith angle

Definition at line 54 of file MuonArrivalTime.h.

References c, utl::EvalPoly(), fLogLambda, fLogMean, fLogSigma, and fTheta.

Referenced by SetThetaAndDistance().

void utl::MuonArrivalTime::SetThetaAndDistance ( const double  theta, const double  distance  )

inline

setup model for given zenith angle and mean production distance

Definition at line 72 of file MuonArrivalTime.h.

References fLogMean, and SetTheta().

Referenced by SdHorizontalReconstructionNS::ShowerFrontFunction::Predict().

return utl::MuonArrivalTime::std::exp ( f1+  f2 )

private

return nmuons* utl::MuonArrivalTime::std::pow	(	1.0-	TimeCDFt,
		nmuons-	1
	)

return nmuons* utl::MuonArrivalTime::std::pow	(	1.0-	ApproximateTimeCDFt,
		nmuons-	1
	)

Member Data Documentation

const double utl::MuonArrivalTime::c = utl::kSpeedOfLight

private

Definition at line 200 of file MuonArrivalTime.h.

Referenced by SetTheta().

double utl::MuonArrivalTime::const

Initial value:

{
      if (t <= 0) return 0

PDF of arrival time of muons.

PDF model of muon energy distribution.

PDF model of muon production distance.

PDF of kinetic time delay due to distribution of muon energy.

PDF of geometric time delay due to distribution of muon production distance.

extreme value distribution of arrival time of first particle using normal approximation in log(t)

approximate PDF of arrival time of muons using normal approximation in log(t)

extreme value distribution of arrival time of first particle

CDF of arrival time of muons.

Definition at line 111 of file MuonArrivalTime.h.

return utl::NormalPDF (std::log(t),fMean,fSigma)/std double utl::MuonArrivalTime::const

Initial value:

{
      if (t <= 0) return 0

CDF of arrival time of muons using normal approximation in log(t)

Definition at line 157 of file MuonArrivalTime.h.

void utl::MuonArrivalTime::const

Initial value:

{
      fApproxMomentArg.fNMuon = nmuon

Definition at line 175 of file MuonArrivalTime.h.

* std::pow (r/x,lamb) *std double utl::MuonArrivalTime::const

private

Initial value:

{
      double result = pars[n-1]

Definition at line 273 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::cosaDa = std::sqrt(1.0-r*r/(z0*z0 + r*r))

private

Definition at line 210 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::dEdt = 0.5*pk*x*1.0/std::sqrt(1.0+2.0*m2/(pk*pk*x*c*t))*m2/(pk*pk*x*c*t*t)

private

Definition at line 234 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::dNdz = 1.0/(z*utl::kLn10)*PDF_dNdlgZ(lgZ)

private

Definition at line 213 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::dzdt = 0.5*(r*r/(c*t*t)+c)

private

Definition at line 208 of file MuonArrivalTime.h.

return cosaDa* dNdz* utl::MuonArrivalTime::dzdt

private

Definition at line 215 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::energy = 0.5*pk*x*(1.0+std::sqrt(1.0+2.0*m2/(pk*pk*x*c*t)))

private

Definition at line 233 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::f2 = 0.5*(fLogSigma*fLogSigma)/(fLogLambda*fLogLambda)

private

Definition at line 245 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::f3 = (logz-fLogMean)/(utl::kSqrt2*fLogSigma)

private

Definition at line 246 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::f4 = fLogSigma/(utl::kSqrt2*fLogLambda)

private

Definition at line 247 of file MuonArrivalTime.h.

utl::VectorIntegrator<ApproxMomentArg, 2> utl::MuonArrivalTime::fApproxMoment

private

Definition at line 376 of file MuonArrivalTime.h.

Referenced by for(), and MuonArrivalTime().

ApproxMomentArg utl::MuonArrivalTime::fApproxMomentArg

mutableprivate

Definition at line 375 of file MuonArrivalTime.h.

double utl::MuonArrivalTime::fDelta

private

Definition at line 361 of file MuonArrivalTime.h.

Referenced by SetCoordinates().

double utl::MuonArrivalTime::fLogLambda

private

Definition at line 362 of file MuonArrivalTime.h.

Referenced by SetTheta().

double utl::MuonArrivalTime::fLogMean

private

Definition at line 363 of file MuonArrivalTime.h.

Referenced by SetTheta(), and SetThetaAndDistance().

double utl::MuonArrivalTime::fLogSigma

private

Definition at line 364 of file MuonArrivalTime.h.

Referenced by SetTheta().

double utl::MuonArrivalTime::fMean

private

Definition at line 367 of file MuonArrivalTime.h.

Referenced by SetCoordinates().

double utl::MuonArrivalTime::fNorm

private

Definition at line 365 of file MuonArrivalTime.h.

Referenced by utl::MuonArrivalTime::TimePDFArg::operator()(), and SetCoordinates().

double utl::MuonArrivalTime::fR

private

Definition at line 360 of file MuonArrivalTime.h.

Referenced by SetCoordinates().

double utl::MuonArrivalTime::fSigma

private

Definition at line 368 of file MuonArrivalTime.h.

Referenced by SetCoordinates().

double utl::MuonArrivalTime::fStart

private

Definition at line 366 of file MuonArrivalTime.h.

Referenced by SetCoordinates().

utl::VectorIntegrator<SuperArg, 4> utl::MuonArrivalTime::fSuper

private

Definition at line 374 of file MuonArrivalTime.h.

Referenced by MuonArrivalTime(), and SetCoordinates().

SuperArg utl::MuonArrivalTime::fSuperArg

mutableprivate

Definition at line 373 of file MuonArrivalTime.h.

fTimePDFArg utl::MuonArrivalTime::fT = t

Definition at line 113 of file MuonArrivalTime.h.

double utl::MuonArrivalTime::fTheta

private

Definition at line 359 of file MuonArrivalTime.h.

Referenced by SetTheta().

utl::Integrator<TimeCDFArg> utl::MuonArrivalTime::fTimeCDF

private

Definition at line 372 of file MuonArrivalTime.h.

Referenced by for(), and MuonArrivalTime().

TimeCDFArg utl::MuonArrivalTime::fTimeCDFArg

mutableprivate

Definition at line 371 of file MuonArrivalTime.h.

utl::Integrator<TimePDFArg> utl::MuonArrivalTime::fTimePDF

private

Definition at line 370 of file MuonArrivalTime.h.

Referenced by MuonArrivalTime(), utl::MuonArrivalTime::TimeCDFArg::operator()(), and utl::MuonArrivalTime::SuperArg::operator()().

TimePDFArg utl::MuonArrivalTime::fTimePDFArg

mutableprivate

Definition at line 369 of file MuonArrivalTime.h.

Referenced by utl::MuonArrivalTime::TimeCDFArg::operator()(), and utl::MuonArrivalTime::SuperArg::operator()().

const double utl::MuonArrivalTime::gam =2.6

private

Definition at line 261 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::kappa =0.8

private

Definition at line 258 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::lamb =1

private

Definition at line 259 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::lgZ = std::log10(z)

private

Definition at line 212 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::lnt = std::log(t)

Definition at line 123 of file MuonArrivalTime.h.

Referenced by utl::MuonArrivalTime::SuperArg::operator()().

const double utl::MuonArrivalTime::m2 = 0.011

private

Definition at line 229 of file MuonArrivalTime.h.

utl::MuonArrivalTime::mean = result[0]

Definition at line 187 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::pk = 0.0002

private

Definition at line 230 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::ptc =0.17

private

Definition at line 260 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::r = fR

private

Definition at line 201 of file MuonArrivalTime.h.

Referenced by SetCoordinates().

return utl::MuonArrivalTime::result = 0

Definition at line 124 of file MuonArrivalTime.h.

Referenced by SetCoordinates().

return utl::MuonArrivalTime::result

Definition at line 131 of file MuonArrivalTime.h.

utl::MuonArrivalTime::stdev = std::sqrt(result[1] - mean*mean)

Definition at line 188 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::x = std::sqrt(z0*z0 + fR*fR)

private

Definition at line 227 of file MuonArrivalTime.h.

Referenced by for().

const double utl::MuonArrivalTime::z = (std::log(t)-fMean)/fSigma - fSigma

Definition at line 159 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::z0 = 0.5*(r*r/(c*t)-c*t)

private

Definition at line 204 of file MuonArrivalTime.h.

const double utl::MuonArrivalTime::zMean = std::pow(10, fLogMean)

private

Definition at line 225 of file MuonArrivalTime.h.

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

• MuonArrivalTime.h