Namespaces
namespace	detail

Classes
class	CachingTF1

class	Chebyshev3D

class	Chebyshev3DCalc

class	Legendre1DPolynominal

class	Legendre2DPolynominal
	.... More...

class	RandomRing

class	Rotation2D
	transformation types More...

struct	StatisticsData

class	SymMatrixSolver

class	Transform3D

struct	TransformType

struct	Tsallis

Typedefs
using	Rotation2Df_t = Rotation2D< float >

using	Rotation2Dd_t = Rotation2D< double >

template<typename T >
using	CircleXY = detail::CircleXY< T >

using	CircleXYf_t = detail::CircleXY< float >

using	CircleXYd_t = detail::CircleXY< double >

template<typename T >
using	IntervalXY = detail::IntervalXY< T >

using	IntervalXYf_t = detail::IntervalXY< float >

using	IntervalXYd_t = detail::IntervalXY< double >

template<typename T >
using	Bracket = detail::Bracket< T >

using	Bracketf_t = detail::Bracket< float >

using	Bracketd_t = detail::Bracket< double >

template<typename T >
using	Point2D = ROOT::Math::PositionVector2D< ROOT::Math::Cartesian2D< T >, ROOT::Math::DefaultCoordinateSystemTag >

template<typename T >
using	Vector2D = ROOT::Math::DisplacementVector2D< ROOT::Math::Cartesian2D< T >, ROOT::Math::DefaultCoordinateSystemTag >

template<typename T >
using	Point3D = ROOT::Math::PositionVector3D< ROOT::Math::Cartesian3D< T >, ROOT::Math::DefaultCoordinateSystemTag >

template<typename T >
using	Vector3D = ROOT::Math::DisplacementVector3D< ROOT::Math::Cartesian3D< T >, ROOT::Math::DefaultCoordinateSystemTag >

template<typename T , uint32_t N>
using	SVector = ROOT::Math::SVector< T, N >

template<class T , uint32_t D1, uint32_t D2, class R >
using	SMatrix = ROOT::Math::SMatrix< T, D1, D2, R >

template<class T , uint32_t D>
using	MatRepSym = ROOT::Math::MatRepSym< T, D >

template<class T , uint32_t D1, uint32_t D2 = D1>
using	MatRepStd = ROOT::Math::MatRepStd< T, D1, D2 >

Functions
template<class T , unsigned int D>
T	Dot (const SVector< T, D > &lhs, const SVector< T, D > &rhs)

template<class T , unsigned int D1, unsigned int D2, class R >
SMatrix< T, D1, D1, MatRepSym< T, D1 > >	Similarity (const SMatrix< T, D1, D2, R > &lhs, const SMatrix< T, D2, D2, MatRepSym< T, D2 > > &rhs)

template<typename T >
TFitResultPtr	fit (const size_t nBins, const T *arr, const T xMin, const T xMax, TF1 &func, std::string_view option="")

template<typename T >
bool	medmadGaus (size_t nBins, const T *arr, const T xMin, const T xMax, std::array< double, 3 > &param)

template<typename T >
Double_t	fitGaus (const size_t nBins, const T *arr, const T xMin, const T xMax, std::vector< T > &param)

template<typename T >
double	fitGaus (size_t nBins, const T arr, const T xMin, const T xMax, std::array< double, 3 > &param, ROOT::Math::SMatrix< double, 3, 3, ROOT::Math::MatRepSym< double, 3 > > covMat=nullptr, int minVal=2, bool applyMAD=true)

template<typename T >
StatisticsData	getStatisticsData (const T *arr, const size_t nBins, const double xMin, const double xMax)

template<typename T , typename R = double>
R	median (std::vector< T > v)

template<typename T >
void	SortData (std::vector< T > const &values, std::vector< size_t > &index)

template<typename T >
bool	LTMUnbinned (const std::vector< T > &data, std::vector< size_t > &index, std::array< float, 7 > &params, float fracKeep)

template<typename T >
void	Reorder (std::vector< T > &data, const std::vector< size_t > &index)

template<typename T >
bool	LTMUnbinnedSig (const std::vector< T > &data, std::vector< size_t > &index, std::array< float, 7 > &params, float fracKeepMin, float sigTgt, bool sorted=false)

template<typename T >
T	selKthMin (int k, int np, T *arr)

template<typename T >
T	MAD2Sigma (int np, T *y)

	GPUdi () float to02Pi(float phi)

	GPUdi () void bringTo02Pi(float &phi)

float	toPMPiGen (float phi)

double	toPMPiGend (double phi)

void	bringToPMPiGen (float &phi)

void	bringToPMPiGend (double &phi)

float	to02PiGen (float phi)

double	to02PiGend (double phi)

void	bringTo02PiGen (float &phi)

void	bringTo02PiGend (double &phi)

float	toPMPi (float phi)

double	toPMPid (double phi)

void	bringToPMPi (float &phi)

void	bringToPMPid (double &phi)

std::tuple< float, float >	rotateZInv (float xG, float yG, float snAlp, float csAlp)

std::tuple< double, double >	rotateZInvd (double xG, double yG, double snAlp, double csAlp)

std::tuple< float, float >	rotateZ (float xL, float yL, float snAlp, float csAlp)

std::tuple< double, double >	rotateZd (double xL, double yL, double snAlp, double csAlp)

void	rotateZ (std::array< float, 3 > &xy, float alpha)

void	rotateZd (std::array< double, 3 > &xy, double alpha)

int	angle2Sector (float phi)

int	angle2Sectord (double phi)

float	sector2Angle (int sect)

double	sector2Angled (int sect)

float	angle2Alpha (float phi)

double	angle2Alphad (double phi)

	GPUhdi () float fastATan2(float y

template<class T >
	GPUhdi () T min(const T x

Variables
float &	s

float float &	c

float	yL

float float &	xG

float float float &	yG

float float float float	snAlp

float float float float float	csAlp

float float &	xL

float	x

const T	y

Typedef Documentation

◆ Bracket

template<typename T >

using o2::math_utils::Bracket = typedef detail::Bracket<T>

Definition at line 39 of file Primitive2D.h.

◆ Bracketd_t

using o2::math_utils::Bracketd_t = typedef detail::Bracket<double>

Definition at line 41 of file Primitive2D.h.

◆ Bracketf_t

using o2::math_utils::Bracketf_t = typedef detail::Bracket<float>

Definition at line 40 of file Primitive2D.h.

◆ CircleXY

template<typename T >

using o2::math_utils::CircleXY = typedef detail::CircleXY<T>

Definition at line 29 of file Primitive2D.h.

◆ CircleXYd_t

using o2::math_utils::CircleXYd_t = typedef detail::CircleXY<double>

Definition at line 31 of file Primitive2D.h.

◆ CircleXYf_t

using o2::math_utils::CircleXYf_t = typedef detail::CircleXY<float>

Definition at line 30 of file Primitive2D.h.

◆ IntervalXY

template<typename T >

using o2::math_utils::IntervalXY = typedef detail::IntervalXY<T>

Definition at line 34 of file Primitive2D.h.

◆ IntervalXYd_t

using o2::math_utils::IntervalXYd_t = typedef detail::IntervalXY<double>

Definition at line 36 of file Primitive2D.h.

◆ IntervalXYf_t

using o2::math_utils::IntervalXYf_t = typedef detail::IntervalXY<float>

Definition at line 35 of file Primitive2D.h.

◆ MatRepStd

template<class T , uint32_t D1, uint32_t D2 = D1>

using o2::math_utils::MatRepStd = typedef ROOT::Math::MatRepStd<T, D1, D2>

Definition at line 63 of file GPUROOTSMatrixFwd.h.

◆ MatRepSym

template<class T , uint32_t D>

using o2::math_utils::MatRepSym = typedef ROOT::Math::MatRepSym<T, D>

Definition at line 61 of file GPUROOTSMatrixFwd.h.

◆ Point2D

template<typename T >

using o2::math_utils::Point2D = typedef ROOT::Math::PositionVector2D<ROOT::Math::Cartesian2D<T>, ROOT::Math::DefaultCoordinateSystemTag>

Definition at line 64 of file GPUROOTCartesianFwd.h.

◆ Point3D

template<typename T >

using o2::math_utils::Point3D = typedef ROOT::Math::PositionVector3D<ROOT::Math::Cartesian3D<T>, ROOT::Math::DefaultCoordinateSystemTag>

Definition at line 68 of file GPUROOTCartesianFwd.h.

◆ Rotation2Dd_t

using o2::math_utils::Rotation2Dd_t = typedef Rotation2D<double>

Definition at line 155 of file Cartesian.h.

◆ Rotation2Df_t

using o2::math_utils::Rotation2Df_t = typedef Rotation2D<float>

Definition at line 154 of file Cartesian.h.

◆ SMatrix

template<class T , uint32_t D1, uint32_t D2, class R >

using o2::math_utils::SMatrix = typedef ROOT::Math::SMatrix<T, D1, D2, R>

Definition at line 59 of file GPUROOTSMatrixFwd.h.

◆ SVector

template<typename T , uint32_t N>

using o2::math_utils::SVector = typedef ROOT::Math::SVector<T, N>

Definition at line 57 of file GPUROOTSMatrixFwd.h.

◆ Vector2D

template<typename T >

using o2::math_utils::Vector2D = typedef ROOT::Math::DisplacementVector2D<ROOT::Math::Cartesian2D<T>, ROOT::Math::DefaultCoordinateSystemTag>

Definition at line 66 of file GPUROOTCartesianFwd.h.

◆ Vector3D

template<typename T >

using o2::math_utils::Vector3D = typedef ROOT::Math::DisplacementVector3D<ROOT::Math::Cartesian3D<T>, ROOT::Math::DefaultCoordinateSystemTag>

Definition at line 70 of file GPUROOTCartesianFwd.h.

Function Documentation

◆ angle2Alpha()

float o2::math_utils::angle2Alpha ( float phi )

inline

Definition at line 203 of file Utils.h.

◆ angle2Alphad()

double o2::math_utils::angle2Alphad ( double phi )

inline

Definition at line 208 of file Utils.h.

◆ angle2Sector()

int o2::math_utils::angle2Sector ( float phi )

inline

Definition at line 183 of file Utils.h.

◆ angle2Sectord()

int o2::math_utils::angle2Sectord ( double phi )

inline

Definition at line 188 of file Utils.h.

◆ bringTo02PiGen()

void o2::math_utils::bringTo02PiGen ( float & phi )

inline

Definition at line 80 of file Utils.h.

◆ bringTo02PiGend()

void o2::math_utils::bringTo02PiGend ( double & phi )

inline

Definition at line 85 of file Utils.h.

◆ bringToPMPi()

void o2::math_utils::bringToPMPi ( float & phi )

inline

Definition at line 100 of file Utils.h.

◆ bringToPMPid()

void o2::math_utils::bringToPMPid ( double & phi )

inline

Definition at line 105 of file Utils.h.

◆ bringToPMPiGen()

void o2::math_utils::bringToPMPiGen ( float & phi )

inline

Definition at line 60 of file Utils.h.

◆ bringToPMPiGend()

void o2::math_utils::bringToPMPiGend ( double & phi )

inline

Definition at line 65 of file Utils.h.

◆ Dot()

template<class T , unsigned int D>

T o2::math_utils::Dot	(	const SVector< T, D > &	lhs,
		const SVector< T, D > &	rhs
	)

inline

Definition at line 257 of file Cartesian.h.

◆ fit()

template<typename T >

TFitResultPtr o2::math_utils::fit	(	const size_t	nBins,
		const T *	arr,
		const T	xMin,
		const T	xMax,
		TF1 &	func,
		std::string_view	option = `""`
	)

fit 1D array of histogrammed data with generic root function

The code was extracted out of ROOT to be able to do fitting on an array with histogrammed data instead of root histograms. It is a stripped down version, so does not provide the same functionality. To be used with care.

Parameters

[in]	nbins	size of the array and number of histogram bins
[in]	arr	array with elements
[in]	xMin	minimum range of the array
[in]	xMax	maximum range of the array
[in]	func	fit function

Definition at line 59 of file fit.h.

◆ fitGaus() [1/2]

template<typename T >

Double_t o2::math_utils::fitGaus	(	const size_t	nBins,
		const T *	arr,
		const T	xMin,
		const T	xMax,
		std::vector< T > &	param
	)

fast fit of an array with ranges (histogram) with gaussian function

Fitting procedure:

Step - make logarithm
Linear fit (parabola) - more robust, always converges, fast

Parameters

[in]	nbins	size of the array and number of histogram bins
[in]	arr	array with elements
[in]	xMin	minimum range of the array
[in]	xMax	maximum range of the array
[out]	param	return paramters of the fit (0-Constant, 1-Mean, 2-Sigma, 3-Sum)

Returns: chi2 or exit code >0: the chi2 returned by TLinearFitter -3: only three points have been used for the calculation - no fitter was used -2: only two points have been used for the calculation - center of gravity was uesed for calculation -1: only one point has been used for the calculation - center of gravity was uesed for calculation -4: invalid result!!

Definition at line 231 of file fit.h.

◆ fitGaus() [2/2]

template<typename T >

double o2::math_utils::fitGaus	(	size_t	nBins,
		const T *	arr,
		const T	xMin,
		const T	xMax,
		std::array< double, 3 > &	param,
		ROOT::Math::SMatrix< double, 3, 3, ROOT::Math::MatRepSym< double, 3 > > *	covMat = `nullptr`,
		int	minVal = `2`,
		bool	applyMAD = `true`
	)

Definition at line 359 of file fit.h.

◆ getStatisticsData()

template<typename T >

StatisticsData o2::math_utils::getStatisticsData	(	const T *	arr,
		const size_t	nBins,
		const double	xMin,
		const double	xMax
	)

calculate statistical parameters on a binned array

The function assumes a binned array of

Parameters

nBins	size of the array
xMin	lower histogram bound
xMax	upper histogram bound

Todo:: make return type templated?

Definition at line 470 of file fit.h.

◆ GPUdi() [1/2]

o2::math_utils::GPUdi ( )

Definition at line 30 of file Utils.h.

◆ GPUdi() [2/2]

o2::math_utils::GPUdi ( ) &

Definition at line 40 of file Utils.h.

◆ GPUhdi() [1/2]

o2::math_utils::GPUhdi ( )

Definition at line 245 of file Utils.h.

◆ GPUhdi() [2/2]

template<class T >

o2::math_utils::GPUhdi ( ) const

◆ LTMUnbinned()

template<typename T >

bool o2::math_utils::LTMUnbinned	(	const std::vector< T > &	data,
		std::vector< size_t > &	index,
		std::array< float, 7 > &	params,
		float	fracKeep
	)

LTM : Trimmed mean of unbinned array

Robust statistic to estimate properties of the distribution To handle binning error special treatment for definition of unbinned data see: http://en.wikipedia.org/w/index.php?title=Trimmed_estimator&oldid=582847999

Parameters

data	Input vector (unsorted)
index	Vector with indices of sorted input data
params	Array with characteristics of distribution
fracKeep	Fraction of data to be kept

Returns

Flag if successfull Characteristics:

area
mean
rms
error estimate of mean
error estimate of RMS
first accepted element (of sorted array)
last accepted element (of sorted array)

Definition at line 569 of file fit.h.

◆ LTMUnbinnedSig()

template<typename T >

bool o2::math_utils::LTMUnbinnedSig	(	const std::vector< T > &	data,
		std::vector< size_t > &	index,
		std::array< float, 7 > &	params,
		float	fracKeepMin,
		float	sigTgt,
		bool	sorted = `false`
	)

Compare this function to LTMUnbinned. A target sigma of the distribution can be specified and it will be trimmed to match that target.

Parameters

data	Input vector (unsorted)
index	Vector with indices of sorted input data
params	Array with characteristics of distribution
fracKeepMin	Minimum fraction to keep of the input data
sigTgt	Target distribution sigma
sorted	Flag if the data is already sorted

Returns: Flag if successfull

Definition at line 648 of file fit.h.

◆ MAD2Sigma()

template<typename T >

T o2::math_utils::MAD2Sigma	(	int	np,
		T *	y
	)

Definition at line 773 of file fit.h.

◆ median()

template<typename T , typename R = double>

R o2::math_utils::median ( std::vector< T > v )

median of values in a std::vector

we need to make a copy of the vector since we need to sort it based on this discussion: https://stackoverflow.com/questions/1719070/what-is-the-right-approach-when-using-stl-container-for-median-calculation/1719155#1719155

Todo:: Is there a better way to do this?

Definition at line 519 of file fit.h.

◆ medmadGaus()

template<typename T >

bool o2::math_utils::medmadGaus	(	size_t	nBins,
		const T *	arr,
		const T	xMin,
		const T	xMax,
		std::array< double, 3 > &	param
	)

fast median estimate of gaussian parameters for histogrammed data

Parameters

[in]	nbins	size of the array and number of histogram bins
[in]	arr	array with elements
[in]	xMin	minimum range of the array
[in]	xMax	maximum range of the array
[out]	param	return paramters of the fit (0-Constant, 1-Mean, 2-Sigma)

Returns: false on failure (empty data)

Definition at line 132 of file fit.h.

◆ Reorder()

template<typename T >

void o2::math_utils::Reorder	(	std::vector< T > &	data,
		const std::vector< size_t > &	index
	)

Rearranges the input vector in the order given by the index vector

Parameters

data	Input vector
index	Index vector

Definition at line 625 of file fit.h.

◆ rotateZ() [1/2]

std::tuple< float, float > o2::math_utils::rotateZ	(	float	xL,
		float	yL,
		float	snAlp,
		float	csAlp
	)

inline

Definition at line 162 of file Utils.h.

◆ rotateZ() [2/2]

void o2::math_utils::rotateZ	(	std::array< float, 3 > &	xy,
		float	alpha
	)

inline

Definition at line 172 of file Utils.h.

◆ rotateZd() [1/2]

std::tuple< double, double > o2::math_utils::rotateZd	(	double	xL,
		double	yL,
		double	snAlp,
		double	csAlp
	)

inline

Definition at line 167 of file Utils.h.

◆ rotateZd() [2/2]

void o2::math_utils::rotateZd	(	std::array< double, 3 > &	xy,
		double	alpha
	)

inline

Definition at line 177 of file Utils.h.

◆ rotateZInv()

std::tuple< float, float > o2::math_utils::rotateZInv	(	float	xG,
		float	yG,
		float	snAlp,
		float	csAlp
	)

inline

Definition at line 142 of file Utils.h.

◆ rotateZInvd()

std::tuple< double, double > o2::math_utils::rotateZInvd	(	double	xG,
		double	yG,
		double	snAlp,
		double	csAlp
	)

inline

Definition at line 147 of file Utils.h.

◆ sector2Angle()

float o2::math_utils::sector2Angle ( int sect )

inline

Definition at line 193 of file Utils.h.

◆ sector2Angled()

double o2::math_utils::sector2Angled ( int sect )

inline

Definition at line 198 of file Utils.h.

◆ selKthMin()

template<typename T >

T o2::math_utils::selKthMin	(	int	k,
		int	np,
		T *	arr
	)

Definition at line 718 of file fit.h.

◆ Similarity()

template<class T , unsigned int D1, unsigned int D2, class R >

SMatrix< T, D1, D1, MatRepSym< T, D1 > > o2::math_utils::Similarity	(	const SMatrix< T, D1, D2, R > &	lhs,
		const SMatrix< T, D2, D2, MatRepSym< T, D2 > > &	rhs
	)

inline

Definition at line 263 of file Cartesian.h.

◆ SortData()

template<typename T >

void o2::math_utils::SortData	(	std::vector< T > const &	values,
		std::vector< size_t > &	index
	)

Fills the index vector with sorted indices of the input vector. The input vector is not modified (similar to TMath::Sort()).

Parameters

values	Vector to be indexed
index	Vector to hold the sorted indices (must have the same size as values)

Definition at line 539 of file fit.h.

◆ to02PiGen()

float o2::math_utils::to02PiGen ( float phi )

inline

Definition at line 70 of file Utils.h.

◆ to02PiGend()

double o2::math_utils::to02PiGend ( double phi )

inline

Definition at line 75 of file Utils.h.

◆ toPMPi()

float o2::math_utils::toPMPi ( float phi )

inline

Definition at line 90 of file Utils.h.

◆ toPMPid()

double o2::math_utils::toPMPid ( double phi )

inline

Definition at line 95 of file Utils.h.

◆ toPMPiGen()

float o2::math_utils::toPMPiGen ( float phi )

inline

Definition at line 50 of file Utils.h.

◆ toPMPiGend()

double o2::math_utils::toPMPiGend ( double phi )

inline

Definition at line 55 of file Utils.h.

Variable Documentation

◆ c

double double & o2::math_utils::c

Initial value:

{

detail::sincos<float>(ang, s, c)

c

uint32_t c

Definition RawData.h:2

Definition at line 110 of file Utils.h.

◆ csAlp

double double double double double o2::math_utils::csAlp

Initial value:

{

return detail::rotateZ<float>(xL, yL, xG, yG, snAlp, csAlp)

Definition at line 121 of file Utils.h.

◆ s

double & o2::math_utils::s

Definition at line 110 of file Utils.h.

◆ snAlp

double double double double o2::math_utils::snAlp

Definition at line 121 of file Utils.h.

◆ x

double o2::math_utils::x

Initial value:

{

return detail::fastATan2<float>(y, x)

int

x

GLint GLenum GLint x

Definition glcorearb.h:403

Definition at line 213 of file Utils.h.

◆ xG

double double & o2::math_utils::xG

Definition at line 121 of file Utils.h.

◆ xL

double double & o2::math_utils::xL

Definition at line 131 of file Utils.h.

◆ y

const double o2::math_utils::y

Initial value:

{

return detail::min<T>(x, y)

Definition at line 224 of file Utils.h.

◆ yG

double o2::math_utils::yG

Definition at line 121 of file Utils.h.

◆ yL

double double double & o2::math_utils::yL

Definition at line 121 of file Utils.h.

Namespaces

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ Bracket

◆ Bracketd_t

◆ Bracketf_t

◆ CircleXY

◆ CircleXYd_t

◆ CircleXYf_t

◆ IntervalXY

◆ IntervalXYd_t

◆ IntervalXYf_t

◆ MatRepStd

◆ MatRepSym

◆ Point2D

◆ Point3D

◆ Rotation2Dd_t

◆ Rotation2Df_t

◆ SMatrix

◆ SVector

◆ Vector2D

◆ Vector3D

Function Documentation

◆ angle2Alpha()

◆ angle2Alphad()

◆ angle2Sector()

◆ angle2Sectord()

◆ bringTo02PiGen()

◆ bringTo02PiGend()

◆ bringToPMPi()

◆ bringToPMPid()

◆ bringToPMPiGen()

◆ bringToPMPiGend()

◆ Dot()

◆ fit()

◆ fitGaus() [1/2]

◆ fitGaus() [2/2]

◆ getStatisticsData()

◆ GPUdi() [1/2]

◆ GPUdi() [2/2]

◆ GPUhdi() [1/2]

◆ GPUhdi() [2/2]

◆ LTMUnbinned()

◆ LTMUnbinnedSig()

◆ MAD2Sigma()

◆ median()

◆ medmadGaus()

◆ Reorder()

◆ rotateZ() [1/2]

◆ rotateZ() [2/2]

◆ rotateZd() [1/2]

◆ rotateZd() [2/2]

◆ rotateZInv()

◆ rotateZInvd()

◆ sector2Angle()

◆ sector2Angled()

◆ selKthMin()

◆ Similarity()

◆ SortData()

◆ to02PiGen()

◆ to02PiGend()

◆ toPMPi()

◆ toPMPid()

◆ toPMPiGen()

◆ toPMPiGend()

Variable Documentation

◆ c

◆ csAlp

◆ s

◆ snAlp

◆ x

◆ xG

◆ xL

◆ y

◆ yG

◆ yL