Functions
double	approxErf (double arg)

template<typename DoubleArray >
double	bernstein (double x, double xmin, double xmax, DoubleArray coefs, int nCoefs)
	The caller needs to make sure that there is at least one coefficient.

template<typename DoubleArray >
double	bernsteinIntegral (double xlo, double xhi, double xmin, double xmax, DoubleArray coefs, int nCoefs)

double	bifurGauss (double x, double mean, double sigmaL, double sigmaR)

double	bifurGaussIntegral (double xMin, double xMax, double mean, double sigmaL, double sigmaR)

template<typename DoubleArray >
unsigned int	binNumber (double x, double coef, DoubleArray boundaries, unsigned int nBoundaries, int nbins, int blo)

double	binomial (int n, int k)
	Calculates the binomial coefficient n over k.

double	cbShape (double m, double m0, double sigma, double alpha, double n)

double	cbShapeIntegral (double mMin, double mMax, double m0, double sigma, double alpha, double n)

template<typename DoubleArray >
double	chebychev (DoubleArray coeffs, unsigned int nCoeffs, double x_in, double xMin, double xMax)

template<typename DoubleArray >
double	chebychevIntegral (DoubleArray coeffs, unsigned int nCoeffs, double xMin, double xMax, double xMinFull, double xMaxFull)

double	chi2Asymmetric (double mu, double weight, double errLo, double errHi)
	Chi-squared contribution of one bin with asymmetric (Poisson-style) data errors.

double	chi2Expected (double mu, double weight)
	Chi-squared contribution of one bin with "expected" errors: \( \sigma^2 = \mu \).

double	chi2Symmetric (double mu, double weight, double sigma2)
	Chi-squared contribution of one bin with a user-supplied symmetric error squared (e.g.

template<typename DoubleArray >
double	constraintSum (DoubleArray comp, unsigned int compSize)

double	efficiency (double effFuncVal, int catIndex, int sigCatIndex)

double	effProd (double eff, double pdf)

double	expm1OverX (double x)
	(exp(x) - 1) / x with the removable singularity at x = 0 filled in.

double	expm1OverXDerivative (double x)
	Derivative of expm1OverX().

double	exponentialIntegral (double xMin, double xMax, double constant)
	Integral of exp(constant * x) from xMin to xMax.

double	exponentialIntegralDConstant (double xMin, double xMax, double constant)
	Derivative of exponentialIntegral() with respect to the constant, i.e.

double	fast_fma (double x, double y, double z) noexcept
	use fast FMA if available, fall back to normal arithmetic if not

template<typename ParamsArray , typename DoubleArray >
double	flexibleInterp (unsigned int code, ParamsArray params, unsigned int n, DoubleArray low, DoubleArray high, double boundary, double nominal, int doCutoff)

double	flexibleInterpSingle (unsigned int code, double low, double high, double boundary, double nominal, double paramVal, double res)

double	gaussian (double x, double mean, double sigma)
	Function to evaluate an un-normalized RooGaussian.

double	gaussianIntegral (double xMin, double xMax, double mean, double sigma)
	Function to calculate the integral of an un-normalized RooGaussian over x.

template<typename DoubleArray >
double	interpolate1d (double low, double high, double val, unsigned int numBins, DoubleArray vals)

double	landau (double x, double mu, double sigma)

double	logNormal (double x, double k, double m0)

double	logNormalIntegral (double xMin, double xMax, double m0, double k)

double	logNormalIntegralStandard (double xMin, double xMax, double mu, double sigma)

double	logNormalStandard (double x, double sigma, double mu)

template<typename DoubleArray >
double	multipdf (int idx, DoubleArray pdfs)

template<typename XArray , typename MuArray , typename CovArray >
double	multiVarGaussian (int n, XArray x, MuArray mu, CovArray covI)

double	nll (double pdf, double weight, int binnedL, int doBinOffset)

double	poisson (double x, double par)

double	poissonIntegral (int code, double mu, double x, double integrandMin, double integrandMax, unsigned int protectNegative)

template<bool pdfMode = false, typename DoubleArray >
double	polynomial (DoubleArray coeffs, int nCoeffs, int lowestOrder, double x)
	In pdfMode, a coefficient for the constant term of 1.0 is implied if lowestOrder > 0.

template<bool pdfMode = false, typename DoubleArray >
double	polynomialIntegral (DoubleArray coeffs, int nCoeffs, int lowestOrder, double xMin, double xMax)
	In pdfMode, a coefficient for the constant term of 1.0 is implied if lowestOrder > 0.

template<typename DoubleArray >
double	product (DoubleArray factors, std::size_t nFactors)

double	ratio (double numerator, double denominator)

template<typename DoubleArray >
unsigned int	rawBinNumber (double x, DoubleArray boundaries, std::size_t nBoundaries)

template<typename DoubleArray >
double	recursiveFraction (DoubleArray a, unsigned int n)

template<typename DoubleArray >
double	stepFunctionIntegral (double xmin, double xmax, std::size_t nBins, DoubleArray boundaries, DoubleArray coefs)

unsigned int	uniformBinNumber (double low, double high, double val, unsigned int numBins, double coef)

Function Documentation

◆ approxErf()

double RooFit::Detail::MathFuncs::approxErf ( double arg )

inline

Definition at line 499 of file MathFuncs.h.

◆ bernstein()

template<typename DoubleArray >

double RooFit::Detail::MathFuncs::bernstein	(	double	x,
		double	xmin,
		double	xmax,
		DoubleArray	coefs,
		int	nCoefs )

The caller needs to make sure that there is at least one coefficient.

Definition at line 50 of file MathFuncs.h.

◆ bernsteinIntegral()

template<typename DoubleArray >

double RooFit::Detail::MathFuncs::bernsteinIntegral	(	double	xlo,
		double	xhi,
		double	xmin,
		double	xmax,
		DoubleArray	coefs,
		int	nCoefs )

Definition at line 860 of file MathFuncs.h.

◆ bifurGauss()

double RooFit::Detail::MathFuncs::bifurGauss	(	double	x,
		double	mean,
		double	sigmaL,
		double	sigmaR )

inline

Definition at line 111 of file MathFuncs.h.

◆ bifurGaussIntegral()

double RooFit::Detail::MathFuncs::bifurGaussIntegral	(	double	xMin,
		double	xMax,
		double	mean,
		double	sigmaL,
		double	sigmaR )

inline

Definition at line 551 of file MathFuncs.h.

◆ binNumber()

template<typename DoubleArray >

unsigned int RooFit::Detail::MathFuncs::binNumber	(	double	x,
		double	coef,
		DoubleArray	boundaries,
		unsigned int	nBoundaries,
		int	nbins,
		int	blo )

Definition at line 211 of file MathFuncs.h.

◆ binomial()

double RooFit::Detail::MathFuncs::binomial	(	int	n,
		int	k )

inline

Calculates the binomial coefficient n over k.

Equivalent to TMath::Binomial, but inlined.

Definition at line 32 of file MathFuncs.h.

◆ cbShape()

double RooFit::Detail::MathFuncs::cbShape	(	double	m,
		double	m0,
		double	sigma,
		double	alpha,
		double	n )

inline

Definition at line 479 of file MathFuncs.h.

◆ cbShapeIntegral()

double RooFit::Detail::MathFuncs::cbShapeIntegral	(	double	mMin,
		double	mMax,
		double	m0,
		double	sigma,
		double	alpha,
		double	n )

inline

Definition at line 795 of file MathFuncs.h.

◆ chebychev()

template<typename DoubleArray >

double RooFit::Detail::MathFuncs::chebychev	(	DoubleArray	coeffs,
		unsigned int	nCoeffs,
		double	x_in,
		double	xMin,
		double	xMax )

Definition at line 144 of file MathFuncs.h.

◆ chebychevIntegral()

template<typename DoubleArray >

double RooFit::Detail::MathFuncs::chebychevIntegral	(	DoubleArray	coeffs,
		unsigned int	nCoeffs,
		double	xMin,
		double	xMax,
		double	xMinFull,
		double	xMaxFull )

Definition at line 661 of file MathFuncs.h.

◆ chi2Asymmetric()

double RooFit::Detail::MathFuncs::chi2Asymmetric	(	double	mu,
		double	weight,
		double	errLo,
		double	errHi )

inline

Chi-squared contribution of one bin with asymmetric (Poisson-style) data errors.

The side facing the prediction is used: errHi when \( \mu > \mathrm{weight} \), otherwise errLo.

Definition at line 435 of file MathFuncs.h.

◆ chi2Expected()

double RooFit::Detail::MathFuncs::chi2Expected	(	double	mu,
		double	weight )

inline

Chi-squared contribution of one bin with "expected" errors: \( \sigma^2 = \mu \).

Empty/no-prediction bins contribute zero; bins with non-positive \( \mu \) but non-empty data yield NaN (to let the minimizer recover).

Definition at line 406 of file MathFuncs.h.

◆ chi2Symmetric()

double RooFit::Detail::MathFuncs::chi2Symmetric	(	double	mu,
		double	weight,
		double	sigma2 )

inline

Chi-squared contribution of one bin with a user-supplied symmetric error squared (e.g.

SumW2 weights from the data).

Definition at line 420 of file MathFuncs.h.

◆ constraintSum()

template<typename DoubleArray >

double RooFit::Detail::MathFuncs::constraintSum	(	DoubleArray	comp,
		unsigned int	compSize )

Definition at line 180 of file MathFuncs.h.

◆ efficiency()

double RooFit::Detail::MathFuncs::efficiency	(	double	effFuncVal,
		int	catIndex,
		int	sigCatIndex )

inline

Definition at line 120 of file MathFuncs.h.

◆ effProd()

double RooFit::Detail::MathFuncs::effProd	(	double	eff,
		double	pdf )

inline

Definition at line 397 of file MathFuncs.h.

◆ expm1OverX()

double RooFit::Detail::MathFuncs::expm1OverX ( double x )

inline

(exp(x) - 1) / x with the removable singularity at x = 0 filled in.

The derivative is expm1OverXDerivative(), also registered with clad at the end of this header: differentiating the branches would give zero at x = 0.

Definition at line 570 of file MathFuncs.h.

◆ expm1OverXDerivative()

double RooFit::Detail::MathFuncs::expm1OverXDerivative ( double x )

inline

Derivative of expm1OverX().

The closed form (x * exp(x) - expm1(x)) / x^2 cancels for small x, so a Taylor expansion is used there. Both branches are accurate to about 1e-15 at the switching point.

Definition at line 578 of file MathFuncs.h.

◆ exponentialIntegral()

double RooFit::Detail::MathFuncs::exponentialIntegral	(	double	xMin,
		double	xMax,
		double	constant )

inline

Integral of exp(constant * x) from xMin to xMax.

The naive form (exp(constant * xMax) - exp(constant * xMin)) / constant cancels when constant * (xMax - xMin) is small. Factoring out the larger exponential and using std::expm1 for the rest is accurate for any constant and only overflows if the integral itself does. The derivative with respect to the constant is exponentialIntegralDConstant(), also registered with clad at the end of this header (https://github.com/root-project/root/issues/23724).

Definition at line 597 of file MathFuncs.h.

◆ exponentialIntegralDConstant()

double RooFit::Detail::MathFuncs::exponentialIntegralDConstant	(	double	xMin,
		double	xMax,
		double	constant )

inline

Derivative of exponentialIntegral() with respect to the constant, i.e.

the integral of x * exp(constant * x). With a the endpoint where constant * x is larger and d the signed distance to the other one, substituting x = a + s gives exp(constant * a) * d * (a * expm1OverX(w) + d * expm1OverXDerivative(w)) with w = constant * d <= 0, so the helpers only see bounded arguments.

Definition at line 615 of file MathFuncs.h.

◆ fast_fma()

double RooFit::Detail::MathFuncs::fast_fma	(	double	x,
		double	y,
		double	z )

inlinenoexcept

use fast FMA if available, fall back to normal arithmetic if not

Definition at line 646 of file MathFuncs.h.

◆ flexibleInterp()

template<typename ParamsArray , typename DoubleArray >

double RooFit::Detail::MathFuncs::flexibleInterp	(	unsigned int	code,
		ParamsArray	params,
		unsigned int	n,
		DoubleArray	low,
		DoubleArray	high,
		double	boundary,
		double	nominal,
		int	doCutoff )

Definition at line 369 of file MathFuncs.h.

◆ flexibleInterpSingle()

double RooFit::Detail::MathFuncs::flexibleInterpSingle	(	unsigned int	code,
		double	low,
		double	high,
		double	boundary,
		double	nominal,
		double	paramVal,
		double	res )

inline

Definition at line 254 of file MathFuncs.h.

◆ gaussian()

double RooFit::Detail::MathFuncs::gaussian	(	double	x,
		double	mean,
		double	sigma )

inline

Function to evaluate an un-normalized RooGaussian.

Definition at line 88 of file MathFuncs.h.

◆ gaussianIntegral()

double RooFit::Detail::MathFuncs::gaussianIntegral	(	double	xMin,
		double	xMax,
		double	mean,
		double	sigma )

inline

Function to calculate the integral of an un-normalized RooGaussian over x.

To calculate the integral over mean, just interchange the respective values of x and mean.

Parameters

xMin	Minimum value of variable to integrate wrt.
xMax	Maximum value of of variable to integrate wrt.
mean	Mean.
sigma	Sigma.

Returns: The integral of an un-normalized RooGaussian over the value in x.

Definition at line 516 of file MathFuncs.h.

◆ interpolate1d()

template<typename DoubleArray >

double RooFit::Detail::MathFuncs::interpolate1d	(	double	low,
		double	high,
		double	val,
		unsigned int	numBins,
		DoubleArray	vals )

Definition at line 219 of file MathFuncs.h.

◆ landau()

double RooFit::Detail::MathFuncs::landau	(	double	x,
		double	mu,
		double	sigma )

inline

Definition at line 380 of file MathFuncs.h.

◆ logNormal()

double RooFit::Detail::MathFuncs::logNormal	(	double	x,
		double	k,
		double	m0 )

inline

Definition at line 387 of file MathFuncs.h.

◆ logNormalIntegral()

double RooFit::Detail::MathFuncs::logNormalIntegral	(	double	xMin,
		double	xMax,
		double	m0,
		double	k )

inline

Definition at line 774 of file MathFuncs.h.

◆ logNormalIntegralStandard()

double RooFit::Detail::MathFuncs::logNormalIntegralStandard	(	double	xMin,
		double	xMax,
		double	mu,
		double	sigma )

inline

Definition at line 784 of file MathFuncs.h.

◆ logNormalStandard()

double RooFit::Detail::MathFuncs::logNormalStandard	(	double	x,
		double	sigma,
		double	mu )

inline

Definition at line 392 of file MathFuncs.h.

◆ multipdf()

template<typename DoubleArray >

double RooFit::Detail::MathFuncs::multipdf	(	int	idx,
		DoubleArray	pdfs )

Definition at line 169 of file MathFuncs.h.

◆ multiVarGaussian()

template<typename XArray , typename MuArray , typename CovArray >

double RooFit::Detail::MathFuncs::multiVarGaussian	(	int	n,
		XArray	x,
		MuArray	mu,
		CovArray	covI )

Definition at line 887 of file MathFuncs.h.

◆ nll()

double RooFit::Detail::MathFuncs::nll	(	double	pdf,
		double	weight,
		int	binnedL,
		int	doBinOffset )

inline

Definition at line 449 of file MathFuncs.h.

◆ poisson()

double RooFit::Detail::MathFuncs::poisson	(	double	x,
		double	par )

inline

Definition at line 239 of file MathFuncs.h.

◆ poissonIntegral()

double RooFit::Detail::MathFuncs::poissonIntegral	(	int	code,
		double	mu,
		double	x,
		double	integrandMin,
		double	integrandMax,
		unsigned int	protectNegative )

inline

Definition at line 727 of file MathFuncs.h.

◆ polynomial()

template<bool pdfMode = false, typename DoubleArray >

double RooFit::Detail::MathFuncs::polynomial	(	DoubleArray	coeffs,
		int	nCoeffs,
		int	lowestOrder,
		double	x )

In pdfMode, a coefficient for the constant term of 1.0 is implied if lowestOrder > 0.

Definition at line 133 of file MathFuncs.h.

◆ polynomialIntegral()

template<bool pdfMode = false, typename DoubleArray >

double RooFit::Detail::MathFuncs::polynomialIntegral	(	DoubleArray	coeffs,
		int	nCoeffs,
		int	lowestOrder,
		double	xMin,
		double	xMax )

In pdfMode, a coefficient for the constant term of 1.0 is implied if lowestOrder > 0.

Definition at line 627 of file MathFuncs.h.

◆ product()

template<typename DoubleArray >

double RooFit::Detail::MathFuncs::product	(	DoubleArray	factors,
		std::size_t	nFactors )

Definition at line 96 of file MathFuncs.h.

◆ ratio()

double RooFit::Detail::MathFuncs::ratio	(	double	numerator,
		double	denominator )

inline

Definition at line 106 of file MathFuncs.h.

◆ rawBinNumber()

template<typename DoubleArray >

unsigned int RooFit::Detail::MathFuncs::rawBinNumber	(	double	x,
		DoubleArray	boundaries,
		std::size_t	nBoundaries )

Definition at line 199 of file MathFuncs.h.

◆ recursiveFraction()

template<typename DoubleArray >

double RooFit::Detail::MathFuncs::recursiveFraction	(	DoubleArray	a,
		unsigned int	n )

Definition at line 468 of file MathFuncs.h.

◆ stepFunctionIntegral()

template<typename DoubleArray >

double RooFit::Detail::MathFuncs::stepFunctionIntegral	(	double	xmin,
		double	xmax,
		std::size_t	nBins,
		DoubleArray	boundaries,
		DoubleArray	coefs )

Definition at line 904 of file MathFuncs.h.

◆ uniformBinNumber()

unsigned int RooFit::Detail::MathFuncs::uniformBinNumber	(	double	low,
		double	high,
		double	val,
		unsigned int	numBins,
		double	coef )

inline

Definition at line 192 of file MathFuncs.h.

Functions

Function Documentation

◆ approxErf()

◆ bernstein()

◆ bernsteinIntegral()

◆ bifurGauss()

◆ bifurGaussIntegral()

◆ binNumber()

◆ binomial()

◆ cbShape()

◆ cbShapeIntegral()

◆ chebychev()

◆ chebychevIntegral()

◆ chi2Asymmetric()

◆ chi2Expected()

◆ chi2Symmetric()

◆ constraintSum()

◆ efficiency()

◆ effProd()

◆ expm1OverX()

◆ expm1OverXDerivative()

◆ exponentialIntegral()

◆ exponentialIntegralDConstant()

◆ fast_fma()

◆ flexibleInterp()

◆ flexibleInterpSingle()

◆ gaussian()

◆ gaussianIntegral()

◆ interpolate1d()

◆ landau()

◆ logNormal()

◆ logNormalIntegral()

◆ logNormalIntegralStandard()

◆ logNormalStandard()

◆ multipdf()

◆ multiVarGaussian()

◆ nll()

◆ poisson()

◆ poissonIntegral()

◆ polynomial()

◆ polynomialIntegral()

◆ product()

◆ ratio()

◆ rawBinNumber()

◆ recursiveFraction()

◆ stepFunctionIntegral()

◆ uniformBinNumber()