MathUtils.hh File Reference

#include "Rivet/Math/MathHeader.hh"
#include "Rivet/Tools/RivetBoost.hh"
#include <cassert>

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Namespaces
namespace	Rivet
namespace	Rivet::BWHelpers
Functions
double	CDF (double x, double mu, double gamma)
	CDF for the Breit-Wigner distribution.
double	antiCDF (double p, double mu, double gamma)
	inverse CDF for the Breit-Wigner distribution
Comparison functions for safe (floating point) equality tests
template<typename NUM >
boost::enable_if_c < boost::is_floating_point < NUM >::value, bool >::type	isZero (NUM val, double tolerance=1e-8)
	Compare a number to zero.
template<typename NUM >
boost::enable_if_c < boost::is_integral< NUM > ::value, bool >::type	isZero (NUM val, double UNUSED(tolerance)=1e-8)
	Compare a number to zero.
template<typename N1 , typename N2 >
boost::enable_if_c < boost::is_arithmetic< N1 > ::value &&boost::is_arithmetic < N2 >::value &&(boost::is_floating_point < N1 >::value||boost::is_floating_point < N2 >::value), bool >::type	fuzzyEquals (N1 a, N2 b, double tolerance=1e-5)
	Compare two numbers for equality with a degree of fuzziness.
template<typename N1 , typename N2 >
boost::enable_if_c < boost::is_integral< N1 > ::value &&boost::is_integral < N2 >::value, bool >::type	fuzzyEquals (N1 a, N2 b, double UNUSED(tolerance)=1e-5)
	Compare two numbers for equality with a degree of fuzziness.
template<typename N1 , typename N2 >
boost::enable_if_c < boost::is_arithmetic< N1 > ::value &&boost::is_arithmetic < N2 >::value, bool >::type	fuzzyGtrEquals (N1 a, N2 b, double tolerance=1e-5)
	Compare two numbers for >= with a degree of fuzziness.
template<typename N1 , typename N2 >
boost::enable_if_c < boost::is_arithmetic< N1 > ::value &&boost::is_arithmetic < N2 >::value, bool >::type	fuzzyLessEquals (N1 a, N2 b, double tolerance=1e-5)
	Compare two floating point numbers for <= with a degree of fuzziness.
Miscellaneous numerical helpers
template<typename NUM >
boost::enable_if_c < boost::is_arithmetic< NUM > ::value, NUM >::type	sqr (NUM a)
	Named number-type squaring operation.
template<typename NUM >
boost::enable_if_c < boost::is_arithmetic< NUM > ::value, NUM >::type	add_quad (NUM a, NUM b)
	Named number-type addition in quadrature operation.
template<typename NUM >
boost::enable_if_c < boost::is_arithmetic< NUM > ::value, NUM >::type	add_quad (NUM a, NUM b, NUM c)
double	safediv (double num, double den, double fail=0.0)
template<typename NUM >
boost::enable_if_c < boost::is_arithmetic< NUM > ::value, NUM >::type	intpow (NUM val, unsigned int exp)
	A more efficient version of pow for raising numbers to integer powers.
template<typename NUM >
boost::enable_if_c < boost::is_arithmetic< NUM > ::value, int >::type	sign (NUM val)
	Find the sign of a number.
Binning helper functions
vector< double >	linspace (size_t nbins, double start, double end, bool include_end=true)
	Make a list of nbins + 1 values equally spaced between start and end inclusive.
vector< double >	logspace (size_t nbins, double start, double end, bool include_end=true)
	Make a list of nbins + 1 values exponentially spaced between start and end inclusive.
vector< double >	BWspace (size_t nbins, double start, double end, double mu, double gamma)
	Make a list of nbins + 1 values spaced for equal area Breit-Wigner binning between start and end inclusive. mu and gamma are the Breit-Wigner parameters.
template<typename NUM >
int	index_between (const NUM &val, const vector< NUM > &binedges)
	Return the bin index of the given value, val, given a vector of bin edges.
Statistics functions
double	mean (const vector< int > &sample)
	Calculate the mean of a sample.
double	mean_err (const vector< int > &sample)
double	covariance (const vector< int > &sample1, const vector< int > &sample2)
	Calculate the covariance (variance) between two samples.
double	covariance_err (const vector< int > &sample1, const vector< int > &sample2)
	Calculate the error on the covariance (variance) of two samples, assuming poissonian errors.
double	correlation (const vector< int > &sample1, const vector< int > &sample2)
	Calculate the correlation strength between two samples.
double	correlation_err (const vector< int > &sample1, const vector< int > &sample2)
	Calculate the error of the correlation strength between two samples assuming Poissonian errors.
Angle range mappings
double	_mapAngleM2PITo2Pi (double angle)
	Reduce any number to the range [-2PI, 2PI].
double	mapAngleMPiToPi (double angle)
	Map an angle into the range (-PI, PI].
double	mapAngle0To2Pi (double angle)
	Map an angle into the range [0, 2PI).
double	mapAngle0ToPi (double angle)
	Map an angle into the range [0, PI].
double	mapAngle (double angle, PhiMapping mapping)
	Map an angle into the enum-specified range.
Phase space measure helpers
double	deltaPhi (double phi1, double phi2)
	Calculate the difference between two angles in radians.
double	deltaEta (double eta1, double eta2)
double	deltaRap (double y1, double y2)
double	deltaR (double rap1, double phi1, double rap2, double phi2)
double	rapidity (double E, double pz)
	Calculate a rapidity value from the supplied energy E and longitudinal momentum pz.
Ranges and intervals
enum	RangeBoundary { OPEN = 0, SOFT = 0, CLOSED = 1, HARD = 1 }
template<typename N1 , typename N2 , typename N3 >
boost::enable_if_c < boost::is_arithmetic< N1 > ::value &&boost::is_arithmetic < N2 >::value &&boost::is_arithmetic< N3 > ::value, bool >::type	inRange (N1 value, N2 low, N3 high, RangeBoundary lowbound=CLOSED, RangeBoundary highbound=OPEN)
	Determine if value is in the range low to high, for floating point numbers.
template<typename N1 , typename N2 , typename N3 >
boost::enable_if_c < boost::is_arithmetic< N1 > ::value &&boost::is_arithmetic < N2 >::value &&boost::is_arithmetic< N3 > ::value, bool >::type	inRange (N1 value, pair< N2, N3 > lowhigh, RangeBoundary lowbound=CLOSED, RangeBoundary highbound=OPEN)
	Alternative version of inRange which accepts a pair for the range arguments.