JMATH Namespace Reference

Auxiliary classes and methods for mathematical operations. More...

Classes
struct	JAdd
	forward declaration for negate of function. More...
struct	JAdd< JF1_t, double >
	Addition of constant value. More...
struct	JAverage
	Auxiliary class to determine average of set of values. More...
struct	JAverage< JQuaternion3D >
	Template spacialisation for averaging quaternions. More...
struct	JBell
	Bell function object. More...
struct	JCalculator
	Auxiliary class for arithmetic operations on objects. More...
struct	JCalculus
	Auxiliary base class for mathematical operations on parameters of function. More...
struct	JCos
	Cosine of function. More...
struct	JDiv
	forward declaration for multiplication of fuction. More...
struct	JDiv< JF1_t, double >
	Division of constant value. More...
struct	JExp
	Exponent of function. More...
struct	JExp< JPolynome< ID_t, 0 > >
	Exponent of zero degree polynomial function. More...
struct	JFn
	forward declaration for division of fuction. More...
struct	JGauss
	Gauss function object. More...
struct	JGauss2D
	2D correlated Gauss function. More...
struct	JGauss3D
	3D correlated Gauss function. More...
struct	JGauss< ID_t, true >
	Gauss function. More...
struct	JGauss_t
	Gauss model. More...
struct	JLegendre
	Template definition for function evaluation of Legendre polynome. More...
struct	JLegendre< JOrdinate_t,(size_t) -1 >
	Template specialisation for function evaluation of of Legendre polynome for undefined number of degrees. More...
struct	JLegendre< JQuaternion3D, N >
	Template specialisation for function evaluation of Legendre polynome of quaternions for defined number of degrees. More...
struct	JLegendre< JQuaternion3D,(size_t) -1 >
	Template specialisation for function evaluation of Legendre polynome of quaternions for undefined number of degrees. More...
struct	JLegendre_t
	Base class for Legendre polynome. More...
struct	JLimits
	Auxiliary class for minimum and maximum values for any class. More...
struct	JLimits< T, false >
	Template spacialisation of JMATH::JRandom for other data types. More...
struct	JLimits< T, true >
	Template spacialisation of JMATH::JLimits for numerical values. More...
struct	JLog
	Logarithm of function. More...
struct	JMake2X
	Make 2D function of x from 1D function. More...
struct	JMake2Y
	Make 2D function of y from 1D function. More...
struct	JMake3X
	Make 3D function of x from 1D function. More...
struct	JMake3Y
	Make 3D function of y from 1D function. More...
struct	JMake3Z
	Make 3D function of z from 1D function. More...
struct	JMath
	Auxiliary base class for aritmetic operations of derived class types. More...
struct	JMath< T, JNullType >
	Template base class for data structures with arithmetic capabilities. More...
struct	JMath_t
	Auxiliary class to hide data type specific methods. More...
struct	JMathlib
	forward declaration for fixed power of function. More...
class	JMatrix1D
	1 x 1 matrix More...
class	JMatrix1S
	1 x 1 symmetric matrix More...
class	JMatrix2D
	2 x 2 matrix More...
class	JMatrix2S
	2 x 2 symmetric matrix More...
class	JMatrix3D
	3 x 3 matrix More...
class	JMatrix3S
	3 x 3 symmetric matrix More...
class	JMatrix4D
	4 x 4 matrix More...
class	JMatrix4S
	4 x 4 symmetric matrix More...
class	JMatrix5D
	5 x 5 matrix More...
class	JMatrix5S
	5 x 5 symmetric matrix More...
struct	JMatrixND
	NxN matrix. More...
struct	JMatrixND_t
	Basic NxN matrix. More...
struct	JMatrixNS
	N x N symmetric matrix. More...
struct	JModel_t
	Fit model. More...
struct	JMul
	forward declaration for subtraction of fuction. More...
struct	JMul< JF1_t, double >
	Multiplication of constant value. More...
struct	JNegate
	Negate of function. More...
struct	JNumber
	Simple wrapper around template data type to ensure that zero is the default value. More...
struct	JPair
	Auxiliary data structure for pair of functions. More...
struct	JPolynome
	Recursive template class for polynomial function. More...
struct	JPolynome< ID_t, 0 >
	Termination class for polynomial function. More...
struct	JPolynome_t
	Polynome model. More...
struct	JPow
	Power of function. More...
struct	JPow< ID_t, _vF >
	Power of x. More...
class	JPower
	Power law function object. More...
struct	JQuantile_t
	Auxiliary data structure for average. More...
struct	JRandom
	Template definition of random value generator. More...
struct	JRandom< T, false >
	Template spacialisation of JMATH::JRandom for non-numerical data types. More...
struct	JRandom< T, true >
	Template spacialisation of JMATH::JRandom for numerical values. More...
struct	JSin
	Sine of function. More...
struct	JSqrt
	Square root of function. More...
struct	JSqrt< _vF >
	Square root of x. More...
struct	JSub
	forward declaration for addition of fuction. More...
struct	JSub< JF1_t, double >
	Subtraction of constant value. More...
class	JSVD3D
	Singular value decomposition. More...
class	JTrigonometric
	Trigonometric function object for sin and cos. More...
struct	JVectorND
	Nx1 matrix. More...
struct	JXn
	Fixed power of x. More...
struct	JZero
	Auxiliary class to assign zero value. More...
struct	make_carray
	void function More...
struct	parameter_list
	Auxiliary data structure for list of parameters. More...

Typedefs
typedef JGauss_t	JBell_t
	Type definition for Bell model.
template<int ID_t>
using	JP0 = JPolynome<ID_t, 0>
	short hand for 0th degree polynome
template<int ID_t>
using	JP1 = JPolynome<ID_t, 1>
	short hand for 1st degree polynome
template<int ID_t>
using	JP2 = JPolynome<ID_t, 2>
	short hand for 2nd degree polynome
template<int ID_t>
using	JP3 = JPolynome<ID_t, 3>
	short hand for 3rd degree polynome
template<int ID_t, size_t N>
using	JPolynome2X = JMake2X< JPolynome<ID_t, N> >
	2D polynomial function of x.
template<int ID_t, size_t N>
using	JPolynome2Y = JMake2Y< JPolynome<ID_t, N> >
	2D polynomial function of y.
template<int ID_t, bool normalise = false>
using	JGauss2X = JMake2X< JGauss<ID_t, normalise> >
	2D Gauss function of x.
template<int ID_t, bool normalise = false>
using	JGauss2Y = JMake2Y< JGauss<ID_t, normalise> >
	2D Gauss function of y.
template<int ID_t, class JF1_t = _vF>
using	JPow2X = JMake2X< JPow<ID_t, JF1_t> >
	2D power of function of x.
template<int ID_t, class JF1_t = _vF>
using	JPow2Y = JMake2Y< JPow<ID_t, JF1_t> >
	2D power of function of y.
template<int N>
using	JXn2X = JMake2X< JXn<N> >
	2D fixed power of x.
template<int N>
using	JXn2Y = JMake2Y< JXn<N> >
	2D fixed power of y.
template<class JF1_t = _vF>
using	JSqrt2X = JMake2X< JSqrt<JF1_t> >
	2D square root of function of x.
template<class JF1_t = _vF>
using	JSqrt2Y = JMake2Y< JSqrt<JF1_t> >
	2D square root of function of y.
template<class JF1_t >
using	JSin2X = JMake2X< JSin<JF1_t> >
	2D sine of function of x.
template<class JF1_t >
using	JSin2Y = JMake2Y< JSin<JF1_t> >
	2D sine of function of y.
template<class JF1_t >
using	JCos2X = JMake2X< JCos<JF1_t> >
	2D cosine of function of x.
template<class JF1_t >
using	JCos2Y = JMake2Y< JCos<JF1_t> >
	2D cosine of function of y.
template<class JF1_t >
using	JExp2X = JMake2X< JExp<JF1_t> >
	2D exponent of function of x.
template<class JF1_t >
using	JExp2Y = JMake2Y< JExp<JF1_t> >
	2D exponent of function of y.
template<class JF1_t >
using	JLog2X = JMake2X< JLog<JF1_t> >
	2D logarithm of function of x.
template<class JF1_t >
using	JLog2Y = JMake2Y< JLog<JF1_t> >
	2D logarithm of function of y.
template<int ID_t, size_t N>
using	JPolynome3X = JMake3X< JPolynome<ID_t, N> >
	3D polynomial function of x.
template<int ID_t, size_t N>
using	JPolynome3Y = JMake3Y< JPolynome<ID_t, N> >
	3D polynomial function of y.
template<int ID_t, size_t N>
using	JPolynome3Z = JMake3Z< JPolynome<ID_t, N> >
	3D polynomial function of z.
template<int ID_t, bool normalise = false>
using	JGauss3X = JMake3X< JGauss<ID_t, normalise> >
	3D Gauss function of x.
template<int ID_t, bool normalise = false>
using	JGauss3Y = JMake3Y< JGauss<ID_t, normalise> >
	3D Gauss function of y.
template<int ID_t, bool normalise = false>
using	JGauss3Z = JMake3Z< JGauss<ID_t, normalise> >
	3D Gauss function of z.
template<int ID_t, class JF1_t = _vF>
using	JPow3X = JMake3X< JPow<ID_t, JF1_t> >
	3D power of function of x.
template<int ID_t, class JF1_t = _vF>
using	JPow3Y = JMake3Y< JPow<ID_t, JF1_t> >
	3D power of function of y.
template<int ID_t, class JF1_t = _vF>
using	JPow3Z = JMake3Z< JPow<ID_t, JF1_t> >
	3D power of function of z.
template<int N>
using	JXn3X = JMake3X< JXn<N> >
	3D fixed power of x.
template<int N>
using	JXn3Y = JMake3Y< JXn<N> >
	3D fixed power of y.
template<int N>
using	JXn3Z = JMake3Z< JXn<N> >
	3D fixed power of z.
template<class JF1_t = _vF>
using	JSqrt3X = JMake3X< JSqrt<JF1_t> >
	3D square root of function of x.
template<class JF1_t = _vF>
using	JSqrt3Y = JMake3Y< JSqrt<JF1_t> >
	3D square root of function of y.
template<class JF1_t = _vF>
using	JSqrt3Z = JMake3Z< JSqrt<JF1_t> >
	3D square root of function of z.
template<class JF1_t >
using	JSin3X = JMake3X< JSin<JF1_t> >
	3D sine of function of x.
template<class JF1_t >
using	JSin3Y = JMake3Y< JSin<JF1_t> >
	3D sine of function of y.
template<class JF1_t >
using	JSin3Z = JMake3Z< JSin<JF1_t> >
	3D sine of function of z.
template<class JF1_t >
using	JCos3X = JMake3X< JCos<JF1_t> >
	3D cosine of function of x.
template<class JF1_t >
using	JCos3Y = JMake3Y< JCos<JF1_t> >
	3D cosine of function of y.
template<class JF1_t >
using	JCos3Z = JMake3Z< JCos<JF1_t> >
	3D cosine of function of z.
template<class JF1_t >
using	JExp3X = JMake3X< JExp<JF1_t> >
	3D exponent of function of x.
template<class JF1_t >
using	JExp3Y = JMake3Y< JExp<JF1_t> >
	3D exponent of function of y.
template<class JF1_t >
using	JExp3Z = JMake3Z< JExp<JF1_t> >
	3D exponent of function of z.
template<class JF1_t >
using	JLog3X = JMake3X< JLog<JF1_t> >
	3D logarithm of function of x.
template<class JF1_t >
using	JLog3Y = JMake3Y< JLog<JF1_t> >
	3D logarithm of function of y.
template<class JF1_t >
using	JLog3Z = JMake3Z< JLog<JF1_t> >
	3D logarithm of function of z.

Functions
template<class T >
const JCalculator< T, 1 > &	operator* (const T &first, const T &second)
	Product evaluation of objects.
template<class T , int N>
const JCalculator< T, N+1 > &	operator* (const T &first, const JCalculator< T, N > &second)
	Recursive product evaluation of objects.
template<class T , int N>
const JCalculator< T, N+1 > &	operator* (const JCalculator< T, N > &first, const T &second)
	Recursive product evaluation of objects.
template<class T >
T	pow (const T &x, const double y)
	Power .
template<class T >
T	interpolate (const T &first, const T &second, const double alpha)
	Interpolation between objects.
template<class T >
std::iterator_traits< T >::value_type	getAverage (T __begin, T __end)
	Get average.
template<class JValue_t , size_t N>
JValue_t	getAverage (const JValue_t(&array)[N])
	Get average.
template<class JElement_t , class JAllocator_t >
JElement_t	getAverage (const array_type< JElement_t, JAllocator_t > &buffer)
	Get average.
template<class T >
std::iterator_traits< T >::value_type	getAverage (T __begin, T __end, typename std::iterator_traits< T >::value_type value)
	Get average.
template<class JValue_t , size_t N>
JValue_t	getAverage (const JValue_t(&array)[N], typename JLANG::JClass< JValue_t >::argument_type value)
	Get average.
template<class JElement_t , class JAllocator_t >
JElement_t	getAverage (const array_type< JElement_t, JAllocator_t > &buffer, typename JLANG::JClass< JElement_t >::argument_type value)
	Get average.
template<class JF1_t >
size_t	getNumberOfParameters ()
	Get number of parameters.
template<class JF1_t >
double	getParameter (const JF1_t &f1, const size_t i)
	Get value of parameter at given index.
template<class JF1_t >
void	setParameters (JF1_t *f1, const double *values)
	Set values of all parameters.
template<class JF1_t >
JPow< JF1_t::ID, JF1_t >	Pow (const JF1_t &f1, const double alpha)
	Power of function.
template<class JF1_t >
JSqrt< JF1_t >	Sqrt (const JF1_t &f1)
	Square root of function.
JSqrt	Sqrt ()
	Square root of x.
template<class JF1_t >
JSin< JF1_t >	Sin (const JF1_t &f1)
	Sine of function.
template<class JF1_t >
JCos< JF1_t >	Cos (const JF1_t &f1)
	Cosine function.
template<class JF1_t >
JExp< JF1_t >	Exp (const JF1_t &f1)
	Exponent of function.
template<class JF1_t >
JLog< JF1_t >	Log (const JF1_t &f1)
	Logarithm of function.
long long int	factorial (const long long int n)
	Determine factorial.
long long int	factorial (const long long int n, const long long int m)
	Determine combinatorics.
double	gauss (const double x, const double sigma)
	Gauss function (normalised to 1 at x = 0).
double	gauss (const double x, const double x0, const double sigma)
	Gauss function (normalised to 1 at x = x0).
double	Gauss (const double x, const double sigma)
	Normalised Gauss function.
double	Gauss (const double x, const double x0, const double sigma)
	Normalised Gauss function.
double	Gamma (const double a, const double x)
	Incomplete gamma function.
double	legendre (const size_t n, const double x)
	Legendre polynome.
double	binomial (const size_t n, const size_t k)
	Binomial function.
double	poisson (const size_t n, const double mu)
	Poisson probability density distribition.
double	Poisson (const size_t n, const double mu)
	Poisson cumulative density distribition.
double	getP (const double stdev)
	Get single-sided Gaussian probability for given number of standard deviations.
size_t	getNs (const double background, const double P)
	Get minimal number of events to exceed Poisson probability given number of background events.
double	getFs (const double background, const double P, const double precision)
	Get minimal number of events to exceed Poisson probability given number of background events.
void	randomize (JMatrix1D *p)
	Randomize matrix.
void	randomize (JMatrix2D *p)
	Randomize matrix.
void	randomize (JMatrix3D *p)
	Randomize matrix.
void	randomize (JMatrix4D *p)
	Randomize matrix.
void	randomize (JMatrix5D *p)
	Randomize matrix.
void	randomize (JMatrix1S *p)
	Randomize matrix.
void	randomize (JMatrix2S *p)
	Randomize matrix.
void	randomize (JMatrix3S *p)
	Randomize matrix.
void	randomize (JMatrix4S *p)
	Randomize matrix.
void	randomize (JMatrix5S *p)
	Randomize matrix.
template<class JFirst_t , class JSecond_t >
bool	equals (const JFirst_t &first, const JSecond_t &second, const double precision=std::numeric_limits< double >::min())
	Check equality.
template<class JFirst_t , class JSecond_t >
double	getDistanceSquared (const JFirst_t &first, const JSecond_t &second)
	Get square of distance between objects.
template<class JFirst_t , class JSecond_t >
double	getDistance (const JFirst_t &first, const JSecond_t &second)
	Get distance between objects.
template<class JFirst_t , class JSecond_t >
double	getDot (const JFirst_t &first, const JSecond_t &second)
	Get dot product of objects.
template<class JFirst_t , class JSecond_t >
double	getAngle (const JFirst_t &first, const JSecond_t &second)
	Get space angle between objects.
template<class JFirst_t , class JSecond_t >
double	getPerpDot (const JFirst_t &first, const JSecond_t &second)
	Get perpendicular dot product of objects.
template<class T >
T	getCross (const T &first, const T &second)
	Get cross product of objects.
template<class T >
std::vector< T >	convolve (const std::vector< T > &input, const std::vector< T > &kernel)
	Convolute data with given kernel.
template<class T >
T	getRandom ()
	Get random value.
template<class T >
T	getRandom (const T min, const T max)
	Get uniformly distributed random value between given limits.
template<class T >
T	getRandom (const T min, const T max, const T precision)
	Get uniformly distributed random value between given limits.
template<>
double	getRandom (const double min, const double max, const double precision)
	Template specialisation for data type double.
template<class T >
T	getZero ()
	Get zero value for a given data type.
template<>
bool	getZero< bool > ()
	Get zero value for bool.
template<>
float	getZero< float > ()
	Get zero value for float.
template<>
double	getZero< double > ()
	Get zero value for double.
template<>
long double	getZero< long double > ()
	Get zero value for long double.

Variables
static const double	PI = acos(-1.0)
	Mathematical constants.
static const double	EULER = 0.577215664901533
	Euler number.
static const long long int	KILOBYTE = 1024
	Computing quantities.
static const long long int	MEGABYTE = KILOBYTE*KILOBYTE
	Number of bytes in a kilo-byte.
static const long long int	GIGABYTE = MEGABYTE*KILOBYTE
	Number of bytes in a mega-byte.
template<int ID_t>
const parameter_list< JPolynome< ID_t, 0 > > JPolynome< ID_t, 0 >::parameters &	JPolynome
	Set parameters.
template<int ID_t>
const parameter_list< JPow< ID_t > > JPow< ID_t >::parameters &	JPow
	Set parameters.
static const JZero	zero
	Function object to assign zero value.

Detailed Description

Auxiliary classes and methods for mathematical operations.

Author

mdejong

Typedef Documentation

JBell_t

typedef JGauss_t JMATH::JBell_t

Type definition for Bell model.

Definition at line 21 of file JBell.hh.

JP0

template<int ID_t>

using JMATH::JP0 = JPolynome<ID_t, 0>

short hand for 0th degree polynome

Definition at line 1570 of file JMathlib.hh.

JP1

template<int ID_t>

using JMATH::JP1 = JPolynome<ID_t, 1>

short hand for 1st degree polynome

Definition at line 1573 of file JMathlib.hh.

JP2

template<int ID_t>

using JMATH::JP2 = JPolynome<ID_t, 2>

short hand for 2nd degree polynome

Definition at line 1576 of file JMathlib.hh.

JP3

template<int ID_t>

using JMATH::JP3 = JPolynome<ID_t, 3>

short hand for 3rd degree polynome

Definition at line 1579 of file JMathlib.hh.

JPolynome2X

template<int ID_t, size_t N>

using JMATH::JPolynome2X = JMake2X< JPolynome<ID_t, N> >

2D polynomial function of x.

Definition at line 158 of file JMathlib2D.hh.

JPolynome2Y

template<int ID_t, size_t N>

using JMATH::JPolynome2Y = JMake2Y< JPolynome<ID_t, N> >

2D polynomial function of y.

Definition at line 159 of file JMathlib2D.hh.

JGauss2X

template<int ID_t, bool normalise = false>

using JMATH::JGauss2X = JMake2X< JGauss<ID_t, normalise> >

2D Gauss function of x.

Definition at line 160 of file JMathlib2D.hh.

JGauss2Y

template<int ID_t, bool normalise = false>

using JMATH::JGauss2Y = JMake2Y< JGauss<ID_t, normalise> >

2D Gauss function of y.

Definition at line 161 of file JMathlib2D.hh.

JPow2X

template<int ID_t, class JF1_t = _vF>

using JMATH::JPow2X = JMake2X< JPow<ID_t, JF1_t> >

2D power of function of x.

Definition at line 162 of file JMathlib2D.hh.

JPow2Y

template<int ID_t, class JF1_t = _vF>

using JMATH::JPow2Y = JMake2Y< JPow<ID_t, JF1_t> >

2D power of function of y.

Definition at line 163 of file JMathlib2D.hh.

JXn2X

template<int N>

using JMATH::JXn2X = JMake2X< JXn<N> >

2D fixed power of x.

Definition at line 164 of file JMathlib2D.hh.

JXn2Y

template<int N>

using JMATH::JXn2Y = JMake2Y< JXn<N> >

2D fixed power of y.

Definition at line 165 of file JMathlib2D.hh.

JSqrt2X

template<class JF1_t = _vF>

using JMATH::JSqrt2X = JMake2X< JSqrt<JF1_t> >

2D square root of function of x.

Definition at line 166 of file JMathlib2D.hh.

JSqrt2Y

template<class JF1_t = _vF>

using JMATH::JSqrt2Y = JMake2Y< JSqrt<JF1_t> >

2D square root of function of y.

Definition at line 167 of file JMathlib2D.hh.

JSin2X

template<class JF1_t >

using JMATH::JSin2X = JMake2X< JSin<JF1_t> >

2D sine of function of x.

Definition at line 168 of file JMathlib2D.hh.

JSin2Y

template<class JF1_t >

using JMATH::JSin2Y = JMake2Y< JSin<JF1_t> >

2D sine of function of y.

Definition at line 169 of file JMathlib2D.hh.

JCos2X

template<class JF1_t >

using JMATH::JCos2X = JMake2X< JCos<JF1_t> >

2D cosine of function of x.

Definition at line 170 of file JMathlib2D.hh.

JCos2Y

template<class JF1_t >

using JMATH::JCos2Y = JMake2Y< JCos<JF1_t> >

2D cosine of function of y.

Definition at line 171 of file JMathlib2D.hh.

JExp2X

template<class JF1_t >

using JMATH::JExp2X = JMake2X< JExp<JF1_t> >

2D exponent of function of x.

Definition at line 172 of file JMathlib2D.hh.

JExp2Y

template<class JF1_t >

using JMATH::JExp2Y = JMake2Y< JExp<JF1_t> >

2D exponent of function of y.

Definition at line 173 of file JMathlib2D.hh.

JLog2X

template<class JF1_t >

using JMATH::JLog2X = JMake2X< JLog<JF1_t> >

2D logarithm of function of x.

Definition at line 174 of file JMathlib2D.hh.

JLog2Y

template<class JF1_t >

using JMATH::JLog2Y = JMake2Y< JLog<JF1_t> >

2D logarithm of function of y.

Definition at line 175 of file JMathlib2D.hh.

JPolynome3X

template<int ID_t, size_t N>

using JMATH::JPolynome3X = JMake3X< JPolynome<ID_t, N> >

3D polynomial function of x.

Definition at line 234 of file JMathlib3D.hh.

JPolynome3Y

template<int ID_t, size_t N>

using JMATH::JPolynome3Y = JMake3Y< JPolynome<ID_t, N> >

3D polynomial function of y.

Definition at line 235 of file JMathlib3D.hh.

JPolynome3Z

template<int ID_t, size_t N>

using JMATH::JPolynome3Z = JMake3Z< JPolynome<ID_t, N> >

3D polynomial function of z.

Definition at line 236 of file JMathlib3D.hh.

JGauss3X

template<int ID_t, bool normalise = false>

using JMATH::JGauss3X = JMake3X< JGauss<ID_t, normalise> >

3D Gauss function of x.

Definition at line 237 of file JMathlib3D.hh.

JGauss3Y

template<int ID_t, bool normalise = false>

using JMATH::JGauss3Y = JMake3Y< JGauss<ID_t, normalise> >

3D Gauss function of y.

Definition at line 238 of file JMathlib3D.hh.

JGauss3Z

template<int ID_t, bool normalise = false>

using JMATH::JGauss3Z = JMake3Z< JGauss<ID_t, normalise> >

3D Gauss function of z.

Definition at line 239 of file JMathlib3D.hh.

JPow3X

template<int ID_t, class JF1_t = _vF>

using JMATH::JPow3X = JMake3X< JPow<ID_t, JF1_t> >

3D power of function of x.

Definition at line 240 of file JMathlib3D.hh.

JPow3Y

template<int ID_t, class JF1_t = _vF>

using JMATH::JPow3Y = JMake3Y< JPow<ID_t, JF1_t> >

3D power of function of y.

Definition at line 241 of file JMathlib3D.hh.

JPow3Z

template<int ID_t, class JF1_t = _vF>

using JMATH::JPow3Z = JMake3Z< JPow<ID_t, JF1_t> >

3D power of function of z.

Definition at line 242 of file JMathlib3D.hh.

JXn3X

template<int N>

using JMATH::JXn3X = JMake3X< JXn<N> >

3D fixed power of x.

Definition at line 243 of file JMathlib3D.hh.

JXn3Y

template<int N>

using JMATH::JXn3Y = JMake3Y< JXn<N> >

3D fixed power of y.

Definition at line 244 of file JMathlib3D.hh.

JXn3Z

template<int N>

using JMATH::JXn3Z = JMake3Z< JXn<N> >

3D fixed power of z.

Definition at line 245 of file JMathlib3D.hh.

JSqrt3X

template<class JF1_t = _vF>

using JMATH::JSqrt3X = JMake3X< JSqrt<JF1_t> >

3D square root of function of x.

Definition at line 246 of file JMathlib3D.hh.

JSqrt3Y

template<class JF1_t = _vF>

using JMATH::JSqrt3Y = JMake3Y< JSqrt<JF1_t> >

3D square root of function of y.

Definition at line 247 of file JMathlib3D.hh.

JSqrt3Z

template<class JF1_t = _vF>

using JMATH::JSqrt3Z = JMake3Z< JSqrt<JF1_t> >

3D square root of function of z.

Definition at line 248 of file JMathlib3D.hh.

JSin3X

template<class JF1_t >

using JMATH::JSin3X = JMake3X< JSin<JF1_t> >

3D sine of function of x.

Definition at line 249 of file JMathlib3D.hh.

JSin3Y

template<class JF1_t >

using JMATH::JSin3Y = JMake3Y< JSin<JF1_t> >

3D sine of function of y.

Definition at line 250 of file JMathlib3D.hh.

JSin3Z

template<class JF1_t >

using JMATH::JSin3Z = JMake3Z< JSin<JF1_t> >

3D sine of function of z.

Definition at line 251 of file JMathlib3D.hh.

JCos3X

template<class JF1_t >

using JMATH::JCos3X = JMake3X< JCos<JF1_t> >

3D cosine of function of x.

Definition at line 252 of file JMathlib3D.hh.

JCos3Y

template<class JF1_t >

using JMATH::JCos3Y = JMake3Y< JCos<JF1_t> >

3D cosine of function of y.

Definition at line 253 of file JMathlib3D.hh.

JCos3Z

template<class JF1_t >

using JMATH::JCos3Z = JMake3Z< JCos<JF1_t> >

3D cosine of function of z.

Definition at line 254 of file JMathlib3D.hh.

JExp3X

template<class JF1_t >

using JMATH::JExp3X = JMake3X< JExp<JF1_t> >

3D exponent of function of x.

Definition at line 255 of file JMathlib3D.hh.

JExp3Y

template<class JF1_t >

using JMATH::JExp3Y = JMake3Y< JExp<JF1_t> >

3D exponent of function of y.

Definition at line 256 of file JMathlib3D.hh.

JExp3Z

template<class JF1_t >

using JMATH::JExp3Z = JMake3Z< JExp<JF1_t> >

3D exponent of function of z.

Definition at line 257 of file JMathlib3D.hh.

JLog3X

template<class JF1_t >

using JMATH::JLog3X = JMake3X< JLog<JF1_t> >

3D logarithm of function of x.

Definition at line 258 of file JMathlib3D.hh.

JLog3Y

template<class JF1_t >

using JMATH::JLog3Y = JMake3Y< JLog<JF1_t> >

3D logarithm of function of y.

Definition at line 259 of file JMathlib3D.hh.

JLog3Z

template<class JF1_t >

using JMATH::JLog3Z = JMake3Z< JLog<JF1_t> >

3D logarithm of function of z.

Definition at line 260 of file JMathlib3D.hh.

Function Documentation

operator*() [1/3]

template<class T >

const JCalculator< T, 1 > & JMATH::operator* ( const T & first, const T & second )

inline

Product evaluation of objects.

Multiply objects.

Parameters

first	first object
second	second object

Returns

calculator

Definition at line 53 of file JCalculator.hh.

  {
    JCalculator<T, 1>::calculator.mul(first, second);
 
    return JCalculator<T, 1>::calculator;
  }

operator*() [2/3]

template<class T , int N>

const JCalculator< T, N+1 > & JMATH::operator* ( const T & first, const JCalculator< T, N > & second )

inline

Recursive product evaluation of objects.

Parameters

first	first object
second	second object

Returns

calculator

Definition at line 69 of file JCalculator.hh.

  {
    JCalculator<T, N+1>::calculator.mul(first, second);
 
    return JCalculator<T, N+1>::calculator;
  }

operator*() [3/3]

template<class T , int N>

const JCalculator< T, N+1 > & JMATH::operator* ( const JCalculator< T, N > & first, const T & second )

inline

Recursive product evaluation of objects.

Parameters

first	first object
second	second object

Returns

calculator

Definition at line 85 of file JCalculator.hh.

  {
    JCalculator<T, N+1>::calculator.mul(first, second);
 
    return JCalculator<T, N+1>::calculator;
  }

pow()

template<class T >

T JMATH::pow ( const T & x, const double y )

inline

Power .

Parameters

x	value
y	power

Returns

result

Definition at line 97 of file JMath.hh.

  {
    using namespace JPP;
 
    return JMath_t::pow(x, y, JBool<JClass<T>::is_primitive>());
  }

interpolate()

template<class T >

T JMATH::interpolate ( const T & first, const T & second, const double alpha )

inline

Interpolation between objects.

The result is equal to result = (1 - alpha) * (first) + (alpha) * (second).

Parameters

first	first object
second	second object
alpha	interpolation factor [0, 1]

Returns

result

Definition at line 397 of file JMath.hh.

  {
    return T(first).interpolate(second, alpha);
  }

getAverage() [1/6]

template<class T >

std::iterator_traits< T >::value_type JMATH::getAverage	(	T	__begin,
		T	__end )

Get average.

Parameters

__begin	begin of data
__end	end of data

Returns

average value

Definition at line 494 of file JMath.hh.

  {
    typedef typename std::iterator_traits<T>::value_type  value_type;
 
    return JAverage<value_type>(__begin, __end);
  }

getAverage() [2/6]

template<class JValue_t , size_t N>

JValue_t JMATH::getAverage ( const JValue_t(&) array[N] )

inline

Get average.

Parameters

array

c-array of values

Returns

average value

Definition at line 509 of file JMath.hh.

  {
    typedef JValue_t  value_type;
    
    return JAverage<value_type>((const value_type*) array, (const value_type*) array  +  N);
  }

getAverage() [3/6]

template<class JElement_t , class JAllocator_t >

JElement_t JMATH::getAverage

(

const array_type< JElement_t, JAllocator_t > &

buffer

)

Get average.

Parameters

buffer

input data

Returns

average value

Definition at line 524 of file JMath.hh.

  {
    return JAverage<JElement_t>(buffer.begin(), buffer.end());
  }

getAverage() [4/6]

template<class T >

std::iterator_traits< T >::value_type JMATH::getAverage	(	T	__begin,
		T	__end,
		typename std::iterator_traits< T >::value_type	value )

Get average.

Parameters

__begin	begin of data
__end	end of data
value	default value

Returns

average value

Definition at line 539 of file JMath.hh.

  {
    try {
      return getAverage(__begin, __end);
    }
    catch(const std::exception&) {
      return value;
    }
  }

getAverage() [5/6]

template<class JValue_t , size_t N>

JValue_t JMATH::getAverage ( const JValue_t(&) array[N], typename JLANG::JClass< JValue_t >::argument_type value )

inline

Get average.

Parameters

array	c-array of values
value	default value

Returns

average value

Definition at line 558 of file JMath.hh.

  {
    try {
      return getAverage(array);
    }
    catch(const std::exception&) {
      return value;
    }
  }

getAverage() [6/6]

template<class JElement_t , class JAllocator_t >

JElement_t JMATH::getAverage	(	const array_type< JElement_t, JAllocator_t > &	buffer,
		typename JLANG::JClass< JElement_t >::argument_type	value )

Get average.

Parameters

buffer	input data
value	default value

Returns

average value

Definition at line 577 of file JMath.hh.

  {
    try {
      return getAverage(buffer);
    }
    catch(const std::exception&) {
      return value;
    }
  }

getNumberOfParameters()

template<class JF1_t >

size_t JMATH::getNumberOfParameters ( )

inline

Get number of parameters.

Returns

number of parameters

Definition at line 155 of file JMathlib.hh.

  {
    return JF1_t::parameters.size();
  }

getParameter()

template<class JF1_t >

double JMATH::getParameter ( const JF1_t & f1, const size_t i )

inline

Get value of parameter at given index.

Parameters

f1	function
i	index

Returns

value

Definition at line 169 of file JMathlib.hh.

  {
    return f1.*JF1_t::parameters.at(i);
  }

setParameters()

template<class JF1_t >

void JMATH::setParameters ( JF1_t * f1, const double * values )

inline

Set values of all parameters.

Parameters

f1	pointer to function
values	pointer to list of values

Definition at line 182 of file JMathlib.hh.

  {
    if (f1 != NULL && values != NULL) {
      for (size_t i = 0; i != JF1_t::parameters.size(); ++i) {
        f1->*JF1_t::parameters[i] = values[i];
      }
    }
  }

Pow()

template<class JF1_t >

JPow< JF1_t::ID, JF1_t > JMATH::Pow	(	const JF1_t &	f1,
		const double	alpha )

Power of function.

Parameters

f1	function
alpha	alpha

Returns

result

Definition at line 1897 of file JMathlib.hh.

  {
    return JPow<JF1_t::ID, JF1_t>(f1, alpha);
  }

Sqrt() [1/2]

template<class JF1_t >

JSqrt< JF1_t > JMATH::Sqrt

(

const JF1_t &

f1

)

Square root of function.

Parameters

f1

function

Returns

result

Definition at line 2136 of file JMathlib.hh.

  {
    return JSqrt<JF1_t>(f1);
  }

Sqrt() [2/2]

JSqrt JMATH::Sqrt

(

)

Square root of x.

Returns

result

Definition at line 2211 of file JMathlib.hh.

  {
    return JSqrt<>();
  }

Sin()

template<class JF1_t >

JSin< JF1_t > JMATH::Sin

(

const JF1_t &

f1

)

Sine of function.

Parameters

f1

function

Returns

result

Definition at line 2302 of file JMathlib.hh.

  {
    return JSin<JF1_t>(f1);
  }

Cos()

template<class JF1_t >

JCos< JF1_t > JMATH::Cos

(

const JF1_t &

f1

)

Cosine function.

Parameters

f1

function

Returns

result

Definition at line 2393 of file JMathlib.hh.

  {
    return JCos<JF1_t>(f1);
  }

Exp()

template<class JF1_t >

JExp< JF1_t > JMATH::Exp

(

const JF1_t &

f1

)

Exponent of function.

Parameters

f1

function

Returns

result

Definition at line 2545 of file JMathlib.hh.

  {
    return JExp<JF1_t>(f1);
  }

Log()

template<class JF1_t >

JLog< JF1_t > JMATH::Log

(

const JF1_t &

f1

)

Logarithm of function.

Parameters

f1

function

Returns

result

Definition at line 2629 of file JMathlib.hh.

  {
    return JLog<JF1_t>(f1);
  }

factorial() [1/2]

long long int JMATH::factorial ( const long long int n )

inline

Determine factorial.

Parameters

n

number

Returns

factorial (= n!)

Definition at line 32 of file JMath/JMathSupportkit.hh.

  {
    if (n < 0) {
      THROW(JValueOutOfRange, "JMATH::factorial(): invalid argument " << n);
    }
 
    if (n != 1)
      return n * factorial(n - 1);
    else
      return 1;
  }

factorial() [2/2]

long long int JMATH::factorial ( const long long int n, const long long int m )

inline

Determine combinatorics.

Parameters

n	number
m	number

Returns

n!/(m!*(n-m)!)

Definition at line 52 of file JMath/JMathSupportkit.hh.

  {
    if (n < 0 || m < 0 || n < m) {
      THROW(JValueOutOfRange, "JMATH::factorial(): invalid argument " << n << ' ' << m);
    }
 
    if      (n == m)
      return 1;
    else if (m == 0)
      return 1;
    else
      return factorial(n - 1, m - 1) + factorial(n - 1, m);
  }

gauss() [1/2]

double JMATH::gauss ( const double x, const double sigma )

inline

Gauss function (normalised to 1 at x = 0).

Parameters

x	x
sigma	sigma

Returns

function value

Definition at line 74 of file JMath/JMathSupportkit.hh.

  {
    const double u = x / sigma;
 
    if (fabs(u) < 20.0)
      return exp(-0.5*u*u);
    else
      return 0.0;
  }

gauss() [2/2]

double JMATH::gauss ( const double x, const double x0, const double sigma )

inline

Gauss function (normalised to 1 at x = x0).

Parameters

x	x
x0	central value
sigma	sigma

Returns

function value

Definition at line 93 of file JMath/JMathSupportkit.hh.

  {
    return gauss(x - x0, sigma);
  }

Gauss() [1/2]

double JMATH::Gauss ( const double x, const double sigma )

inline

Normalised Gauss function.

Parameters

x	x
sigma	sigma

Returns

function value

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

  {
    return gauss(x, sigma) / sqrt(2.0*PI) / sigma;
  }

Gauss() [2/2]

double JMATH::Gauss ( const double x, const double x0, const double sigma )

inline

Normalised Gauss function.

Parameters

x	x
x0	central value
sigma	sigma

Returns

function value

Definition at line 120 of file JMath/JMathSupportkit.hh.

  {
    return Gauss(x - x0, sigma);
  }

Gamma()

double JMATH::Gamma ( const double a, const double x )

inline

Incomplete gamma function.

Source code is taken from reference: Numerical Recipes in C++, W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Cambridge University Press.

Parameters

a	a
x	x

Returns

function value

Definition at line 137 of file JMath/JMathSupportkit.hh.

  {
    using namespace std;
 
    const int max = 1000000;
 
    if (x <  0.0) { THROW(JValueOutOfRange, "x <  0 " << x); }
    if (a <= 0.0) { THROW(JValueOutOfRange, "a <= 0 " << a); }
 
    const double gln = lgamma(a);
 
    if (x < a + 1.0) {
 
      if (x < 0.0) { 
        THROW(JValueOutOfRange, "x <= 0 " << x);
      }
 
      if (x == 0.0) {
        return 0.0;
      }
 
      double ap  = a;
      double sum = 1.0 / a;
      double del = sum;
 
      for (int i = 0; i != max; ++i) {
 
        ap  += 1.0;
        del *= x/ap;
        sum += del;
 
        if (fabs(del) < fabs(sum)*numeric_limits<double>::epsilon()) {
          return sum*exp(-x + a*log(x) - gln);
        }
      }
 
      THROW(JValueOutOfRange, "i == " << max);
 
    } else {
 
      const double FPMIN = numeric_limits<double>::min() / numeric_limits<double>::epsilon();
 
      double b = x + 1.0 - a;
      double c = 1.0 / FPMIN;
      double d = 1.0 / b;
      double h = d;
 
      for (int i = 1; i != max; ++i) {
 
        const double an = -i * (i-a);
 
        b += 2.0;
        d  = an*d + b;
 
        if (fabs(d) < FPMIN) {
          d = FPMIN;
        }
 
        c  = b + an/c;
 
        if (fabs(c) < FPMIN) {
          c = FPMIN;
        }
 
        d  = 1.0/d;
 
        const double del = d*c;
        
        h *= del;
        
        if (fabs(del - 1.0) < numeric_limits<double>::epsilon()) {
          return 1.0 - exp(-x + a*log(x) - gln) * h;
        }
      }
 
      THROW(JValueOutOfRange, "i == " << max);
    }
  }

legendre()

double JMATH::legendre ( const size_t n, const double x )

inline

Legendre polynome.

Parameters

n	degree
x	x

Returns

function value

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

  {
    switch (n) {
 
    case 0:
      return 1.0;
 
    case 1:
      return x;
 
    default:
      {
        double p0;
        double p1 = 1.0;
        double p2 = x;
 
        for (size_t i = 2; i <= n; ++i) {
          p0 = p1;
          p1 = p2;
          p2 = ((2*i-1) * x*p1  -  (i-1) * p0) / i;
        }
 
        return p2;
      }
    }
  }

binomial()

double JMATH::binomial ( const size_t n, const size_t k )

inline

Binomial function.

Parameters

n	n
k	k

Returns

function value

Definition at line 259 of file JMath/JMathSupportkit.hh.

  {
    if (n == 0 || n < k) {
      return 0.0;
    }
 
    if (k == 0 || n == k) {
      return 1.0;
    }
 
    const int k1 = std::min(k, n - k);
    const int k2 = n - k1;
 
    double value = k2 + 1;
 
    for (int i = k1; i != 1; --i) {
      value *= (double) (k2 + i) / (double) i;
    }
 
    return value;
  }

poisson()

double JMATH::poisson ( const size_t n, const double mu )

inline

Poisson probability density distribition.

Parameters

n	number of occurences
mu	expectation value

Returns

probability

Definition at line 289 of file JMath/JMathSupportkit.hh.

  {
    using namespace std;
 
    if (mu > 0.0) {
 
      if (n > 0)
        return exp(n*log(mu) - lgamma(n+1) - mu);
      else
        return exp(-mu);
    } else if (mu == 0.0) {
 
      return (n == 0 ? 1.0 : 0.0);
    }
 
    THROW(JValueOutOfRange, "mu <= 0 " << mu);
  }

Poisson()

double JMATH::Poisson ( const size_t n, const double mu )

inline

Poisson cumulative density distribition.

Parameters

n	number of occurences
mu	expectation value

Returns

probability

Definition at line 315 of file JMath/JMathSupportkit.hh.

  {
    return 1.0 - Gamma(n + 1, mu);
  }

getP()

double JMATH::getP ( const double stdev )

inline

Get single-sided Gaussian probability for given number of standard deviations.

Parameters

stdev

number of standard deviations

Returns

probability

Definition at line 327 of file JMath/JMathSupportkit.hh.

  {
    return (2.0 *                             // single-sided Gauss
            0.5 *                             // compensate factor 2 in C++ erfc
            erfc(stdev / sqrt(2.0)));         // compensate absent 1/2 in exponent of Gauss in C++ erfc
  }

getNs()

size_t JMATH::getNs ( const double background, const double P )

inline

Get minimal number of events to exceed Poisson probability given number of background events.

Parameters

background	number of background events
P	probability

Returns

number of events

Definition at line 342 of file JMath/JMathSupportkit.hh.

  {
    double y = exp(-background);
    double Y = y;                             // P(0)
    size_t k = 1;
  
    for ( ; Y < 1.0 - P; ++k) {
      y *= background / (double) k;           // P(k)
      Y += y;
    }
 
    return k;
  }

getFs()

double JMATH::getFs ( const double background, const double P, const double precision )

inline

Get minimal number of events to exceed Poisson probability given number of background events.

The precision refers to a step size. When set to one, the result is identical to that of method JMATH::getNs.

Parameters

background	number of background events
P	probability
precision	precision

Returns

number of events

Definition at line 368 of file JMath/JMathSupportkit.hh.

  {
    double u = 1.0 + floor(background);
 
    for ( ; Gamma(u, background) > P; u += precision) {}
 
    return u;
  }

randomize() [1/10]

void JMATH::randomize ( JMatrix1D * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 33 of file JMathTestkit.hh.

  {
    new (p) JMatrix1D(getRandom<double>(-1.0, +1.0));
  }

randomize() [2/10]

void JMATH::randomize ( JMatrix2D * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 44 of file JMathTestkit.hh.

  {
    new (p) JMatrix2D(getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0));
  }

randomize() [3/10]

void JMATH::randomize ( JMatrix3D * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 56 of file JMathTestkit.hh.

  {
    new (p) JMatrix3D(getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0));
  }

randomize() [4/10]

void JMATH::randomize ( JMatrix4D * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 69 of file JMathTestkit.hh.

  {
    new (p) JMatrix4D(getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0));
  }

randomize() [5/10]

void JMATH::randomize ( JMatrix5D * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 83 of file JMathTestkit.hh.

  {
    new (p) JMatrix5D(getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0));
  }

randomize() [6/10]

void JMATH::randomize ( JMatrix1S * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 98 of file JMathTestkit.hh.

  {
    new (p) JMatrix1S(getRandom<double>(-1.0, +1.0));
  }

randomize() [7/10]

void JMATH::randomize ( JMatrix2S * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 109 of file JMathTestkit.hh.

  {
    new (p) JMatrix2S(getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0));
    
    p->a01 = p->a10;
  }

randomize() [8/10]

void JMATH::randomize ( JMatrix3S * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 123 of file JMathTestkit.hh.

  {
    new (p) JMatrix3S(getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0));
 
    p->a01 = p->a10;
    p->a02 = p->a20;
    p->a12 = p->a21;
  }

randomize() [9/10]

void JMATH::randomize ( JMatrix4S * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 140 of file JMathTestkit.hh.

  {
    new (p) JMatrix4S(getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0));
    
    p->a01 = p->a10;
    p->a02 = p->a20;
    p->a03 = p->a30;
    p->a12 = p->a21;
    p->a13 = p->a31;
    p->a23 = p->a32;
  }

randomize() [10/10]

void JMATH::randomize ( JMatrix5S * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 161 of file JMathTestkit.hh.

  {
    new (p) JMatrix5S(getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0),
                      getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0), getRandom<double>(-1.0,+1.0));
 
    p->a01 = p->a10;
    p->a02 = p->a20;
    p->a03 = p->a30;
    p->a04 = p->a40;
    p->a12 = p->a21;
    p->a13 = p->a31;
    p->a14 = p->a41;
    p->a23 = p->a32;
    p->a24 = p->a42;
    p->a34 = p->a43;
  }

equals()

template<class JFirst_t , class JSecond_t >

bool JMATH::equals ( const JFirst_t & first, const JSecond_t & second, const double precision = std::numeric_limits<double>::min() )

inline

Check equality.

Parameters

first	first object
second	second object
precision	precision

Returns

true if two objects are equals; else false

Definition at line 42 of file JMathToolkit.hh.

  {
    return first.equals(second, precision);
  }

getDistanceSquared()

template<class JFirst_t , class JSecond_t >

double JMATH::getDistanceSquared ( const JFirst_t & first, const JSecond_t & second )

inline

Get square of distance between objects.

Parameters

first	first object
second	second object

Returns

square of distance

Definition at line 58 of file JMathToolkit.hh.

  {
    return first.getDistanceSquared(second);    
  }

getDistance()

template<class JFirst_t , class JSecond_t >

double JMATH::getDistance ( const JFirst_t & first, const JSecond_t & second )

inline

Get distance between objects.

Parameters

first	first object
second	second object

Returns

distance

Definition at line 73 of file JMathToolkit.hh.

  {
    return first.getDistance(second);
  }

getDot()

template<class JFirst_t , class JSecond_t >

double JMATH::getDot ( const JFirst_t & first, const JSecond_t & second )

inline

Get dot product of objects.

Parameters

first	first object
second	second object

Returns

dot product

Definition at line 88 of file JMathToolkit.hh.

  {
    return first.getDot(second);
  }

getAngle()

template<class JFirst_t , class JSecond_t >

double JMATH::getAngle ( const JFirst_t & first, const JSecond_t & second )

inline

Get space angle between objects.

Parameters

first	first object
second	second object

Returns

angle [deg]

Definition at line 103 of file JMathToolkit.hh.

  {
    const double dot = getDot(first,second);
 
    if      (dot >= +1.0)
      return   0.0;
    else if (dot <= -1.0)
      return 180.0;
    else
      return acos(dot) * 180.0 / acos(-1.0);
  }

getPerpDot()

template<class JFirst_t , class JSecond_t >

double JMATH::getPerpDot ( const JFirst_t & first, const JSecond_t & second )

inline

Get perpendicular dot product of objects.

Parameters

first	first object
second	second object

Returns

perpendicular dot product

Definition at line 125 of file JMathToolkit.hh.

  {
    return first.getPerpDot(second);
  }

getCross()

template<class T >

T JMATH::getCross ( const T & first, const T & second )

inline

Get cross product of objects.

Parameters

first	first object
second	second object

Returns

cross product

Definition at line 140 of file JMathToolkit.hh.

  {
    return T().getCross(first, second);
  }

convolve()

template<class T >

std::vector< T > JMATH::convolve ( const std::vector< T > & input, const std::vector< T > & kernel )

inline

Convolute data with given kernel.

Parameters

input	input data
kernel	convolution kernel

Returns

convoluted data

Definition at line 155 of file JMathToolkit.hh.

  {
    const size_t k = kernel.size();
    const size_t n = input .size() - k + 1;
    
    std::vector<T> out(n, getZero<T>());
     
    for (size_t i = 0; i != n; ++i) {
      for (size_t j = 0; j != k; ++j) {
        out[i] += input[i + j] * kernel[k - j - 1]; 
      }
    }
 
    return out;
  }

getRandom() [1/4]

template<class T >

T JMATH::getRandom ( )

inline

Get random value.

Returns

random value

Definition at line 113 of file JMath/JRandom.hh.

  {
    return JRandom<T>::getRandom();
  }

getRandom() [2/4]

template<class T >

T JMATH::getRandom ( const T min, const T max )

inline

Get uniformly distributed random value between given limits.

Parameters

min	minimal value
max	maximal value

Returns

random value

Definition at line 127 of file JMath/JRandom.hh.

  {
    return JRandom<T, true>::getRandom(min, max);
  }

getRandom() [3/4]

template<class T >

T JMATH::getRandom ( const T min, const T max, const T precision )

inline

Get uniformly distributed random value between given limits.

Parameters

min	minimal value
max	maximal value
precision	precision

Returns

random value

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

  {
    return JRandom<T, true>::getRandom(min, max);
  }

getRandom() [4/4]

template<>

double JMATH::getRandom ( const double min, const double max, const double precision )

inline

Template specialisation for data type double.

Definition at line 155 of file JMath/JRandom.hh.

  {
    double value = getRandom<double>(min, max);
 
    if (precision != 0.0) {
 
      const long long int ip = (long long int) (1.0 / precision);
 
      value = ((double) ((long long int) (value * ip))) / ip;
    }
 
    return value;
  }

getZero()

template<class T >

T JMATH::getZero ( )

inline

Get zero value for a given data type.

The default implementation of this method returns an object which is created with the default constructor. This method should be specialised if this value does not correspond to the equivalent of a zero result.

Returns

zero

Definition at line 26 of file JZero.hh.

  {
    return T();
  }

getZero< bool >()

template<>

bool JMATH::getZero< bool > ( )

inline

Get zero value for bool.

Returns

false

Definition at line 37 of file JZero.hh.

  {
    return false;
  }

getZero< float >()

template<>

float JMATH::getZero< float > ( )

inline

Get zero value for float.

Returns

zero

Definition at line 48 of file JZero.hh.

  { 
    return float(0.0);
  }

getZero< double >()

template<>

double JMATH::getZero< double > ( )

inline

Get zero value for double.

Returns

zero

Definition at line 60 of file JZero.hh.

  {
    return double(0.0);
  }

getZero< long double >()

template<>

long double JMATH::getZero< long double > ( )

inline

Get zero value for long double.

Returns

zero

Definition at line 72 of file JZero.hh.

  {
    return (long double)(0.0);
  }

Variable Documentation

PI

const double JMATH::PI = acos(-1.0)

static

Mathematical constants.

pi

Definition at line 20 of file JMath/JConstants.hh.

EULER

const double JMATH::EULER = 0.577215664901533

static

Euler number.

Definition at line 21 of file JMath/JConstants.hh.

KILOBYTE

const long long int JMATH::KILOBYTE = 1024

static

Computing quantities.

Definition at line 26 of file JMath/JConstants.hh.

MEGABYTE

const long long int JMATH::MEGABYTE = KILOBYTE*KILOBYTE

static

Number of bytes in a kilo-byte.

Definition at line 27 of file JMath/JConstants.hh.

GIGABYTE

const long long int JMATH::GIGABYTE = MEGABYTE*KILOBYTE

static

Number of bytes in a mega-byte.

Definition at line 28 of file JMath/JConstants.hh.

JPolynome

template<int ID_t>

const parameter_list< JPolynome<ID_t, 0> > JPolynome<ID_t,0>::parameters& JMATH::JPolynome

Set parameters.

Definition at line 1566 of file JMathlib.hh.

JPow

template<int ID_t>

const parameter_list< JPow<ID_t> > JPow<ID_t>::parameters& JMATH::JPow

Set parameters.

Definition at line 1979 of file JMathlib.hh.

zero

const JZero JMATH::zero

static

Function object to assign zero value.

Definition at line 105 of file JZero.hh.