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

Classes
struct	JCalculator
	Auxiliary class for arithmetic operations on objects. More...

class	JGauss
	Data structure for Gaussian function on top of a flat background. 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	JMath
	Auxiliary base class for aritmetic operations of derived class types. More...

struct	JMath< T, JNullType >
	Template class for data structures with arithmetic capabilities. 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...

class	JMatrixND
	N x N matrix. More...

struct	JMatrixND_t
	Type definition of a NxN matrix. More...

class	JMatrixNS
	N x N symmetric matrix. More...

struct	JNumber
	Simple wrapper around template data type to ensure that zero is the default value. More...

class	JPolynome
	Polynome function object. More...

class	JPower
	Power law function object. 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...

class	JTrigonometric
	Trigonometric function object for `sin` and `cos`. More...

struct	JZero
	Auxiliary class to assign zero value. More...

Typedefs
typedef std::vector< std::pair< int, int > >	JPermutationMatrix
	Type definition of permutation matrix. More...

Functions
template<class T >
const JCalculator< T, 1 > &	operator* (const T &first, const T &second)
	Product evaluation of objects. More...

template<class T , int N>
const JCalculator< T, N+1 > &	operator* (const T &first, const JCalculator< T, N > &second)
	Recursive product evaluation of objects. More...

template<class T , int N>
const JCalculator< T, N+1 > &	operator* (const JCalculator< T, N > &first, const T &second)
	Recursive product evaluation of objects. More...

long long int	factorial (const long long int n)
	Determine factorial. More...

long long int	factorial (const long long int n, const long long int m)
	Determine combinatorics. More...

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. More...

template<class JFirst_t , class JSecond_t >
double	getDistanceSquared (const JFirst_t &first, const JSecond_t &second)
	Get square of distance between objects. More...

template<class JFirst_t , class JSecond_t >
double	getDistance (const JFirst_t &first, const JSecond_t &second)
	Get distance between objects. More...

template<class JFirst_t , class JSecond_t >
double	getDot (const JFirst_t &first, const JSecond_t &second)
	Get dot product of objects. More...

template<class JFirst_t , class JSecond_t >
double	getAngle (const JFirst_t &first, const JSecond_t &second)
	Get space angle between objects. More...

template<class JFirst_t , class JSecond_t >
double	getPerpDot (const JFirst_t &first, const JSecond_t &second)
	Get perpendicular dot product of objects. More...

template<class T >
T	interpolate (const T &first, const T &second, const double alpha)
	Interpolation between objects. More...

template<class T >
double	getDot (T __begin, T __end, const JMatrixND &V)
	Determine dot product `Y^T x V x Y`, where. More...

template<class T >
T	getRandom ()
	Get random value. More...

template<class T >
T	getRandom (const T min, const T max)
	Get uniformly distributed random value between given limits. More...

template<class T >
T	getRandom (const T min, const T max, const T precision)
	Get uniformly distributed random value between given limits. More...

template<>
double	getRandom (const double min, const double max, const double precision)
	Template specialisation for data type `double`. More...

template<class T >
T	getZero ()
	Get zero value for a given data type. More...

template<>
float	getZero< float > ()
	Get zero value for float. More...

template<>
double	getZero< double > ()
	Get zero value for double. More...

template<>
long double	getZero< long double > ()
	Get zero value for long double. More...

Variables
static const JZero	zero
	Function object to assign zero value. More...

Detailed Description

Auxiliary classes and methods for mathematical operations.

Author: mdejong

Typedef Documentation

◆ JPermutationMatrix

typedef std::vector< std::pair<int,int> > JMATH::JPermutationMatrix

Type definition of permutation matrix.

Definition at line 57 of file JMatrixND.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;
   }

◆ 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 41 of file JMathToolkit.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 61 of file JMathToolkit.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);
   }

◆ 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 85 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 101 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 116 of file JMathToolkit.hh.

   {
     return first.getDistance(second);
   }

◆ getDot() [1/2]

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 131 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 146 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 168 of file JMathToolkit.hh.

   {
     return first.getPerpDot(second);
   }

◆ 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) x (first) + (alpha) x (second).

Parameters

first	first object
second	second object
alpha	interpolation factor (normally between 0 and 1)

Returns: result

Definition at line 185 of file JMathToolkit.hh.

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

◆ getDot() [2/2]

template<class T >

double JMATH::getDot	(	T	__begin,
		T	__end,
		const JMatrixND &	V
	)

inline

Determine dot product Y^T x V x Y, where.

Y is a 1xN matrix; and
V is a NxN matrix.

Parameters

__begin	begin of data
__end	end of data
V	matrix

Returns: dot product

Definition at line 647 of file JMatrixND.hh.

   {
     double dot = 0.0;
  
     T yl = __begin;
     
     for (JMatrixND::const_row_type row = V.begin(); row != V.end(); ++row, ++yl) {
  
       T yr = __begin;
  
       for (JMatrixND::const_col_type col = row->begin(); col != row->end(); ++col, ++yr) {
         dot += (*yl) * (*col) * (*yr);
       }
     }
     
     return dot;
   }

◆ getRandom() [1/4]

template<class T >

T JMATH::getRandom ( )

inline

Get random value.

Returns: random value

Definition at line 113 of file 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 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 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 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< float >()

template<>

float JMATH::getZero< float > ( )

inline

Get zero value for float.

Returns: zero

Definition at line 37 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 49 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 61 of file JZero.hh.

   {
     return (long double)(0.0);
   }

Variable Documentation

◆ zero

const JZero JMATH::zero

static

Function object to assign zero value.

Definition at line 94 of file JZero.hh.

Classes

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ JPermutationMatrix

Function Documentation

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ factorial() [1/2]

◆ factorial() [2/2]

◆ equals()

◆ getDistanceSquared()

◆ getDistance()

◆ getDot() [1/2]

◆ getAngle()

◆ getPerpDot()

◆ interpolate()

◆ getDot() [2/2]

◆ getRandom() [1/4]

◆ getRandom() [2/4]

◆ getRandom() [3/4]

◆ getRandom() [4/4]

◆ getZero()

◆ getZero< float >()

◆ getZero< double >()

◆ getZero< long double >()

Variable Documentation

◆ zero