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

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

struct	JGauss_t
	Gauss model. More...

struct	JGauss
	Gauss function object. More...

struct	JLimits
	Auxiliary class for minimum and maximum values for any class. More...

struct	JLimits< T, true >
	Template spacialisation of JMATH::JLimits for numerical values. More...

struct	JLimits< T, false >
	Template spacialisation of JMATH::JRandom for other data types. 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...

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_t
	Basic NxN matrix. More...

struct	JMatrixND
	NxN matrix. More...

struct	JMatrixNS
	N x N symmetric matrix. More...

struct	JModel_t
	Fit model. More...

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

struct	JPolynome_t
	Polynome model. More...

struct	JPolynome
	Polynome function object. More...

class	JPower
	Power law function object. More...

struct	JRandom
	Template definition of random value generator. More...

struct	JRandom< T, true >
	Template spacialisation of JMATH::JRandom for numerical values. More...

struct	JRandom< T, false >
	Template spacialisation of JMATH::JRandom for non-numerical data types. More...

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

struct	JVectorND
	Nx1 matrix. More...

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

double	gauss (const double x, const double sigma)
	Gauss function (normalised to 1 at x = 0). More...

double	gauss (const double x, const double x0, const double sigma)
	Gauss function (normalised to 1 at x = x0). More...

double	Gauss (const double x, const double sigma)
	Normalised Gauss function. More...

double	Gauss (const double x, const double x0, const double sigma)
	Normalised Gauss function. More...

double	Gamma (const double a, const double x)
	Incomplete gamma function. More...

void	randomize (JMatrix1S *p)
	Randomize matrix. More...

void	randomize (JMatrix2S *p)
	Randomize matrix. More...

void	randomize (JMatrix3S *p)
	Randomize matrix. More...

void	randomize (JMatrix4S *p)
	Randomize matrix. More...

void	randomize (JMatrix5S *p)
	Randomize matrix. 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 >
std::vector< T >	convolve (const std::vector< T > &in, const std::vector< T > &ker)
	Convolves a vector (in) with another vector (ker). 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<>
bool	getZero< bool > ()
	Get zero value for `bool`. 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

Function Documentation

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;
   }

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;
   }

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;
   }

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 26 of file JMath/JMathSupportkit.hh.

   {
     const double u = x / sigma;
 
     if (fabs(u) < 10.0)
       return exp(-0.5*u*u);
     else
       return 0.0;
   }

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 45 of file JMath/JMathSupportkit.hh.

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

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

inline

Normalised Gauss function.

Parameters

x	x
sigma	sigma

Returns: function value

Definition at line 58 of file JMath/JMathSupportkit.hh.

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

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 72 of file JMath/JMathSupportkit.hh.

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

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

inline

Incomplete gamma function.

Parameters

a	a
x	x

Returns: function value

Definition at line 85 of file JMath/JMathSupportkit.hh.

   {
     using namespace std;
 
     const int max = 100;
 
     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);
       }
 
       double ap  = a;
       double sum = 1.0 /a;
       double del = sum;
 
       for (int i = 1; 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);
         }
       }
 
     } else {
 
       double b = x + 1.0 - a;
       double c = numeric_limits<double>::epsilon() / numeric_limits<double>::min();
       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) < numeric_limits<double>::min()) {
           d = numeric_limits<double>::min();
         }
 
         c  = b + an/c;
 
         if (fabs(c) < numeric_limits<double>::min()) {
           c = numeric_limits<double>::min();
         }
 
         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, "a " << a);
     }
 
     return 0.0;
   }

void JMATH::randomize ( JMatrix1S * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 29 of file JMathTestkit.hh.

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

void JMATH::randomize ( JMatrix2S * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 40 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;
   }

void JMATH::randomize ( JMatrix3S * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 54 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;
   }

void JMATH::randomize ( JMatrix4S * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 71 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;
   }

void JMATH::randomize ( JMatrix5S * p )

inline

Randomize matrix.

Parameters

p	pointer to valid object

Definition at line 92 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;
   }

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;
   }

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);
   }

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);
   }

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);    
   }

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);
   }

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);
   }

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);
   }

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);
   }

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);
   }

template<class T >

std::vector<T> JMATH::convolve	(	const std::vector< T > &	in,
		const std::vector< T > &	ker
	)

inline

Convolves a vector (in) with another vector (ker).

Parameters

in	input vector (data)
ker	convolution kernel

Returns: convolution of in with ker

Definition at line 200 of file JMathToolkit.hh.

                                                                                 {
 
     const int k = ker.size();
     const int n = in.size() - k + 1;
     
     std::vector<T> out(n, 0);
      
     for (int i = 0; i < n; i++) {
       for (int j = 0; j < k; j++) {
         out[i] += in[i + j] * ker[k - j - 1]; 
       }
     }
 
     return out;
   
   }

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();
   }

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);
   }

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);
   }

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;
   }

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();
   }

template<>

bool JMATH::getZero< bool > ( )

inline

Get zero value for bool.

Returns: false

Definition at line 37 of file JZero.hh.

   {
     return false;
   }

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);
   }

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);
   }

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

const JZero JMATH::zero

static

Function object to assign zero value.

Definition at line 105 of file JZero.hh.

Classes

Functions

Variables

Detailed Description

Function Documentation

Variable Documentation