JMATH Namespace Reference

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

Classes
struct	JAverage< JQuaternion3D >
	Template spacialisation for averaging quaternions. 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< JQuaternion3D, N >
	Template specialisation for function evaluation of Legendre polynome of quaternions for defined number of degrees. More...
struct	JCalculator
	Auxiliary class for arithmetic operations on objects. More...
struct	JGauss_t
	Gauss model. More...
struct	JGauss
	Gauss function object. More...
struct	JLegendre_t
	Base class for Legendre polynome. 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	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_t
	Auxiliary class to hide data type specific methods. 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	JAverage
	Auxiliary class to determine average of set of values. 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	JSVD3D
	Singular value decomposition. 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...
template<class T >
T	pow (const T &x, const double y)
	Power . More...
template<class T >
T	interpolate (const T &first, const T &second, const double alpha)
	Interpolation between objects. More...
template<class T >
std::iterator_traits< T > ::value_type	getAverage (T __begin, T __end)
	Get average. More...
template<class JValue_t , size_t N>
JValue_t	getAverage (const JValue_t(&array)[N])
	Get average. More...
template<class JElement_t , class JAllocator_t >
JElement_t	getAverage (const array_type< JElement_t, JAllocator_t > &buffer)
	Get average. More...
template<class T >
std::iterator_traits< T > ::value_type	getAverage (T __begin, T __end, typename std::iterator_traits< T >::value_type value)
	Get average. More...
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. More...
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. 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...
double	legendre (const size_t n, const double x)
	Legendre polynome. More...
double	binomial (const size_t n, const size_t k)
	Binomial function. More...
double	poisson (const size_t n, const double mu)
	Poisson probability density distribition. More...
double	Poisson (const size_t n, const double mu)
	Poisson cumulative density distribition. More...
void	randomize (JMatrix1D *p)
	Randomize matrix. More...
void	randomize (JMatrix2D *p)
	Randomize matrix. More...
void	randomize (JMatrix3D *p)
	Randomize matrix. More...
void	randomize (JMatrix4D *p)
	Randomize matrix. More...
void	randomize (JMatrix5D *p)
	Randomize matrix. 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	getCross (const T &first, const T &second)
	Get cross product of objects. More...
template<class T >
std::vector< T >	convolve (const std::vector< T > &input, const std::vector< T > &kernel)
	Convolute data with given kernel. 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 double	PI = acos(-1.0)
	Mathematical constants. More...
static const double	EULER = 0.577215664901533
	Euler number. More...
static const long long int	KILOBYTE = 1024
	Computing quantities. More...
static const long long int	MEGABYTE = KILOBYTE*KILOBYTE
	Number of bytes in a kilo-byte. More...
static const long long int	GIGABYTE = MEGABYTE*KILOBYTE
	Number of bytes in a mega-byte. More...
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;
  }

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>());
  }

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);
  }

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);
  }

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);
  }

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());
  }

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;
    }
  }

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;
    }
  }

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;
    }
  }

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 33 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;
  }

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 52 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 65 of file JMath/JMathSupportkit.hh.

  {
    return gauss(x, sigma) / sqrt(2.0*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 79 of file JMath/JMathSupportkit.hh.

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

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 96 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);
    }
  }

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

inline

Legendre polynome.

Parameters

n	degree
x	x

Returns

function value

Definition at line 183 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;
      }
    }
  }

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 218 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;
  }

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 248 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);
  }

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 274 of file JMath/JMathSupportkit.hh.

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

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));
  }

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));
  }

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));
  }

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));
  }

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));
  }

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));
  }

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;
  }

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;
  }

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;
  }

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;
  }

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

inline

Determine factorial.

Parameters

n

number

Returns

factorial (= n!)

Definition at line 42 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 62 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 86 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 102 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 117 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 132 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 147 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 169 of file JMathToolkit.hh.

  {
    return first.getPerpDot(second);
  }

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 184 of file JMathToolkit.hh.

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

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 199 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;
  }

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 double JMATH::PI = acos(-1.0)

static

Mathematical constants.

pi

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

const double JMATH::EULER = 0.577215664901533

static

Euler number.

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

const long long int JMATH::KILOBYTE = 1024

static

Computing quantities.

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

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.

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.

const JZero JMATH::zero

static

Function object to assign zero value.

Definition at line 105 of file JZero.hh.