JMATH::JBell Struct Reference

Bell function object. More...

#include <JBell.hh>

Inheritance diagram for JMATH::JBell:

Public Types
typedef double JBell_t::*	parameter_type
	Type definition of fit parameter.

Public Member Functions
	JBell ()
	Default constructor.
	JBell (const JBell_t &bell, const double alpha=2.0)
	Copy constructor.
	JBell (const double mean, const double sigma, const double signal=1.0, const double background=0.0, const double alpha=2.0)
	Constructor.
double	getValue (const double x) const
	Function value.
double	getDerivative (const double x) const
	Derivative value.
double	operator() (const double x) const
	Function value.
const JBell_t &	getGradient (const double x) const
	Get gradient.
bool	equals (const JGauss_t &gauss, const double eps=std::numeric_limits< double >::min()) const
	Equality.
JGauss_t &	add (const JGauss_t &gauss)
	Add gauss.
JGauss_t &	sub (const JGauss_t &gauss)
	Subtract gauss.
JGauss_t &	mul (const double factor)
	Scale gauss.
JGauss_t &	mul (const JSecond_t &object)
	Multiply with object.

Public Attributes
double	mean
double	sigma
double	signal
double	background

Private Member Functions
double	get (const double u) const
	Get ordinate value.

Static Private Member Functions
static double	_f (const double x, const double a)
	Power.

Private Attributes
double	alpha
	power
double	V
	normalisation constant
JBell_t	gradient

Detailed Description

Bell function object.

This function object correspods to a Gauss with a different power (alpha) for the exponential term.

Evaluates function, derivative and gradient values.

Definition at line 30 of file JBell.hh.

Member Typedef Documentation

parameter_type

double JBell_t::* JMATH::JBell::parameter_type

Type definition of fit parameter.

Definition at line 36 of file JBell.hh.

Constructor & Destructor Documentation

JBell() [1/3]

JMATH::JBell::JBell ( )

inline

Default constructor.

Definition at line 42 of file JBell.hh.

            :
      JBell_t()
    {}

JBell() [2/3]

JMATH::JBell::JBell ( const JBell_t & bell, const double alpha = 2.0 )

inline

Copy constructor.

Parameters

bell	bell
alpha	alpha

Definition at line 53 of file JBell.hh.

                                         :
      JBell_t(bell),
      alpha(alpha),
      V(2.0 * pow(2.0,1.0/alpha) * tgamma(1.0/alpha) / alpha)
    {}

JBell() [3/3]

JMATH::JBell::JBell ( const double mean, const double sigma, const double signal = 1.0, const double background = 0.0, const double alpha = 2.0 )

inline

Constructor.

Parameters

mean	mean
sigma	sigma
signal	signal
background	background
alpha	alpha

Definition at line 70 of file JBell.hh.

                                         :
      JBell(JBell_t(mean, sigma, signal, background), alpha)
    {}

Member Function Documentation

getValue()

double JMATH::JBell::getValue ( const double x ) const

inline

Function value.

Parameters

x	abscissa value

Returns

function value

Definition at line 85 of file JBell.hh.

    {
      const double u  = (x - mean) / sigma;
 
      return signal * get(u) + background;
    }

getDerivative()

double JMATH::JBell::getDerivative ( const double x ) const

inline

Derivative value.

Parameters

x	abscissa value

Returns

derivative value

Definition at line 99 of file JBell.hh.

    {
      const double u  = (x - mean) / sigma;
 
      return signal * get(u) * copysign(_f(u, alpha - 1.0), -u) * alpha / sigma;
    }

operator()()

double JMATH::JBell::operator() ( const double x ) const

inline

Function value.

Parameters

x	abscissa value

Returns

function value

Definition at line 113 of file JBell.hh.

    {
      return getValue(x);
    }

getGradient()

const JBell_t & JMATH::JBell::getGradient ( const double x ) const

inline

Get gradient.

Parameters

x	abscissa value

Returns

gradient

Definition at line 125 of file JBell.hh.

    {
      const double w  = 1.0 / sigma;
      const double u  = (x - mean) * w;
      const double f0 =  get(u);
      const double fs =  signal * f0;
 
      gradient.mean       =  fs * copysign(_f(u, alpha - 1.0), u) * alpha * w;      // d(f)/d(mean)
      gradient.sigma      =  fs *        -(_f(u, alpha) * alpha + 1.0)    * w;      // d(f)/d(sigma)
      gradient.signal     =  f0;                                                    // d(f)/d(signal)
      gradient.background =  1.0;                                                   // d(f)/d(background)
 
      return gradient;
    }

_f()

static double JMATH::JBell::_f ( const double x, const double a )

inlinestaticprivate

Power.

Parameters

x	abscissa value
a	power

Returns

ordinate value

Definition at line 151 of file JBell.hh.

    {
      return -0.5 * pow(fabs(x), a);
    }

get()

double JMATH::JBell::get ( const double u ) const

inlineprivate

Get ordinate value.

Parameters

u	abscissa value

Returns

ordinate value

Definition at line 163 of file JBell.hh.

    {
      const double v = _f(u, alpha);
 
      return exp(v) / (sigma * V);
    }

equals()

bool JMATH::JGauss_t::equals ( const JGauss_t & gauss, const double eps = std::numeric_limits<double>::min() ) const

inlineinherited

Equality.

Parameters

gauss	gauss
eps	numerical precision

Returns

true if gauss's identical; else false

Definition at line 70 of file JGauss.hh.

    {
      return (fabs(mean       - gauss.mean)       <=  eps  &&
              fabs(sigma      - gauss.sigma)      <=  eps  &&
              fabs(signal     - gauss.signal)     <=  eps  &&
              fabs(background - gauss.background) <=  eps);
    }

add()

JGauss_t & JMATH::JGauss_t::add ( const JGauss_t & gauss )

inlineinherited

Add gauss.

Parameters

gauss

gauss

Returns

this gauss

Definition at line 86 of file JGauss.hh.

    {
      mean       += gauss.mean;
      sigma      += gauss.sigma;
      signal     += gauss.signal;
      background += gauss.background;
 
      return *this;
    }

sub()

JGauss_t & JMATH::JGauss_t::sub ( const JGauss_t & gauss )

inlineinherited

Subtract gauss.

Parameters

gauss

gauss

Returns

this gauss

Definition at line 103 of file JGauss.hh.

    {
      mean       -= gauss.mean;
      sigma      -= gauss.sigma;
      signal     -= gauss.signal;
      background -= gauss.background;
 
      return *this;
    }

mul() [1/2]

JGauss_t & JMATH::JGauss_t::mul ( const double factor )

inlineinherited

Scale gauss.

Parameters

factor

multiplication factor

Returns

this gauss

Definition at line 120 of file JGauss.hh.

    {
      mean       *= factor;
      sigma      *= factor;
      signal     *= factor;
      background *= factor;
 
      return *this;
    }

mul() [2/2]

JGauss_t & JMATH::JMath< JGauss_t, JSecond_t >::mul ( const JSecond_t & object )

inlineinherited

Multiply with object.

Parameters

object

object

Returns

result object

Definition at line 354 of file JMath.hh.

    {
      return static_cast<JFirst_t&>(*this) = JFirst_t().mul(static_cast<const JFirst_t&>(*this), object);
    }

Member Data Documentation

alpha

double JMATH::JBell::alpha

private

power

Definition at line 141 of file JBell.hh.

V

double JMATH::JBell::V

private

normalisation constant

Definition at line 142 of file JBell.hh.

gradient

JBell_t JMATH::JBell::gradient

mutableprivate

Definition at line 170 of file JBell.hh.

mean

double JMATH::JGauss_t::mean

inherited

Definition at line 161 of file JGauss.hh.

sigma

double JMATH::JGauss_t::sigma

inherited

Definition at line 162 of file JGauss.hh.

signal

double JMATH::JGauss_t::signal

inherited

Definition at line 163 of file JGauss.hh.

background

double JMATH::JGauss_t::background

inherited

Definition at line 164 of file JGauss.hh.

---

The documentation for this struct was generated from the following file:

• JBell.hh