JMATH::JGauss< ID_t, normalised > Struct Template Reference

Gauss function object. More...

#include <JGauss.hh>

Inheritance diagram for JMATH::JGauss< ID_t, normalised >:

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

Public Member Functions
	JGauss ()
	Default constructor.
	JGauss (const JGauss_t &gauss)
	Copy constructor.
	JGauss (const double mean, const double sigma, const double signal=1.0, const double background=0.0)
	Constructor.
double	getValue (const double x) const
	Function value.
double	getDerivative (const double x) const
	Derivative value.
double	getIntegral (const double xmin, const double xmax) const
	Integral value.
double	operator() (const double x) const
	Function value.
const JGauss_t &	getGradient (const double x) const
	Get gradient.
	JGauss ()
	Default constructor.
	JGauss (const double center, const double sigma)
	Constructor.
double	getValue (const double x) const
	Function value.
double	getDerivative (const double x) const
	Derivative value.
JGauss	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.
double	operator() (const Args &...args) const
	Function value.
double	operator[] (const size_t i) const
	Get value of parameter at given index.
double &	operator[] (const size_t i)
	Get value of parameter at given index.
JGauss< ID_t > &	negate ()
	Negate function.
JGauss< ID_t > &	add (const JGauss< ID_t > &f1)
	Add function.
JGauss< ID_t > &	sub (const JGauss< ID_t > &f1)
	Subtract function.
JGauss< ID_t > &	mul (const double factor)
	Scale function.
JGauss< ID_t > &	div (const double factor)
	Scale function.

Static Public Member Functions
static size_t	size ()
	Get size of parameter.

Public Attributes
double	center
	center
double	sigma
	sigma
double	mean
double	signal
double	background

Static Public Attributes
static const int	ID = ID_t
static constexpr parameter_list< JGauss, 2 >	parameters { &JGauss::center, &JGauss::sigma }

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

Private Attributes
JGauss_t	gradient

Detailed Description

template<int ID_t, bool normalised = false>
struct JMATH::JGauss< ID_t, normalised >

Gauss function object.

Gauss function.

Evaluates function, derivative and gradient values.

Definition at line 1997 of file JMathlib.hh.

Member Typedef Documentation

parameter_type

template<int ID_t, bool normalised = false>

double JGauss_t::* JMATH::JGauss< ID_t, normalised >::parameter_type

Type definition of fit parameter.

Definition at line 182 of file JGauss.hh.

Constructor & Destructor Documentation

JGauss() [1/5]

template<int ID_t, bool normalised = false>

JMATH::JGauss< ID_t, normalised >::JGauss ( )

inline

Default constructor.

Definition at line 188 of file JGauss.hh.

             :
      JGauss_t()
    {}

JGauss() [2/5]

template<int ID_t, bool normalised = false>

JMATH::JGauss< ID_t, normalised >::JGauss ( const JGauss_t & gauss )

inline

Copy constructor.

Parameters

gauss

gauss

Definition at line 198 of file JGauss.hh.

                                  :
      JGauss_t(gauss)
    {}

JGauss() [3/5]

template<int ID_t, bool normalised = false>

JMATH::JGauss< ID_t, normalised >::JGauss ( const double mean, const double sigma, const double signal = 1.0, const double background = 0.0 )

inline

Constructor.

Parameters

mean	mean
sigma	sigma
signal	signal
background	background

Definition at line 211 of file JGauss.hh.

                                          :
      JGauss_t(mean, sigma, signal, background)
    {}

JGauss() [4/5]

template<int ID_t, bool normalised = false>

JMATH::JGauss< ID_t, normalised >::JGauss ( )

inline

Default constructor.

Definition at line 2007 of file JMathlib.hh.

             :
      center(0.0),
      sigma (0.0)
    {}

JGauss() [5/5]

template<int ID_t, bool normalised = false>

JMATH::JGauss< ID_t, normalised >::JGauss ( const double center, const double sigma )

inline

Constructor.

Parameters

center	center
sigma	sigma

Definition at line 2019 of file JMathlib.hh.

                               :
      center(center),
      sigma (sigma)
    {}

Member Function Documentation

getValue() [1/2]

template<int ID_t, bool normalised = false>

double JMATH::JGauss< ID_t, normalised >::getValue ( const double x ) const

inline

Function value.

Note that an error will be thrown if sigma <= 0.0.

Parameters

x	abscissa value

Returns

function value

Definition at line 227 of file JGauss.hh.

    {
      if (sigma <= 0.0) { THROW(JValueOutOfRange, "JGauss::getValue: Invalid sigma " << sigma); }
      
      const double u  = (x - mean) / sigma;
 
      return signal * get(u) + background;
    }

getDerivative() [1/2]

template<int ID_t, bool normalised = false>

double JMATH::JGauss< ID_t, normalised >::getDerivative ( const double x ) const

inline

Derivative value.

Note that an error will be thrown if sigma <= 0.0.

Parameters

x	abscissa value

Returns

derivative value

Definition at line 245 of file JGauss.hh.

    {
      if (sigma <= 0.0) { THROW(JValueOutOfRange, "JGauss::getDerivative: Invalid sigma " << sigma); }
 
      const double u  = (x - mean) / sigma;
 
      return signal * get(u) * -u / sigma;
    }

getIntegral()

template<int ID_t, bool normalised = false>

double JMATH::JGauss< ID_t, normalised >::getIntegral ( const double xmin, const double xmax ) const

inline

Integral value.

Note that an error will be thrown if sigma <= 0.0. Note that zero will be returned if xmin is equal to xmax. Note that the integration limits can be set to infinity using std::numeric_limits<double>::inifinity().

Parameters

xmin	lower limit
xmax	upper limit

Definition at line 265 of file JGauss.hh.

    {
      if (sigma <= 0.0) { THROW(JValueOutOfRange, "JGauss::getIntegral: Invalid sigma " << sigma); }
 
      double zmin = xmin;
      double zmax = xmax;
 
      if (xmax < xmin) {
 
        zmin = xmax;
        zmax = xmin;
      }
        
      if (zmin < zmax) {
 
        const double umin = (zmin - mean) / sigma / sqrt(2.0);
        const double umax = (zmax - mean) / sigma / sqrt(2.0);
        
        double I;
 
        if        (std::isinf(zmin) && std::isinf(zmax)) {
 
          I = 1.0;
        
        } else if (std::isinf(zmin)) {
 
          I = 0.5 * (1 + erf(umax));
 
        } else if (std::isinf(zmax)) {
 
          I = 0.5 * erfc(umin);
 
        } else {
 
          I = 0.5 * (erfc(umin) - erfc(umax));
        }
 
        return signal * I + background;
      
      } else {
 
        return 0.0;
      }
    }

operator()() [1/2]

template<int ID_t, bool normalised = false>

double JMATH::JGauss< ID_t, normalised >::operator() ( const double x ) const

inline

Function value.

Parameters

x	abscissa value

Returns

function value

Definition at line 317 of file JGauss.hh.

    {
      return getValue(x);
    }

getGradient() [1/2]

template<int ID_t, bool normalised = false>

const JGauss_t & JMATH::JGauss< ID_t, normalised >::getGradient ( const double x ) const

inline

Get gradient.

Note that an error will be thrown if sigma <= 0.0.

Parameters

x	abscissa value

Returns

gradient

Definition at line 331 of file JGauss.hh.

    {
      if (sigma <= 0.0) { THROW(JValueOutOfRange, "JGauss::getGradient: Invalid sigma " << sigma); }
 
      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 * (u)                   * w;             // d(f)/d(mean)
      gradient.sigma      =  fs * (u + 1.0) * (u - 1.0) * w;             // d(f)/d(sigma)
      gradient.signal     =  f0;                                         // d(f)/d(signal)
      gradient.background =  1.0;                                        // d(f)/d(background)
 
      return gradient;
    }

get() [1/2]

template<int ID_t, bool normalised = false>

double JMATH::JGauss< ID_t, normalised >::get ( const double u ) const

inlineprivate

Get ordinate value.

Note that an error will be thrown if sigma <= 0.0.

Parameters

u	abscissa value

Returns

ordinate value

Definition at line 357 of file JGauss.hh.

    {
      if (sigma <= 0.0) { THROW(JValueOutOfRange, "JGauss::get: Invalid sigma " << sigma); }
 
      return exp(-0.5*u*u) / (sqrt(2.0*PI) * sigma);
    }

getValue() [2/2]

template<int ID_t, bool normalised = false>

double JMATH::JGauss< ID_t, normalised >::getValue ( const double x ) const

inline

Function value.

Parameters

x	abscissa value

Returns

function value

Definition at line 2032 of file JMathlib.hh.

    {
      const double u  = (x - center) / sigma;
 
      return get(u);
    }

getDerivative() [2/2]

template<int ID_t, bool normalised = false>

double JMATH::JGauss< ID_t, normalised >::getDerivative ( const double x ) const

inline

Derivative value.

Parameters

x	abscissa value

Returns

derivative value

Definition at line 2046 of file JMathlib.hh.

    {
      const double w  = 1.0 / sigma;
      const double u  = (x - center) / sigma;
 
      return get(u) * -u * w;
    }

getGradient() [2/2]

template<int ID_t, bool normalised = false>

JGauss JMATH::JGauss< ID_t, normalised >::getGradient ( const double x ) const

inline

Get gradient.

Parameters

x	abscissa value

Returns

gradient

Definition at line 2061 of file JMathlib.hh.

    {
      JGauss gradient;
 
      const double w  = 1.0 / sigma;
      const double u  = (x - center) * w;
      const double f0 =  get(u);
 
      gradient.center =  f0 * u * w;                          // d(f)/d(center)
      gradient.sigma  =  f0 * u * u * w;                      // d(f)/d(sigma)
 
      return gradient;
    }

get() [2/2]

template<int ID_t, bool normalised = false>

double JMATH::JGauss< ID_t, normalised >::get ( const double u ) const

inlineprivate

Get ordinate value.

Parameters

u	abscissa value

Returns

ordinate value

Definition at line 2087 of file JMathlib.hh.

    {
      return exp(-0.5*u*u);
    }

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 73 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() [1/2]

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

inlineinherited

Add gauss.

Parameters

gauss

gauss

Returns

this gauss

Definition at line 89 of file JGauss.hh.

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

sub() [1/2]

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

inlineinherited

Subtract gauss.

Parameters

gauss

gauss

Returns

this gauss

Definition at line 106 of file JGauss.hh.

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

mul() [1/3]

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

inlineinherited

Scale gauss.

Parameters

factor

multiplication factor

Returns

this gauss

Definition at line 123 of file JGauss.hh.

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

mul() [2/3]

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);
    }

operator()() [2/2]

double JMATH::JMathlib< JGauss< ID_t > >::operator() ( const Args &... args ) const

inlineinherited

Function value.

Parameters

args	abscissa value(s)

Returns

function value

Definition at line 331 of file JMathlib.hh.

    {
      return static_cast<const JF1_t&>(*this).getValue(args...);
    }

size()

static size_t JMATH::JMathlib< JGauss< ID_t > >::size ( )

inlinestaticinherited

Get size of parameter.

Returns

size

Definition at line 538 of file JMathlib.hh.

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

operator[]() [1/2]

double JMATH::JMathlib< JGauss< ID_t > >::operator[] ( const size_t i ) const

inlineinherited

Get value of parameter at given index.

Parameters

i

index

Returns

value

Definition at line 550 of file JMathlib.hh.

    {
      return static_cast<const JF1_t&>(*this).*JF1_t::parameters[i];
    }

operator[]() [2/2]

double & JMATH::JMathlib< JGauss< ID_t > >::operator[] ( const size_t i )

inlineinherited

Get value of parameter at given index.

Parameters

i

index

Returns

value

Definition at line 562 of file JMathlib.hh.

    {
      return static_cast<JF1_t&>(*this).*JF1_t::parameters[i];
    }

negate()

JGauss< ID_t > & JMATH::JCalculus< JGauss< ID_t > >::negate ( )

inlineinherited

Negate function.

Returns

this function

Definition at line 170 of file JMathlib.hh.

    {
      for (const auto& i : JF1_t::parameters) {
        static_cast<JF1_t&>(*this).*i = -(static_cast<JF1_t&>(*this).*i);
      }
 
      return static_cast<JF1_t&>(*this);
    }

add() [2/2]

JGauss< ID_t > & JMATH::JCalculus< JGauss< ID_t > >::add ( const JGauss< ID_t > & f1 )

inlineinherited

Add function.

Parameters

f1

function

Returns

this function

Definition at line 186 of file JMathlib.hh.

    {
      for (const auto& i : JF1_t::parameters) {
        static_cast<JF1_t&>(*this).*i += f1.*i;
      }
 
      return static_cast<JF1_t&>(*this);
    }

sub() [2/2]

JGauss< ID_t > & JMATH::JCalculus< JGauss< ID_t > >::sub ( const JGauss< ID_t > & f1 )

inlineinherited

Subtract function.

Parameters

f1

function

Returns

this function

Definition at line 202 of file JMathlib.hh.

    {
      for (const auto& i : JF1_t::parameters) {
        static_cast<JF1_t&>(*this).*i -= f1.*i;
      }
 
      return static_cast<JF1_t&>(*this);
    }

mul() [3/3]

JGauss< ID_t > & JMATH::JCalculus< JGauss< ID_t > >::mul ( const double factor )

inlineinherited

Scale function.

Parameters

factor

factor

Returns

this function

Definition at line 218 of file JMathlib.hh.

    {
      for (const auto& i : JF1_t::parameters) {
        static_cast<JF1_t&>(*this).*i *= factor;
      }
 
      return static_cast<JF1_t&>(*this);
    }

div()

JGauss< ID_t > & JMATH::JCalculus< JGauss< ID_t > >::div ( const double factor )

inlineinherited

Scale function.

Parameters

factor

factor

Returns

this function

Definition at line 234 of file JMathlib.hh.

    {
      for (const auto& i : JF1_t::parameters) {
        static_cast<JF1_t&>(*this).*i /= factor;
      }
 
      return static_cast<JF1_t&>(*this);
    }

Member Data Documentation

gradient

template<int ID_t, bool normalised = false>

JGauss_t JMATH::JGauss< ID_t, normalised >::gradient

mutableprivate

Definition at line 364 of file JGauss.hh.

ID

template<int ID_t, bool normalised = false>

const int JMATH::JGauss< ID_t, normalised >::ID = ID_t

static

Definition at line 2001 of file JMathlib.hh.

center

template<int ID_t, bool normalised = false>

double JMATH::JGauss< ID_t, normalised >::center

center

Definition at line 2075 of file JMathlib.hh.

sigma

template<int ID_t, bool normalised = false>

double JMATH::JGauss< ID_t, normalised >::sigma

sigma

Definition at line 2076 of file JMathlib.hh.

parameters

template<int ID_t, bool normalised = false>

parameter_list<JGauss, 2> JMATH::JGauss< ID_t, normalised >::parameters { &JGauss::center, &JGauss::sigma }

staticconstexpr

Definition at line 2078 of file JMathlib.hh.

{ &JGauss::center, &JGauss::sigma };

mean

double JMATH::JGauss_t::mean

inherited

Definition at line 164 of file JGauss.hh.

signal

double JMATH::JGauss_t::signal

inherited

Definition at line 166 of file JGauss.hh.

background

double JMATH::JGauss_t::background

inherited

Definition at line 167 of file JGauss.hh.

---

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

• JGauss.hh
• JMathlib.hh