JMATH::JGauss3D< ID_t, normalise > Struct Template Reference

3D correlated Gauss function. More...

#include <JMathlib3D.hh>

Inheritance diagram for JMATH::JGauss3D< ID_t, normalise >:

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

Public Member Functions
	JGauss3D ()
	Default constructor.
	JGauss3D (const double mean, const double sigma)
	Constructor.
double	getValue (const double x, const double y, const double z) const
	Function value.
const JGauss3D &	getGradient (const double x, const double y, const double z) const
	Get gradient.
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.
double	getValue (const double x) const
	Function value.
double	getDerivative (const double x) const
	Derivative 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.
double	operator() (const Args &...args) const
	Function value.
const JGauss_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< ID_t > &	add (const JGauss< ID_t > &f1)
	Add function.
JGauss_t &	sub (const JGauss_t &gauss)
	Subtract gauss.
JGauss< ID_t > &	sub (const JGauss< ID_t > &f1)
	Subtract function.
JGauss_t &	mul (const double factor)
	Scale gauss.
JGauss_t &	mul (const JSecond_t &object)
	Multiply with object.
JGauss< ID_t > &	mul (const double factor)
	Scale function.
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 > &	div (const double factor)
	Scale function.

Static Public Member Functions
static size_t	size ()
	Get size of parameter.
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
static constexpr parameter_list< JGauss, 2 >	parameters

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 normalise = false>
struct JMATH::JGauss3D< ID_t, normalise >

3D correlated Gauss function.

Definition at line 267 of file JMathlib3D.hh.

Member Typedef Documentation

parameter_type

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

inherited

Type definition of fit parameter.

Definition at line 182 of file JGauss.hh.

Constructor & Destructor Documentation

JGauss3D() [1/2]

template<int ID_t, bool normalise = false>

JMATH::JGauss3D< ID_t, normalise >::JGauss3D ( )

inline

Default constructor.

Definition at line 277 of file JMathlib3D.hh.

    {}

JGauss3D() [2/2]

template<int ID_t, bool normalise = false>

JMATH::JGauss3D< ID_t, normalise >::JGauss3D ( const double mean, const double sigma )

inline

Constructor.

Parameters

mean	mean
sigma	sigma

Definition at line 287 of file JMathlib3D.hh.

                                 :
      JGauss<ID_t, normalise>(mean, sigma)
    {}

Member Function Documentation

getValue() [1/2]

template<int ID_t, bool normalise = false>

double JMATH::JGauss3D< ID_t, normalise >::getValue ( const double x, const double y, const double z ) const

inline

Function value.

Parameters

x	abscissa value
y	abscissa value
z	abscissa value

Returns

function value

Definition at line 301 of file JMathlib3D.hh.

    {
      typedef JGauss<ID_t, normalise>  JGauss_t;
 
      return (static_cast<const JGauss_t&>(*this).getValue(x) *
              static_cast<const JGauss_t&>(*this).getValue(y) *
              static_cast<const JGauss_t&>(*this).getValue(z));
    }

getGradient() [1/2]

template<int ID_t, bool normalise = false>

const JGauss3D & JMATH::JGauss3D< ID_t, normalise >::getGradient ( const double x, const double y, const double z ) const

inline

Get gradient.

Parameters

x	abscissa value
y	abscissa value
z	abscissa value

Returns

gradient

Definition at line 319 of file JMathlib3D.hh.

    {
      static JGauss3D gradient;
 
      typedef JGauss<ID_t, normalise>  JGauss_t;
 
      static_cast<JGauss_t&>(gradient)  = JGauss_t(static_cast<const JGauss_t&>(*this).getGradient(x)).mul(static_cast<const JGauss_t&>(*this).getValue(y) * static_cast<const JGauss_t&>(*this).getValue(z));
      static_cast<JGauss_t&>(gradient) += JGauss_t(static_cast<const JGauss_t&>(*this).getGradient(y)).mul(static_cast<const JGauss_t&>(*this).getValue(x) * static_cast<const JGauss_t&>(*this).getValue(z));
      static_cast<JGauss_t&>(gradient) += JGauss_t(static_cast<const JGauss_t&>(*this).getGradient(z)).mul(static_cast<const JGauss_t&>(*this).getValue(x) * static_cast<const JGauss_t&>(*this).getValue(y));
 
      return gradient;
    }

operator()() [1/3]

double JMATH::JMathlib< JGauss3D< ID_t, false > >::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() [1/2]

static size_t JMATH::JMathlib< JGauss3D< ID_t, false > >::size ( )

inlinestaticinherited

Get size of parameter.

Returns

size

Definition at line 538 of file JMathlib.hh.

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

operator[]() [1/4]

double JMATH::JMathlib< JGauss3D< ID_t, false > >::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[]() [2/4]

double & JMATH::JMathlib< JGauss3D< ID_t, false > >::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];
    }

getValue() [2/2]

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

inlineinherited

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]

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

inlineinherited

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;
    }

getDerivative() [2/2]

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

inlineinherited

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;
    }

getIntegral()

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

inlineinherited

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()() [2/3]

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

inlineinherited

Function value.

Parameters

x	abscissa value

Returns

function value

Definition at line 317 of file JGauss.hh.

    {
      return getValue(x);
    }

operator()() [3/3]

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...);
    }

getGradient() [2/2]

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

inlineinherited

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]

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

inlineprivateinherited

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);
    }

get() [2/2]

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

inlineprivateinherited

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;
    }

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() [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;
    }

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() [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);
    }

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);
    }

size() [2/2]

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[]() [3/4]

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[]() [4/4]

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);
    }

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

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

mutableprivateinherited

Definition at line 364 of file JGauss.hh.

ID

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

staticinherited

Definition at line 2001 of file JMathlib.hh.

center

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

inherited

center

Definition at line 2075 of file JMathlib.hh.

sigma

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

inherited

sigma

Definition at line 2076 of file JMathlib.hh.

parameters

parameter_list<JGauss, 2> JMATH::JGauss< ID_t, normalised >::parameters

staticconstexprinherited

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 file:

• JMathlib3D.hh