MathFunctions::Gaussian< 1, Fr > Class Template Reference

1D Gaussian \(f = A \exp\left(-\frac{(x-x_0)^2}{w^2}\right)\) More...

#include <Gaussian.hpp>

Classes
struct	Amplitude
struct	Center
struct	Width

Public Types
using	options = tmpl::list<Amplitude, Width, Center>
Public Types inherited from MathFunction< VolumeDim, Fr >
using	frame = Fr
Public Types inherited from MathFunction< 1, Fr >
using	frame = Fr

Public Member Functions
	WRAPPED_PUPable_decl_base_template (SINGLE_ARG(MathFunction< 1, Fr >), Gaussian)
	Gaussian (CkMigrateMessage *)
	Gaussian (double amplitude, double width, double center)
	Gaussian (double amplitude, double width, const std::array< double, 1 > &center)
std::unique_ptr< MathFunction< 1, Fr > >	get_clone () const override
double	operator() (const double &x) const override
	Returns the function value at the coordinate 'x'.
DataVector	operator() (const DataVector &x) const override
double	first_deriv (const double &x) const override
	Returns the first derivative at 'x'.
DataVector	first_deriv (const DataVector &x) const override
double	second_deriv (const double &x) const override
	Returns the second derivative at 'x'.
DataVector	second_deriv (const DataVector &x) const override
double	third_deriv (const double &x) const override
	Returns the third derivative at 'x'.
DataVector	third_deriv (const DataVector &x) const override
bool	operator== (const MathFunction< 1, Fr > &other) const override
bool	operator!= (const MathFunction< 1, Fr > &other) const override
bool	operator== (const Gaussian< 1, Fr > &other) const
bool	operator!= (const Gaussian< 1, Fr > &other) const
void	pup (PUP::er &p) override
Public Member Functions inherited from MathFunction< VolumeDim, Fr >
	WRAPPED_PUPable_abstract (MathFunction)
virtual bool	operator== (const MathFunction< VolumeDim, Fr > &other) const =0
virtual bool	operator!= (const MathFunction< VolumeDim, Fr > &other) const =0
virtual Scalar< double >	operator() (const tnsr::I< double, VolumeDim, Fr > &x) const =0
	Returns the value of the function at the coordinate 'x'.
virtual Scalar< DataVector >	operator() (const tnsr::I< DataVector, VolumeDim, Fr > &x) const =0
	Returns the value of the function at the coordinate 'x'.
virtual tnsr::i< double, VolumeDim, Fr >	first_deriv (const tnsr::I< double, VolumeDim, Fr > &x) const =0
	Returns the first partial derivatives of the function at 'x'.
virtual tnsr::i< DataVector, VolumeDim, Fr >	first_deriv (const tnsr::I< DataVector, VolumeDim, Fr > &x) const =0
	Returns the first partial derivatives of the function at 'x'.
virtual tnsr::ii< double, VolumeDim, Fr >	second_deriv (const tnsr::I< double, VolumeDim, Fr > &x) const =0
	Returns the second partial derivatives of the function at 'x'.
virtual tnsr::ii< DataVector, VolumeDim, Fr >	second_deriv (const tnsr::I< DataVector, VolumeDim, Fr > &x) const =0
	Returns the second partial derivatives of the function at 'x'.
virtual tnsr::iii< double, VolumeDim, Fr >	third_deriv (const tnsr::I< double, VolumeDim, Fr > &x) const =0
	Returns the third partial derivatives of the function at 'x'.
virtual tnsr::iii< DataVector, VolumeDim, Fr >	third_deriv (const tnsr::I< DataVector, VolumeDim, Fr > &x) const =0
	Returns the third partial derivatives of the function at 'x'.
Public Member Functions inherited from MathFunction< 1, Fr >
	WRAPPED_PUPable_abstract (MathFunction)
Scalar< double >	operator() (const tnsr::I< double, 1, Fr > &x) const
Scalar< DataVector >	operator() (const tnsr::I< DataVector, 1, Fr > &x) const
tnsr::i< double, 1, Fr >	first_deriv (const tnsr::I< double, 1, Fr > &x) const
tnsr::i< DataVector, 1, Fr >	first_deriv (const tnsr::I< DataVector, 1, Fr > &x) const
tnsr::ii< double, 1, Fr >	second_deriv (const tnsr::I< double, 1, Fr > &x) const
tnsr::ii< DataVector, 1, Fr >	second_deriv (const tnsr::I< DataVector, 1, Fr > &x) const
tnsr::iii< double, 1, Fr >	third_deriv (const tnsr::I< double, 1, Fr > &x) const
tnsr::iii< DataVector, 1, Fr >	third_deriv (const tnsr::I< DataVector, 1, Fr > &x) const

Static Public Attributes
static constexpr Options::String	help
Static Public Attributes inherited from MathFunction< VolumeDim, Fr >
static constexpr size_t	volume_dim = VolumeDim
Static Public Attributes inherited from MathFunction< 1, Fr >
static constexpr size_t	volume_dim = 1

Detailed Description

template<typename Fr>
class MathFunctions::Gaussian< 1, Fr >

1D Gaussian \(f = A \exp\left(-\frac{(x-x_0)^2}{w^2}\right)\)

Details

Input file options are: Amplitude, Width, and Center. The function takes input of type double or DataVector and returns the same type as the input type.

Member Function Documentation

first_deriv() [1/2]

template<typename Fr>

DataVector MathFunctions::Gaussian< 1, Fr >::first_deriv ( const DataVector & x ) const

overridevirtual

Implements MathFunction< 1, Fr >.

first_deriv() [2/2]

template<typename Fr>

double MathFunctions::Gaussian< 1, Fr >::first_deriv ( const double & x ) const

overridevirtual

Returns the first derivative at 'x'.

Implements MathFunction< 1, Fr >.

get_clone()

template<typename Fr>

std::unique_ptr< MathFunction< 1, Fr > > MathFunctions::Gaussian< 1, Fr >::get_clone ( ) const

overridevirtual

Implements MathFunction< VolumeDim, Fr >.

operator!=()

template<typename Fr>

bool MathFunctions::Gaussian< 1, Fr >::operator!= ( const MathFunction< 1, Fr > & other ) const

overridevirtual

Implements MathFunction< 1, Fr >.

operator()() [1/2]

template<typename Fr>

DataVector MathFunctions::Gaussian< 1, Fr >::operator() ( const DataVector & x ) const

overridevirtual

Implements MathFunction< 1, Fr >.

operator()() [2/2]

template<typename Fr>

double MathFunctions::Gaussian< 1, Fr >::operator() ( const double & x ) const

overridevirtual

Returns the function value at the coordinate 'x'.

Implements MathFunction< 1, Fr >.

operator==()

template<typename Fr>

bool MathFunctions::Gaussian< 1, Fr >::operator== ( const MathFunction< 1, Fr > & other ) const

overridevirtual

Implements MathFunction< 1, Fr >.

second_deriv() [1/2]

template<typename Fr>

DataVector MathFunctions::Gaussian< 1, Fr >::second_deriv ( const DataVector & x ) const

overridevirtual

Implements MathFunction< 1, Fr >.

second_deriv() [2/2]

template<typename Fr>

double MathFunctions::Gaussian< 1, Fr >::second_deriv ( const double & x ) const

overridevirtual

Returns the second derivative at 'x'.

Implements MathFunction< 1, Fr >.

third_deriv() [1/2]

template<typename Fr>

DataVector MathFunctions::Gaussian< 1, Fr >::third_deriv ( const DataVector & x ) const

overridevirtual

Implements MathFunction< 1, Fr >.

third_deriv() [2/2]

template<typename Fr>

double MathFunctions::Gaussian< 1, Fr >::third_deriv ( const double & x ) const

overridevirtual

Returns the third derivative at 'x'.

Implements MathFunction< 1, Fr >.

Member Data Documentation

help

template<typename Fr>

Options::String MathFunctions::Gaussian< 1, Fr >::help

staticconstexpr

Initial value:

= {
      "Computes a Gaussian about an arbitrary coordinate center with given "
      "width and amplitude"}

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

• src/PointwiseFunctions/MathFunctions/Gaussian.hpp