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< 1, Fr >
using	frame = Fr

Public Member Functions
	WRAPPED_PUPable_decl_base_template (SINGLE_ARG(MathFunction< 1, Fr >), Gaussian)
	Gaussian (CkMigrateMessage *) noexcept
	Gaussian (double amplitude, double width, double center) noexcept
	Gaussian (double amplitude, double width, const std::array< double, 1 > &center) noexcept
	Gaussian (const Gaussian &)=delete
Gaussian &	operator= (const Gaussian &)=delete
	Gaussian (Gaussian &&) noexcept=default
Gaussian &	operator= (Gaussian &&) noexcept=default
double	operator() (const double &x) const noexcept override
	Returns the function value at the coordinate 'x'. More...
DataVector	operator() (const DataVector &x) const noexcept override
double	first_deriv (const double &x) const noexcept override
	Returns the first derivative at 'x'. More...
DataVector	first_deriv (const DataVector &x) const noexcept override
double	second_deriv (const double &x) const noexcept override
	Returns the second derivative at 'x'. More...
DataVector	second_deriv (const DataVector &x) const noexcept override
double	third_deriv (const double &x) const noexcept override
	Returns the third derivative at 'x'. More...
DataVector	third_deriv (const DataVector &x) const noexcept override
void	pup (PUP::er &p) override
Public Member Functions inherited from MathFunction< 1, Fr >
	WRAPPED_PUPable_abstract (MathFunction)
	MathFunction (const MathFunction &)=delete
MathFunction &	operator= (const MathFunction &)=delete
	MathFunction (MathFunction &&) noexcept=default
MathFunction &	operator= (MathFunction &&) noexcept=default
Scalar< double >	operator() (const tnsr::I< double, 1, Fr > &x) const noexcept
Scalar< DataVector >	operator() (const tnsr::I< DataVector, 1, Fr > &x) const noexcept
tnsr::i< double, 1, Fr >	first_deriv (const tnsr::I< double, 1, Fr > &x) const noexcept
tnsr::i< DataVector, 1, Fr >	first_deriv (const tnsr::I< DataVector, 1, Fr > &x) const noexcept
tnsr::ii< double, 1, Fr >	second_deriv (const tnsr::I< double, 1, Fr > &x) const noexcept
tnsr::ii< DataVector, 1, Fr >	second_deriv (const tnsr::I< DataVector, 1, Fr > &x) const noexcept
tnsr::iii< double, 1, Fr >	third_deriv (const tnsr::I< double, 1, Fr > &x) const noexcept
tnsr::iii< DataVector, 1, Fr >	third_deriv (const tnsr::I< DataVector, 1, Fr > &x) const noexcept

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

Friends
bool	operator== (const Gaussian< 1, Fr > &lhs, const Gaussian< 1, Fr > &rhs) noexcept

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

overridevirtualnoexcept

Implements MathFunction< 1, Fr >.

first_deriv() [2/2]

template<typename Fr >

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

overridevirtualnoexcept

Returns the first derivative at 'x'.

Implements MathFunction< 1, Fr >.

operator()() [1/2]

template<typename Fr >

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

overridevirtualnoexcept

Implements MathFunction< 1, Fr >.

operator()() [2/2]

template<typename Fr >

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

overridevirtualnoexcept

Returns the function value at the coordinate 'x'.

Implements MathFunction< 1, Fr >.

second_deriv() [1/2]

template<typename Fr >

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

overridevirtualnoexcept

Implements MathFunction< 1, Fr >.

second_deriv() [2/2]

template<typename Fr >

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

overridevirtualnoexcept

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

overridevirtualnoexcept

Implements MathFunction< 1, Fr >.

third_deriv() [2/2]

template<typename Fr >

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

overridevirtualnoexcept

Returns the third derivative at 'x'.

Implements MathFunction< 1, Fr >.

Member Data Documentation

help

template<typename Fr >

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

staticconstexpr

Initial value:

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