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

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

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

Friends
bool	operator== (const Gaussian &lhs, const Gaussian &rhs) noexcept

Detailed Description

template<size_t VolumeDim, typename Fr>
class MathFunctions::Gaussian< VolumeDim, Fr >

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 coordinates of type tnsr::I<T, VolumeDim, Fr>, where T is e.g. double or DataVector, Fr is a frame (e.g. Frame::Inertial), and VolumeDim is the dimension of the spatial volume, i.e. 2 or 3. (The case of VolumeDim == 1 is handled specially by Gaussian<1, T, Frame::Inertial>.)

Member Function Documentation

first_deriv() [1/2]

template<size_t VolumeDim, typename Fr >

tnsr::i< DataVector, VolumeDim, Fr > MathFunctions::Gaussian< VolumeDim, Fr >::first_deriv ( const tnsr::I< DataVector, VolumeDim, Fr > &  x ) const

overridevirtualnoexcept

Returns the first partial derivatives of the function at 'x'.

Implements MathFunction< VolumeDim, Fr >.

first_deriv() [2/2]

template<size_t VolumeDim, typename Fr >

tnsr::i< double, VolumeDim, Fr > MathFunctions::Gaussian< VolumeDim, Fr >::first_deriv ( const tnsr::I< double, VolumeDim, Fr > &  x ) const

overridevirtualnoexcept

Returns the first partial derivatives of the function at 'x'.

Implements MathFunction< VolumeDim, Fr >.

operator()() [1/2]

template<size_t VolumeDim, typename Fr >

Scalar< DataVector > MathFunctions::Gaussian< VolumeDim, Fr >::operator() ( const tnsr::I< DataVector, VolumeDim, Fr > &  x ) const

overridevirtualnoexcept

Returns the value of the function at the coordinate 'x'.

Implements MathFunction< VolumeDim, Fr >.

operator()() [2/2]

template<size_t VolumeDim, typename Fr >

Scalar< double > MathFunctions::Gaussian< VolumeDim, Fr >::operator() ( const tnsr::I< double, VolumeDim, Fr > &  x ) const

overridevirtualnoexcept

Returns the value of the function at the coordinate 'x'.

Implements MathFunction< VolumeDim, Fr >.

second_deriv() [1/2]

template<size_t VolumeDim, typename Fr >

tnsr::ii< DataVector, VolumeDim, Fr > MathFunctions::Gaussian< VolumeDim, Fr >::second_deriv ( const tnsr::I< DataVector, VolumeDim, Fr > &  x ) const

overridevirtualnoexcept

Returns the second partial derivatives of the function at 'x'.

Implements MathFunction< VolumeDim, Fr >.

second_deriv() [2/2]

template<size_t VolumeDim, typename Fr >

tnsr::ii< double, VolumeDim, Fr > MathFunctions::Gaussian< VolumeDim, Fr >::second_deriv ( const tnsr::I< double, VolumeDim, Fr > &  x ) const

overridevirtualnoexcept

Returns the second partial derivatives of the function at 'x'.

Implements MathFunction< VolumeDim, Fr >.

third_deriv() [1/2]

template<size_t VolumeDim, typename Fr >

tnsr::iii< DataVector, VolumeDim, Fr > MathFunctions::Gaussian< VolumeDim, Fr >::third_deriv ( const tnsr::I< DataVector, VolumeDim, Fr > &  x ) const

overridevirtualnoexcept

Returns the third partial derivatives of the function at 'x'.

Implements MathFunction< VolumeDim, Fr >.

third_deriv() [2/2]

template<size_t VolumeDim, typename Fr >

tnsr::iii< double, VolumeDim, Fr > MathFunctions::Gaussian< VolumeDim, Fr >::third_deriv ( const tnsr::I< double, VolumeDim, Fr > &  x ) const

overridevirtualnoexcept

Returns the third partial derivatives of the function at 'x'.

Implements MathFunction< VolumeDim, Fr >.

Member Data Documentation

help

template<size_t VolumeDim, typename Fr >

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

staticconstexpr

Initial value:

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