tensorium_RG::ChristoffelSym< T > Class Template Reference

Stores and computes Christoffel symbols \( \Gamma^\lambda_{\mu\nu} \). More...

#include <ChristoffelSymbol.hpp>

Collaboration diagram for tensorium_RG::ChristoffelSym< T >:

Public Member Functions
	ChristoffelSym (size_t dim)
	Construct a Christoffel symbol tensor.
T &	operator() (size_t i, size_t j, size_t k, size_t l)
	Mutable access to component \( \Gamma^\lambda_{\mu\nu} \).
const T &	operator() (size_t i, size_t j, size_t k, size_t l) const
	Const access to component \( \Gamma^\lambda_{\mu\nu} \).
void	fill (T value)
	Fill all components with a constant value.
void	print () const
	Print all non-zero Christoffel components to stdout.
	__attribute__ ((always_inline, hot, flatten)) static inline ChristoffelSym< T > compute_christoffel(const tensorium
	Compute Christoffel symbols numerically from a metric.

Public Attributes
aligned_vector< T >	data
size_t	dim

Static Public Attributes
static constexpr size_t	rank = 4

Detailed Description

template<typename T>
class tensorium_RG::ChristoffelSym< T >

Stores and computes Christoffel symbols \( \Gamma^\lambda_{\mu\nu} \).

This class represents a tensor of Christoffel symbols for a 4D metric and supports:

• Storage in a flattened aligned vector
• Numerical computation from the metric via centered finite differences

The Christoffel symbols are given by:

\[\Gamma^\lambda_{\mu\nu} = \frac{1}{2} g^{\lambda\kappa} \left( \partial_\mu g_{\nu\kappa} + \partial_\nu g_{\mu\kappa} - \partial_\kappa g_{\mu\nu} \right) \]

Template Parameters

T	Scalar type (e.g., float or double)

Constructor & Destructor Documentation

ChristoffelSym()

template<typename T>

tensorium_RG::ChristoffelSym< T >::ChristoffelSym ( size_t dim )

inline

Construct a Christoffel symbol tensor.

Parameters

dim	Dimensionality of the space

References data, and dim.

Referenced by __attribute__().

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Member Function Documentation

__attribute__()

template<typename T>

tensorium_RG::ChristoffelSym< T >::__attribute__ ( (always_inline, hot, flatten) ) const

inline

Compute Christoffel symbols numerically from a metric.

Uses centered finite differences on the metric tensor and contracts with \( g^{\mu\nu} \).

Parameters

X	Coordinates \( X^\mu \)
h	Step size
g	Metric tensor \( g_{\mu\nu} \)
g_inv	Inverse metric \( g^{\mu\nu} \)
metric_generator	A callable that generates \( g_{\mu\nu}(X) \)

Returns

Christoffel symbol tensor \( \Gamma^\lambda_{\mu\nu} \)

References ChristoffelSym(), dim, fill(), and X().

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fill()

template<typename T>

void tensorium_RG::ChristoffelSym< T >::fill ( T value )

inline

Fill all components with a constant value.

Parameters

value

Value to fill

References data.

Referenced by __attribute__().

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operator()() [1/2]

template<typename T>

T & tensorium_RG::ChristoffelSym< T >::operator() ( size_t i, size_t j, size_t k, size_t l )

inline

Mutable access to component \( \Gamma^\lambda_{\mu\nu} \).

References data, and dim.

operator()() [2/2]

template<typename T>

const T & tensorium_RG::ChristoffelSym< T >::operator() ( size_t i, size_t j, size_t k, size_t l ) const

inline

Const access to component \( \Gamma^\lambda_{\mu\nu} \).

References data, and dim.

print()

template<typename T>

void tensorium_RG::ChristoffelSym< T >::print ( ) const

inline

Print all non-zero Christoffel components to stdout.

References dim.

Member Data Documentation

data

template<typename T>

aligned_vector<T> tensorium_RG::ChristoffelSym< T >::data

Referenced by ChristoffelSym(), fill(), operator()(), and operator()().

dim

template<typename T>

size_t tensorium_RG::ChristoffelSym< T >::dim

Referenced by __attribute__(), ChristoffelSym(), operator()(), operator()(), and print().

rank

template<typename T>

size_t tensorium_RG::ChristoffelSym< T >::rank = 4

staticconstexpr

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

• includes/Tensorium/Physics/DiffGeometry/ChristoffelSymbol.hpp