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

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 \( g_{\mu\nu}(X) \)