srfm::tensor::ChristoffelN Class Reference

Computes Christoffel symbols Γ^λ_μν for an NAssetManifold. More...

#include <christoffel_n.hpp>

Public Member Functions
	ChristoffelN (const NAssetManifold &manifold) noexcept
	Construct from a manifold reference.
std::optional< double >	symbol (int lambda, int mu, int nu, const Eigen::VectorXd &x) const noexcept
	Compute a single Christoffel symbol Γ^lambda_mu_nu at point x.
std::optional< std::vector< std::vector< std::vector< double > > > >	all_symbols (const Eigen::VectorXd &x) const noexcept
	Compute all Christoffel symbols at point x.
bool	verify_symmetry (const Eigen::VectorXd &x, double tol=1e-10) const noexcept
	Verify that Γ^λ_μν = Γ^λ_νμ for all indices at point x.
int	dim () const noexcept
	Return the dimension of the manifold.

Static Public Attributes
static constexpr double	FD_STEP = 1e-5
	Central finite-difference step size used for metric derivatives.

Detailed Description

Computes Christoffel symbols Γ^λ_μν for an NAssetManifold.

Metric derivatives are approximated by central finite differences with step size FD_STEP. For a constant metric all derivatives vanish and every Christoffel symbol is exactly zero.

Definition at line 44 of file christoffel_n.hpp.

Constructor & Destructor Documentation

ChristoffelN()

srfm::tensor::ChristoffelN::ChristoffelN ( const NAssetManifold &  manifold )

explicitnoexcept

Construct from a manifold reference.

The manifold must remain valid for the lifetime of this object.

Parameters

manifold

The NAssetManifold providing the metric.

Definition at line 28 of file christoffel_n.cpp.

Member Function Documentation

all_symbols()

std::optional< std::vector< std::vector< std::vector< double > > > > srfm::tensor::ChristoffelN::all_symbols ( const Eigen::VectorXd &  x ) const

noexcept

Compute all Christoffel symbols at point x.

Returns a dim() × dim() × dim() tensor stored as nested std::vector: result[lambda][mu][nu] = Γ^lambda_mu_nu

Parameters

x	Coordinate point of length dim().

Returns

Full tensor, or std::nullopt on failure.

Definition at line 101 of file christoffel_n.cpp.

dim()

int srfm::tensor::ChristoffelN::dim ( ) const

inlinenoexcept

Return the dimension of the manifold.

Returns

manifold_.dim().

Definition at line 151 of file christoffel_n.hpp.

symbol()

std::optional< double > srfm::tensor::ChristoffelN::symbol ( int  lambda, int  mu, int  nu, const Eigen::VectorXd &  x  ) const

noexcept

Compute a single Christoffel symbol Γ^lambda_mu_nu at point x.

Uses the formula: Γ^λ_μν = ½ g^λσ (∂_μ g_νσ + ∂_ν g_μσ - ∂_σ g_μν)

Metric derivatives are approximated by central FD with step FD_STEP.

Parameters

lambda	Contravariant index, in [0, dim).
mu	First covariant index, in [0, dim).
nu	Second covariant index, in [0, dim).
x	Coordinate point, must have length dim().

Returns

Γ^lambda_mu_nu, or std::nullopt on dimension mismatch or metric inversion failure.

Definition at line 67 of file christoffel_n.cpp.

verify_symmetry()

bool srfm::tensor::ChristoffelN::verify_symmetry ( const Eigen::VectorXd &  x, double  tol = 1e-10  ) const

noexcept

Verify that Γ^λ_μν = Γ^λ_νμ for all indices at point x.

Checks the symmetry of the lower two indices, which holds for torsion-free connections.

Parameters

x	Coordinate point of length dim().
tol	Tolerance for the symmetry check (default 1e-10).

Returns

true if symmetric within tolerance, false otherwise. Returns false (not nullopt) on dimension mismatch.

Definition at line 159 of file christoffel_n.cpp.

Member Data Documentation

FD_STEP

constexpr double srfm::tensor::ChristoffelN::FD_STEP = 1e-5

staticconstexpr

Central finite-difference step size used for metric derivatives.

Definition at line 47 of file christoffel_n.hpp.

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

• include/srfm/tensor/christoffel_n.hpp
• src/tensor/christoffel_n.cpp