Classes
class	CachedChristoffelSymbols

class	CachedMetricTensor

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

class	ChristoffelSymbols

class	ChristoffelSymbolsDual

struct	DualNumber

class	GeodesicDeviationCalculator

struct	GeodesicSignal

class	GeodesicSolver

class	GeodesicSolverN
	RK4 integrator for geodesics on an NAssetManifold. More...

struct	GeodesicState
	Position and 4-velocity state on the manifold. More...

class	MetricTensor

class	NAssetManifold
	(N+1)-dimensional Lorentzian manifold for N financial assets. More...

Typedefs
using	DualSpacetimePoint = Eigen::Matrix< DualNumber, SPACETIME_DIM, 1 >

using	DualMetricMatrix = Eigen::Matrix< DualNumber, SPACETIME_DIM, SPACETIME_DIM >
	A 4×4 matrix of dual numbers — the metric evaluated at a dual-number point.

using	DualMetricFunction = std::function< DualMetricMatrix(const DualSpacetimePoint &)>

using	MetricFunction = std::function< MetricMatrix(const SpacetimePoint &)>

using	ChristoffelArray = std::array< MetricMatrix, SPACETIME_DIM >

Functions
std::vector< std::vector< GeodesicState > >	integrate_batch (const GeodesicSolver &solver, const std::vector< std::pair< SpacetimePoint, FourVelocity > > &initial_conditions, int steps)

Variables
static constexpr double	TIKHONOV_LAMBDA = 1e-10

static constexpr double	TIKHONOV_CONDITION = 1e-10
	Relative pivot threshold below which inverse() regularizes the metric.

Typedef Documentation

◆ ChristoffelArray

using srfm::tensor::ChristoffelArray = typedef std::array<MetricMatrix, SPACETIME_DIM>

Christoffel symbols as an array of 4×4 matrices. Access pattern: gamma[lambda](mu, nu) = Γ^λ_μν.

Definition at line 148 of file tensor.hpp.

◆ DualMetricFunction

using srfm::tensor::DualMetricFunction = typedef std::function<DualMetricMatrix(const DualSpacetimePoint&)>

A callable mapping a dual-number spacetime point to a dual-number metric. Implement this alongside MetricFunction to enable exact autodiff derivatives.

Definition at line 138 of file tensor.hpp.

◆ DualMetricMatrix

using srfm::tensor::DualMetricMatrix = typedef Eigen::Matrix<DualNumber, SPACETIME_DIM, SPACETIME_DIM>

A 4×4 matrix of dual numbers — the metric evaluated at a dual-number point.

Definition at line 134 of file tensor.hpp.

◆ DualSpacetimePoint

using srfm::tensor::DualSpacetimePoint = typedef Eigen::Matrix<DualNumber, SPACETIME_DIM, 1>

A 4-vector of dual numbers — one per spacetime coordinate. Used to seed the autodiff direction when computing metric derivatives.

Definition at line 131 of file tensor.hpp.

◆ MetricFunction

using srfm::tensor::MetricFunction = typedef std::function<MetricMatrix(const SpacetimePoint&)>

A callable that maps a spacetime point to the metric matrix at that point. Used for position-dependent (curved) metrics.

Definition at line 144 of file tensor.hpp.

Function Documentation

◆ integrate_batch()

std::vector< std::vector< GeodesicState > > srfm::tensor::integrate_batch	(	const GeodesicSolver &	solver,
		const std::vector< std::pair< SpacetimePoint, FourVelocity > > &	initial_conditions,
		int	steps
	)

inline

Integrate a batch of geodesics in parallel using std::execution::par_unseq.

Each geodesic is independent (different initial conditions), so the per-geodesic integrations can be run concurrently without any shared mutable state. The solver object itself is read-only; each lambda call operates on its own trajectory vector.

This provides a straightforward way to amortise the overhead of multiple-asset geodesic integration — one call per portfolio rebalance instead of a sequential for-loop.

Requirements

The C++ standard library parallel STL backend must be available.

On Linux with libstdc++: link with -ltbb (Intel TBB).
On MSVC: std::execution::par_unseq works out of the box.
On libc++ (macOS/LLVM): may require -fexperimental-library and TBB.

Arguments

solver — Configured GeodesicSolver (read-only).
initial_conditions — Vector of (initial_position, initial_velocity) pairs.
steps — Number of RK4 steps per trajectory.

Returns

Vector of trajectories (one per initial condition), each containing steps + 1 GeodesicState entries in proper-time order.

Thread safety

The GeodesicSolver and MetricTensor are accessed as const; parallel calls are safe provided the MetricFunction stored in the solver's MetricTensor is itself thread-safe for concurrent const calls.

Definition at line 629 of file tensor.hpp.

Variable Documentation

◆ TIKHONOV_CONDITION

constexpr double srfm::tensor::TIKHONOV_CONDITION = 1e-10

staticconstexpr

Relative pivot threshold below which inverse() regularizes the metric.

Definition at line 19 of file metric_tensor.cpp.

◆ TIKHONOV_LAMBDA

constexpr double srfm::tensor::TIKHONOV_LAMBDA = 1e-10