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

#include <n_asset_manifold.hpp>

Public Member Functions
	NAssetManifold (int n_assets, Eigen::MatrixXd covariance, double c_market=1.0) noexcept
	Construct an NAssetManifold directly.

int	dim () const noexcept
	Returns the full manifold dimension = n_assets + 1.

int	n_assets () const noexcept
	Returns the number of asset (spatial) dimensions.

std::optional< Eigen::MatrixXd >	metric_at (const Eigen::VectorXd &x) const noexcept
	Evaluate the metric tensor at point x.

std::optional< Eigen::MatrixXd >	inverse_metric_at (const Eigen::VectorXd &x) const noexcept
	Evaluate the inverse metric g^μν at point x.

std::optional< double >	line_element_sq (const Eigen::VectorXd &x, const Eigen::VectorXd &dx) const noexcept
	Compute the squared line element ds² = g_μν dx^μ dx^ν.

bool	is_flat () const noexcept
	Returns true if the metric has no coordinate dependence.

std::optional< Eigen::MatrixXd >	covariance () const noexcept
	Returns the covariance matrix used to build the metric.

bool	reduces_to_4d (const NAssetManifold &other) const noexcept
	Check structural compatibility with a 4D (N=3) manifold.

double	c_market () const noexcept
	Return the market speed-of-light parameter.

const Eigen::MatrixXd &	metric () const noexcept
	Direct metric accessor (no coordinate argument).

const Eigen::MatrixXd &	inverse_metric () const noexcept
	Direct inverse metric accessor.

Static Public Member Functions
static std::optional< NAssetManifold >	make (int n, Eigen::MatrixXd cov, double c_market=1.0) noexcept
	Factory: validate inputs then construct.

Detailed Description

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

The manifold dimension is n_assets + 1 (one time axis plus N price axes). The metric is assembled from a user-supplied N×N positive-definite covariance matrix and a market speed-of-light parameter c_market.

Definition at line 48 of file n_asset_manifold.hpp.

Constructor & Destructor Documentation

◆ NAssetManifold()

srfm::tensor::NAssetManifold::NAssetManifold	(	int	n_assets,
		Eigen::MatrixXd	covariance,
		double	c_market = `1.0`
	)

noexcept

Construct an NAssetManifold directly.

Prefer the factory make() which validates inputs and returns std::nullopt on failure instead of constructing an invalid object.

Parameters

n_assets	Number of asset price dimensions (spatial dimensions).
covariance	N×N positive-definite covariance matrix Σ.
c_market	Market speed-of-light parameter (must be > 0).

Definition at line 17 of file n_asset_manifold.cpp.

Member Function Documentation

◆ c_market()

double srfm::tensor::NAssetManifold::c_market ( ) const

inlinenoexcept

Return the market speed-of-light parameter.

Returns: c_market_.

Definition at line 239 of file n_asset_manifold.hpp.

◆ covariance()

std::optional< Eigen::MatrixXd > srfm::tensor::NAssetManifold::covariance ( ) const

noexcept

Returns the covariance matrix used to build the metric.

Returns: The N×N covariance matrix, or std::nullopt on internal error.

Definition at line 141 of file n_asset_manifold.cpp.

◆ dim()

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

inlinenoexcept

Returns the full manifold dimension = n_assets + 1.

Returns: n_assets_ + 1.

Definition at line 226 of file n_asset_manifold.hpp.

◆ inverse_metric()

const Eigen::MatrixXd & srfm::tensor::NAssetManifold::inverse_metric ( ) const

inlinenoexcept

Direct inverse metric accessor.

Returns the pre-built inverse metric matrix.

Returns: (N+1)×(N+1) inverse metric tensor.

Definition at line 247 of file n_asset_manifold.hpp.

◆ inverse_metric_at()

std::optional< Eigen::MatrixXd > srfm::tensor::NAssetManifold::inverse_metric_at ( const Eigen::VectorXd & x ) const

noexcept

Evaluate the inverse metric g^μν at point x.

Computed via LU decomposition of the metric matrix.

Parameters

x	Coordinate vector of length dim().

Returns: The inverse metric, or std::nullopt on failure.

Definition at line 117 of file n_asset_manifold.cpp.

◆ is_flat()

bool srfm::tensor::NAssetManifold::is_flat ( ) const

inlinenoexcept

Returns true if the metric has no coordinate dependence.

For NAssetManifold the metric is always constant, so this always returns true.

Returns: true.

Definition at line 234 of file n_asset_manifold.hpp.

◆ line_element_sq()

std::optional< double > srfm::tensor::NAssetManifold::line_element_sq	(	const Eigen::VectorXd &	x,
		const Eigen::VectorXd &	dx
	)		const

noexcept

Compute the squared line element ds² = g_μν dx^μ dx^ν.

Parameters

x	Base point (unused for flat manifold, validated for dimension).
dx	Displacement vector of length dim().

Returns: ds², or std::nullopt if dimensions are inconsistent.

Definition at line 130 of file n_asset_manifold.cpp.

◆ make()

std::optional< NAssetManifold > srfm::tensor::NAssetManifold::make	(	int	n,
		Eigen::MatrixXd	cov,
		double	c_market = `1.0`
	)

staticnoexcept

Factory: validate inputs then construct.

Validates:

n_assets >= 1
covariance is N×N
covariance is symmetric
covariance is positive-definite (all eigenvalues > 0)
c_market > 0

Parameters

n	Number of assets.
cov	N×N covariance matrix.
c_market	Market speed of light (default 1.0).

Returns: Constructed manifold or std::nullopt if inputs are invalid.

Definition at line 32 of file n_asset_manifold.cpp.

◆ metric()

const Eigen::MatrixXd & srfm::tensor::NAssetManifold::metric ( ) const

inlinenoexcept

Direct metric accessor (no coordinate argument).

Returns the pre-built constant metric matrix.

Returns: (N+1)×(N+1) metric tensor.

Definition at line 243 of file n_asset_manifold.hpp.

◆ metric_at()

std::optional< Eigen::MatrixXd > srfm::tensor::NAssetManifold::metric_at ( const Eigen::VectorXd & x ) const

noexcept

Evaluate the metric tensor at point x.

Because this is a constant (flat) manifold the result does not depend on x. The parameter is accepted for API uniformity with curved manifolds.

Returns a (N+1)×(N+1) matrix: row/col 0 → time component (g_00 = -c_market²) rows/cols 1..N → spatial block (g_ij = Σ_ij)

Parameters

x	Coordinate vector of length dim() (unused for flat manifolds).

Returns: The metric matrix, or std::nullopt if x has wrong dimension.

Definition at line 108 of file n_asset_manifold.cpp.

◆ n_assets()

int srfm::tensor::NAssetManifold::n_assets ( ) const

inlinenoexcept

Returns the number of asset (spatial) dimensions.

Returns: n_assets_.

Definition at line 230 of file n_asset_manifold.hpp.

◆ reduces_to_4d()

bool srfm::tensor::NAssetManifold::reduces_to_4d ( const NAssetManifold & other ) const

noexcept

Check structural compatibility with a 4D (N=3) manifold.

Returns true if other has n_assets == 3 and this manifold's spatial block is consistent with being an extension of a 4D manifold. Concretely: returns true when other.n_assets() == 3 and this->n_assets() >= 3.

Parameters

other Manifold to compare against.

Returns: true if compatible.

Definition at line 145 of file n_asset_manifold.cpp.

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

include/srfm/tensor/n_asset_manifold.hpp
src/tensor/n_asset_manifold.cpp

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ NAssetManifold()

Member Function Documentation

◆ c_market()

◆ covariance()

◆ dim()

◆ inverse_metric()

◆ inverse_metric_at()

◆ is_flat()

◆ line_element_sq()

◆ make()

◆ metric()

◆ metric_at()

◆ n_assets()

◆ reduces_to_4d()