tensor.hpp File Reference

Tensor Calculus & Covariance Engine — AGT-04 public API. More...

#include "srfm/types.hpp"
#include "srfm/constants.hpp"
#include <Eigen/Dense>
#include <algorithm>
#include <array>
#include <execution>
#include <functional>
#include <optional>
#include <utility>
#include <vector>

Go to the source code of this file.

Classes
struct	srfm::tensor::DualNumber
class	srfm::tensor::MetricTensor
class	srfm::tensor::CachedMetricTensor
class	srfm::tensor::ChristoffelSymbols
class	srfm::tensor::CachedChristoffelSymbols
class	srfm::tensor::ChristoffelSymbolsDual
struct	srfm::tensor::GeodesicState
	Position and 4-velocity state on the manifold. More...
class	srfm::tensor::GeodesicSolver

Namespaces
namespace	srfm
namespace	srfm::tensor

Typedefs
using	srfm::tensor::DualSpacetimePoint = Eigen::Matrix< DualNumber, SPACETIME_DIM, 1 >
using	srfm::tensor::DualMetricMatrix = Eigen::Matrix< DualNumber, SPACETIME_DIM, SPACETIME_DIM >
	A 4×4 matrix of dual numbers — the metric evaluated at a dual-number point.
using	srfm::tensor::DualMetricFunction = std::function< DualMetricMatrix(const DualSpacetimePoint &)>
using	srfm::tensor::MetricFunction = std::function< MetricMatrix(const SpacetimePoint &)>
using	srfm::tensor::ChristoffelArray = std::array< MetricMatrix, SPACETIME_DIM >

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

Detailed Description

Tensor Calculus & Covariance Engine — AGT-04 public API.

Module: Tensor Calculus & Covariance Engine

Responsibility

Implements the differential geometry machinery for the financial spacetime manifold. Provides:

• DualNumber — Scalar dual number for forward-mode autodiff
• MetricTensor — 4×4 position-dependent g_μν encoding covariance
• ChristoffelSymbols — Γ^λ_μν = ½ g^λσ(∂_μg_νσ + ∂_νg_μσ − ∂_σg_μν)
• GeodesicSolver — integrates d²x^λ/dτ² + Γ^λ_μν ẋ^μ ẋ^ν = 0

Physical Interpretation

In the financial spacetime manifold, the metric g_μν encodes the covariance structure of the market: the time-time component g₀₀ scales with market time; the spatial block g_ij carries the asset covariance matrix. Christoffel symbols Γ^λ_μν therefore measure the rate of change of correlations through market space. The geodesic equation describes the natural, force-free price path through this curved geometry.

Autodifferentiation (Dual Numbers)

ChristoffelSymbolsDual replaces the O(h²) central finite-difference metric derivative with exact forward-mode automatic differentiation via dual numbers: x = a + b·ε, ε² = 0 Evaluating g_μν at x = (x₀ + ε·ê_σ) propagates the partial derivative ∂g_μν/∂x^σ exactly through any polynomial or rational metric function, with zero truncation error and no step-size tuning.

Guarantees

• No undefined behaviour: all fallible operations return std::optional
• No raw pointers: ownership is by value or const-reference
• Thread-safe reads: const member functions are safe to call concurrently
• Eigen3 is used for all matrix arithmetic (LAPACK-quality numerics)

NOT Responsible For

• Lorentz boosts (see src/lorentz/)
• Market manifold topology / spacetime intervals (see src/manifold/)
• Backtesting or portfolio construction (see src/backtest/)

Definition in file tensor.hpp.