Expand description
Auto-generated module
🤖 Generated with SplitRS
Constants§
- MAX_DIM
- Maximum dimension supported for general metric tensor operations.
Functions§
- add3
- Add two 3-vectors.
- christoffel_
symbols_ numerical - Numerically approximate Christoffel symbols Γ^k_ij for a surface defined by a mapping r(u, v) via finite differences.
- covariant_
derivative_ covector - Covariant derivative of a covector (1-form) field.
- covariant_
derivative_ vector - Covariant derivative of a vector field.
- cross3
- Cross product of two 3-vectors.
- dot3
- Dot product of two 3-vectors.
- einstein_
tensor - Einstein tensor G_{mu nu} = R_{mu nu} - 0.5 g_{mu nu} R.
- gauss_
bonnet_ 2d_ integrand - Compute the Gauss-Bonnet integrand in N=2 dimensions.
- gauss_
bonnet_ integral - Numerically integrate Gaussian curvature over a patch of a surface.
- geodesic_
curve - Compute a geodesic curve on a surface given initial conditions.
- geodesic_
deviation - Geodesic deviation equation (Jacobi equation).
- geodesic_
equation_ solve - Solve the geodesic equation in N dimensions.
- geodesic_
step - Integrate a geodesic on a surface by one step (Euler).
- killing_
equation_ violation - Check if a vector field is a Killing vector field.
- kretschner_
scalar - Kretschner scalar K = R_{abcd} R^{abcd} (fully contracted Riemann tensor).
- lie_
bracket_ mat3 - Lie bracket [A, B] = AB - BA for 3×3 matrices (elements of gl(3)).
- mat3_
add - Add two 3×3 matrices.
- mat3_
det - 3×3 determinant.
- mat3_
exp - Compute matrix exponential of a 3×3 matrix via Cayley-Hamilton theorem.
- mat3_
frobenius_ norm - Frobenius norm of a 3×3 matrix.
- mat3_
identity - 3×3 identity matrix.
- mat3_
mul - Matrix–matrix multiply: A·B.
- mat3_
mul_ vec3 - Matrix–vector multiply: M·v.
- mat3_
scale - Scale a 3×3 matrix by scalar.
- mat3_
trace - Matrix trace.
- mat3_
transpose - Matrix transpose.
- mat3_
zero - 3×3 zero matrix.
- norm3
- Norm of a 3-vector.
- normalize3
- Normalize a 3-vector (returns zero vector if near zero).
- parallel_
transport - Parallel transport along a sequence of angular velocities.
- parallel_
transport_ nd - Parallel transport a vector along a curve in N dimensions.
- parallel_
transport_ step - Parallel transport of a vector along a curve on SO(3).
- ricci_
scalar - Ricci scalar R = g^{mu nu} R_{mu nu}.
- ricci_
scalar_ from_ metric_ fn - Compute the Ricci scalar directly from a metric function at a point.
- scale3
- Scale a 3-vector.
- skew3
- Skew-symmetric (hat) operator: converts a 3-vector ω to [ω]×.
- so3_
adjoint - Adjoint action of SO(3) on so(3): Ad_R(ω) = R ω.
- so3_
coadjoint - Coadjoint action of SO(3) on so(3): Ad_R(μ) = R⁻ᵀ μ = R μ.
- so3_
exp_ map - Riemannian exponential map on SO(3) at base point R₀.
- so3_
geodesic - Geodesic on SO(3) between two rotations, sampled at parameter t ∈ [0,1].
- so3_
lie_ bracket - Lie bracket for so(3) elements (skew-symmetric matrices): [ω̂₁, ω̂₂] = ω̂₁×ω̂₂ hat.
- so3_
log_ map - Riemannian logarithm map on SO(3): log_{R₀}(R₁).
- so3_
log_ matrix - Compute matrix logarithm of a rotation matrix (SO(3)) via Rodrigues formula.
- so3_
small_ adjoint - Small adjoint (ad): ad_ω₁(ω₂) = ω₁ × ω₂.
- sub3
- Subtract two 3-vectors.
- vee3
- Vee (inverse hat) operator: extracts 3-vector from skew-symmetric matrix.
- wedge
- Wedge product of two 1-forms: α ∧ β.
- weyl_
tensor - Weyl tensor C^rho_{sigma mu nu} for dim >= 3.