Riemannian geometry, manifold optimization, and geodesic computation in Rust
Complete Cartan matrix attention mechanisms with proper Lie algebra structures
Portable GPU compute primitives for the cartan ecosystem: wgpu device/buffer/kernel abstractions plus VkFFT-backed FFT.
Core no_std Semantic Cartan Matrix implementation for rUv-FANN
Raw FFI bindings to VkFFT (vendored). Internal to the cartan-gpu stack.
Geodesic computation and geometric tools for cartan: geodesic curves, curvature queries, Jacobi fields
Concrete Riemannian manifold implementations for cartan: Sphere, SO(n), SPD(n), Grassmann, Euclidean
Riemannian optimization algorithms for cartan: Riemannian gradient descent, conjugate gradient, trust region
Discrete exterior calculus on Riemannian manifolds: simplicial complexes, Hodge operators, and covariant differential operators built on cartan-core
Mean-field and full-field homogenisation of random media on SPD manifolds, generic over tensor order
Stochastic analysis on manifolds: orthonormal frame bundle, horizontal lift, Stratonovich development. Foundation for Eells-Elworthy-Malliavin Brownian motion and Bismut-Elworthy-Li Greeks.
Core traits for Riemannian geometry and fiber bundles: Manifold, Fiber, DiscreteConnection, ParallelTransport, Curvature