Struct GeodesicEuler 

pub struct GeodesicEuler;

Geodesic Euler-Maruyama on a Riemannian manifold. x_{n+1} = Exp_{x_n}( f(x_n,t)*dt + g(x_n,t)*dW ) Strong order 0.5. Keeps state exactly on the manifold by using the Riemannian exponential map after each step.

Implementations

impl GeodesicEuler

pub fn step<M, D, G>( &self, sde: &ManifoldSDE<M, D, G>, x: &M::Point, t: f64, dt: f64, inc: &Increment<f64>, ) -> M::Point

where M: Manifold, D: Fn(&M::Point, f64) -> M::Tangent + Send + Sync, G: Fn(&M::Point, f64) -> M::Tangent + Send + Sync,

Advance x by one step of geodesic Euler-Maruyama.

Computes the tangent displacement f(x,t)*dt + g(x,t)*dW and maps it back to the manifold via Exp_x. Since all v0.1 cartan manifolds are complete, Exp is total and always succeeds.

Trait Implementations

impl<M, D, G> GeoScheme<M, D, G> for GeodesicEuler

where M: Manifold + ParallelTransport, D: Fn(&M::Point, f64) -> M::Tangent + Send + Sync, G: Fn(&M::Point, f64) -> M::Tangent + Send + Sync,

fn step_geo( &self, sde: &ManifoldSDE<M, D, G>, x: &M::Point, t: f64, dt: f64, inc: &Increment<f64>, ) -> M::Point

Advance x by one scheme step.