Distributions

The following functions and types provide support for manifold-valued and tangent space-valued distributions:

Manifolds.FVectorDistribution — Type

FVectorDistribution{TSpace<:VectorSpaceFiber, T}

An abstract distribution for vector bundle fiber-valued distributions (values from a fiber of a vector bundle at point x from the given manifold). For example used for tangent vector-valued distributions.

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Manifolds.FVectorSupport — Type

FVectorSupport(space::AbstractManifold, VectorSpaceFiber)

Value support for vector bundle fiber-valued distributions (values from a fiber of a vector bundle at a point from the given manifold). For example used for tangent vector-valued distributions.

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Manifolds.FVectorvariate — Type

FVectorvariate

Structure that subtypes VariateForm, indicating that a single sample is a vector from a fiber of a vector bundle.

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Manifolds.MPointDistribution — Type

MPointDistribution{TM<:AbstractManifold}

An abstract distribution for points on manifold of type TM.

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Manifolds.MPointSupport — Type

MPointSupport(M::AbstractManifold)

Value support for manifold-valued distributions (values from given AbstractManifold M).

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Manifolds.MPointvariate — Type

MPointvariate

Structure that subtypes VariateForm, indicating that a single sample is a point on a manifold.

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Distributions.support — Method

support(d::FVectorDistribution)

Get the object of type FVectorSupport for the distribution d.

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Manifolds.ProjectedFVectorDistribution — Type

ProjectedFVectorDistribution(type::VectorSpaceFiber, p, d, project!)

Generates a random vector from ambient space of manifold type.manifold at point p and projects it to vector space of type type using function project!, see project for documentation. Generated arrays are of type TResult.

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Manifolds.ProjectedPointDistribution — Type

ProjectedPointDistribution(M::AbstractManifold, d, proj!, p)

Generates a random point in ambient space of M and projects it to M using function proj!. Generated arrays are of type TResult, which can be specified by providing the p argument.

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Manifolds.normal_tvector_distribution — Method

normal_tvector_distribution(M::Euclidean, p, σ)

Normal distribution in ambient space with standard deviation σ projected to tangent space at p.

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Manifolds.projected_distribution — Function

projected_distribution(M::AbstractManifold, d, [p=rand(d)])

Wrap the standard distribution d into a manifold-valued distribution. Generated points will be of similar type to p. By default, the type is not changed.

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