geometry.manifolds.euclidean.Euclidean¶
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class
geometry.manifolds.euclidean.Euclidean(dimension)[source]¶ This is the usual Euclidean space of finite dimension; this is mostly used for debugging.
There is no proper Haar measure; as an arbitrary choice, the
sample_uniform()returns a sample from a Gaussian distribution centered at 0.Methods
assert_close(a, b[, atol, msg])Asserts that two points on the manifold are close to the given tolerance. distance(a, b)Computes the geodesic distance between two points. embed_in(M, my_point)Embeds a point on this manifold to the target manifold M. friendly(a)Returns a friendly description string for a point on the manifold. from_yaml(yaml_structure)Recovers a value from a Yaml structure. geodesic(a, b, t)Returns the point interpolated along the geodesic. get_dimension()Returns the intrinsic dimension of this manifold. norm(v)Return the norm of a vector in the algebra. project_from(M, his_point)Projects a point on a bigger manifold to this manifold. tangent_bundle()Returns the manifold corresponding to the tangent bundle. zero()Returns the zero element for this algebra. belongs belongs_ts can_convert_to can_represent convert_to embeddable_in embedding expmap interesting_points isomorphism logmap normalize project project_to project_ts relations_descriptions riemannian_mean sample_uniform to_yaml -
belongs(x)[source]¶ Raises an Exception if the point does not belong to this manifold.
This function wraps some checks around
belongs_(), which is implemented by the subclasses.
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interesting_points()[source]¶ Returns a list of “interesting points” on this manifold that should be used for testing various properties.
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