geometry.manifolds.todo package¶
Submodules¶
geometry.manifolds.todo.grassman module¶
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class
geometry.manifolds.todo.grassman.Grassman(p, n)[source]¶ Bases:
geometry.manifolds.differentiable_manifold.DifferentiableManifoldINCOMPLETE – The Grassman manifold Grass(n,p) is the set of rank-p subspaces in R^n. It is seen here as Grass(n,p) = ST(n,p)/GL_p.
For a reference, see the paper by Absil, Mahony, and Sepulchre (2004) where all these operations are explained. Also their book should contain essentially the same info, but with more background.
Methods
assert_close(a, b[, atol, msg])Asserts that two points on the manifold are close to the given tolerance. belongs_ts(bv)Checks that a vector vx belongs to the tangent space at the given point base. 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. interesting_points()Returns a list of “interesting points” on this manifold that should be used for testing various properties. project_from(M, his_point)Projects a point on a bigger manifold to this manifold. riemannian_mean(points)TODO: work out exceptions tangent_bundle()Returns the manifold corresponding to the tangent bundle. belongs can_convert_to can_represent convert_to distance embeddable_in embedding expmap isomorphism logmap normalize project_to project_ts relations_descriptions sample_uniform to_yaml -
belongs(a)[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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expmap(a, vel)[source]¶ Computes the exponential map from base for the velocity vector v.
This function wraps some checks around
expmap_(), which is implemented by the subclasses.
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logmap(a, b)[source]¶ Computes the logarithmic map from base point base to target b. # XXX: what should we do in the case there is more than one logmap?
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normalize(x)[source]¶ Normalizes the coordinates to the canonical representation for this manifold. See TorusW.
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geometry.manifolds.todo.moebius module¶
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class
geometry.manifolds.todo.moebius.Moebius(n)[source]¶ Bases:
geometry.manifolds.differentiable_manifold.DifferentiableManifoldINCOMPLETE - The Moebius strip – still to be implemented.
Methods
assert_close(a, b[, atol, msg])Asserts that two points on the manifold are close to the given tolerance. belongs(x)Raises an Exception if the point does not belong to this manifold. belongs_ts(bv)Checks that a vector vx belongs to the tangent space at the given point base. 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. expmap(bv)Computes the exponential map from base for the velocity vector v. 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. interesting_points()Returns a list of “interesting points” on this manifold that should be used for testing various properties. logmap(base, p)Computes the logarithmic map from base point base to target b. project_from(M, his_point)Projects a point on a bigger manifold to this manifold. project_ts(bv)Projects a vector bv in the ambient space to the tangent space at point base. riemannian_mean(points)TODO: work out exceptions tangent_bundle()Returns the manifold corresponding to the tangent bundle. belongs_ can_convert_to can_represent convert_to distance_ embeddable_in embedding expmap_ isomorphism logmap_ normalize project_to project_ts_ relations_descriptions sample_uniform to_yaml
geometry.manifolds.todo.orthogonal_group module¶
geometry.manifolds.todo.posdef_matrices module¶
geometry.manifolds.todo.stiefel module¶
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class
geometry.manifolds.todo.stiefel.NonCompactStiefel(p, n)[source]¶ Bases:
geometry.manifolds.differentiable_manifold.DifferentiableManifoldINCOMPLETE – Matrices of fixed rank.
Methods
assert_close(a, b[, atol, msg])Asserts that two points on the manifold are close to the given tolerance. belongs_ts(bv)Checks that a vector vx belongs to the tangent space at the given point base. 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. interesting_points()Returns a list of “interesting points” on this manifold that should be used for testing various properties. project_from(M, his_point)Projects a point on a bigger manifold to this manifold. riemannian_mean(points)TODO: work out exceptions tangent_bundle()Returns the manifold corresponding to the tangent bundle. belongs can_convert_to can_represent convert_to distance embeddable_in embedding expmap isomorphism logmap normalize project_to project_ts relations_descriptions sample_uniform to_yaml -
belongs(a)[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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expmap(a, vel)[source]¶ Computes the exponential map from base for the velocity vector v.
This function wraps some checks around
expmap_(), which is implemented by the subclasses.
-
logmap(a, b)[source]¶ Computes the logarithmic map from base point base to target b. # XXX: what should we do in the case there is more than one logmap?
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normalize(x)[source]¶ Normalizes the coordinates to the canonical representation for this manifold. See TorusW.
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