Class DifferentiableManifold

x.__init__(...) initializes x; see help(type(x)) for signature

Overrides: object.__init__

(inherited documentation)

           Asserts that two points on the manifold are close to the given
           tolerance. 
       


:param a: 
:type a:  ``belongs``

:param b: 
:type b:  ``belongs``

Raises an Exception if the point does not belong to this manifold.

This function wraps some checks around :py:func:`belongs_`, which is implemented by the subclasses.

           Checks that a vector *vx* belongs to the tangent space
           at the given point *base*.

       


:param bv: 
:type bv:  ``tuple(belongs,*)``

           Computes the geodesic distance between two points.  
       


:param a: 
:type a:  ``belongs``

:param b: 
:type b:  ``belongs``

:rtype:  ``>=0``

Embeds a point on this manifold to the target manifold M.

:param my_point: :type my_point: ``belongs``

           Computes the exponential map from *base* for the velocity 
           vector *v*. 

           This function wraps some checks around :py:func:`expmap_`, 
           which is implemented by the subclasses. 
           
       


:param bv: 
:type bv:  ``belongs_ts``

:rtype:  ``belongs``

           Returns a friendly description string for a point on the manifold. 
       


:param a: 
:type a:  ``belongs``

Recovers a value from a Yaml structure.

:param yaml_structure: :type yaml_structure: ``list|dict``

:rtype: ``belongs``

Returns the point interpolated along the geodesic.

:param a: :type a: ``belongs``

:param b: :type b: ``belongs``

:param t: :type t: ``>=0,<=1``

:rtype: ``belongs``

           Returns a list of "interesting points" on this manifold that
           should be used for testing various properties. 
       


:rtype:  ``list(belongs)``

           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?
       


:param p: 
:type p:  ``belongs``

:param base: 
:type base:  ``belongs``

:rtype:  ``belongs_ts``

Projects a point on a bigger manifold to this manifold.

:rtype: ``belongs``

           Projects a vector *v_ambient* in the ambient space
           to the tangent space at point *base*.
       


:param bv: 
:type bv:  ``tuple(belongs,*)``

Returns the manifold corresponding to the tangent bundle. The default gives a generic implementation. MatrixLieGroup have a different one.

__abstractmethods__

Value:

frozenset(['belongs', 'distance', 'expmap', 'logmap', 'project_ts'])