class_docstr: Class for complex manifolds.
  
  Parameters
  ----------
  dim : int
      Dimension of the manifold.
  shape : tuple of int
      Shape of one element of the manifold.
      Optional, default : None.
  default_coords_type : str, {'intrinsic', 'extrinsic', etc}
      Coordinate type.
      Optional, default: 'intrinsic'.
  equip : bool
      If True, equip space with default metric.
class_docstr_tok: ["Class","for","complex","manifolds",".","Parameters","--","--","--","--","--","dim",":","int","Dimension","of","the","manifold",".","shape",":","tuple","of","int","Shape","of","one","element","of","the","manifold",".","Optional",",","default",":","None",".","default_coords_type",":","str",",","{","'intrinsic","'",",","'extrinsic","'",",","etc","}","Coordinate","type",".","Optional",",","default",":","'intrinsic","'",".","equip",":","bool","If","True",",","equip","space","with","default","metric","."]
docstr: Equip manifold with Metric.
  
  Parameters
  ----------
  Metric : Connection object
      If None, default metric will be used.
docstr_tok: ["Equip","manifold","with","Metric",".","Parameters","--","--","--","--","--","Metric",":","Connection","object","If","None",",","default","metric","will","be","used","."]
code: def equip_with_metric(self, Metric=None, **metric_kwargs):
      """Equip manifold with Metric.
  
      Parameters
      ----------
      Metric : Connection object
          If None, default metric will be used.
      """
      if Metric is None:
          out = self.default_metric()
          if isinstance(out, tuple):
              Metric, kwargs = out
              kwargs.update(metric_kwargs)
              metric_kwargs = kwargs
          else:
              Metric = out
  
      self.metric = Metric(self, **metric_kwargs)
  
file_path: geomstats/geomstats/geometry/complex_manifold.py
imports: import abc
  import geomstats.backend
label_desc: Use image node_id 2 for calling the ComplexManifold obj's underlying member method code with example usage: obj.equip_with_metric(Metric) without return types