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.
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code: def __init__(
      self,
      dim,
      shape,
      default_coords_type="intrinsic",
      equip=True,
  ):
      self.dim = dim
      self.shape = shape
      self.default_coords_type = default_coords_type
  
      self.point_ndim = len(self.shape)
      if self.point_ndim == 1:
          self.default_point_type = "vector"
      elif self.point_ndim == 2:
          self.default_point_type = "matrix"
      else:
          self.default_point_type = "other"
  
      if equip:
          self.equip_with_metric()
  
file_path: geomstats/geomstats/geometry/complex_manifold.py
imports: import abc
  import geomstats.backend
label_desc: Use image node_id 1 to create a new ComplexManifold object from inherited base classes: abc with example: obj = ComplexManifold(dim, shape, default_coords_type, equip)