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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docstr: Project a vector to a tangent space of the manifold.
  
  Parameters
  ----------
  vector : array-like, shape=[..., *point_shape]
      Vector.
  base_point : array-like, shape=[..., *point_shape]
      Point on the manifold.
  
  Returns
  -------
  tangent_vec : array-like, shape=[..., *point_shape]
      Tangent vector at base point.
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code: def to_tangent(self, vector, base_point):
      """Project a vector to a tangent space of the manifold.
  
      Parameters
      ----------
      vector : array-like, shape=[..., *point_shape]
          Vector.
      base_point : array-like, shape=[..., *point_shape]
          Point on the manifold.
  
      Returns
      -------
      tangent_vec : array-like, shape=[..., *point_shape]
          Tangent vector at base point.
      """
  
file_path: geomstats/geomstats/geometry/complex_manifold.py
imports: import abc
  import geomstats.backend
label_desc: Use image node_id 5 for calling the ComplexManifold obj's underlying member method code with example usage: obj.to_tangent(vector, base_point) without return types