class_docstr: The Arc-cosine family of kernels which mimics the computation in neural
  networks. The order parameter specifies the assumed activation function.
  The Multi Layer Perceptron (MLP) kernel is closely related to the ArcCosine
  kernel of order 0.
  
  The key reference is :cite:t:`NIPS2009_3628`.
class_docstr_tok: ["The","Arc-cosine","family","of","kernels","which","mimics","the","computation","in","neural","networks",".","The","order","parameter","specifies","the","assumed","activation","function",".","The","Multi","Layer","Perceptron","(","MLP",")","kernel","is","closely","related","to","the","ArcCosine","kernel","of","order","0",".","The","key","reference","is",":","cite",":","t",":","`","NIPS2009_3628","`","."]
docstr: Implements the order dependent family of functions defined in equations
  4 to 7 in the reference paper.
docstr_tok: ["Implements","the","order","dependent","family","of","functions","defined","in","equations","4","to","7","in","the","reference","paper","."]
code: def _J(self, theta: TensorType) -> TensorType:
      """
      Implements the order dependent family of functions defined in equations
      4 to 7 in the reference paper.
      """
      if self.order == 0:
          return np.pi - theta
      elif self.order == 1:
          return tf.sin(theta) + (np.pi - theta) * tf.cos(theta)
      else:
          assert (
              self.order == 2
          ), f"Don't know how to handle order {self.order}."
          return 3.0 * tf.sin(theta) * tf.cos(theta) + (
              np.pi - theta
          ) * (1.0 + 2.0 * tf.cos(theta) ** 2)
  
imports: from typing import Optional
  import numpy
  import tensorflow
  from check_shapes import check_shape
  from check_shapes import check_shapes, inherit_check_shapes
  from ..base import AnyNDArray, Parameter, TensorType
  from ..utilities import positive, to_default_float
  from .base import ActiveDims, Kernel
label_desc: Use image node_id 5 for calling the ArcCosine obj's underlying member method code with example usage: obj._J(theta) and returns: unknown, unknown, unknown