docstr: Kernel for a single layer
docstr_tok: ["Kernel","for","a","single","layer"]
code: def _single_layer_K(
      self, x1norm, x2norm, x1sum, x2sum, cos_theta, x2_none=False
  ):
      """
      Kernel for a single layer
      """
      mu_tilde_1 = np.divide(
          x1sum, x1norm, out=np.zeros_like(x1sum), where=x1norm != 0
      )
      mu_tilde_2 = np.divide(
          x2sum, x2norm, out=np.zeros_like(x2sum), where=x2norm != 0
      )
  
      pdf1 = norm.pdf(-mu_tilde_1)
      pdf2 = norm.pdf(-mu_tilde_2)
      cdf1 = norm.cdf(-mu_tilde_1)
      cdf2 = norm.cdf(-mu_tilde_2)
      erf1 = erf(mu_tilde_1 / np.sqrt(2))
      erf2 = erf(mu_tilde_2 / np.sqrt(2))
  
      # cross1 is expected value of X_1 |X_2|
      term1 = cos_theta * (
          (1 + mu_tilde_2**2) * (1 - 2 * cdf2) + 2 * mu_tilde_2 * pdf2
      )
      term2 = (mu_tilde_2 * erf2 + 2 * pdf2) * (
          mu_tilde_1 - cos_theta * mu_tilde_2
      )
      cross1 = (term1 + term2) * x1norm * x2norm
      # cross2 is expected value of X_2 |X_1|
      term1 = cos_theta * (
          (1 + mu_tilde_1**2) * (1 - 2 * cdf1) + 2 * mu_tilde_1 * pdf1
      )
      term2 = (mu_tilde_1 * erf1 + 2 * pdf1) * (
          mu_tilde_2 - cos_theta * mu_tilde_1
      )
      cross2 = (term1 + term2) * x1norm * x2norm
  
      k_abs = self.kernel_abs._single_layer_K(
          x1norm, x2norm, x1sum, x2sum, cos_theta, x2_none
      )
      k_lin = self.kernel_lin._single_layer_K(
          x1norm, x2norm, x1sum, x2sum, cos_theta, x2_none
      )
  
      return (k_abs + k_lin + cross1 + cross2) / 4.0
  
file_path: elu-gelu-kernels/code/kernels/nn_kernel_relu.py
imports: import numpy
  from scipy.stats import multivariate_normal
  from scipy.stats import norm
  from scipy.special import erf
  import GPy
  import abc
  from .nn_kernel import NNKernel
  from .nn_kernel_linear import NNKernelLinear
  from .nn_kernel_abs import NNKernelAbs
label_desc: Use image node_id 2 for calling the NNKernelRelu obj's underlying member method code with example usage: obj._single_layer_K(x1norm, x2norm, x1sum, x2sum, cos_theta, x2_none) and returns: unknown