code: def test_dot_general(
      self,
      same_inputs,
      n,
      batch_dims,
      contracting_dims,
      c_dims,
      b_dims,
      r_permutation,
      channel_axis,
      is_rhs,
      diagonal_spatial,
      diagonal_batch,
      batch_axis,
  ):
      if n != 2:
          test_utils.skip_test(self)
  
      if default_backend() == "tpu":
          atol = 1.0
      else:
          atol = 0.1
  
      n_b = 2
      n_c = 1
      key1, key2, key3 = random.split(random.PRNGKey(1), 3)
  
      x_shape_n_c = [2, 4, 6, 8, 10, 12, 14][: n - 2]
      x_shape = list(x_shape_n_c)
  
      for a in sorted((batch_axis, channel_axis)):
          x_shape.insert(a, n_b if a == batch_axis else n_c)
  
      mask_constant = 10.0
  
      x1 = jnp.cos(random.normal(key1, x_shape))
      mask1 = random.bernoulli(key1, p=0.8, shape=x1.shape)
      x1 = jnp.where(mask1, mask_constant, x1)
  
      if same_inputs:
          x2 = None
      else:
          x2_shape = (
              x_shape[:batch_axis]
              + [
                  4
                  if (batch_axis not in contracting_dims + batch_dims)
                  else x_shape[batch_axis]
              ]
              + x_shape[batch_axis + 1 :]
          )
          x2 = jnp.cos(random.normal(key2, x2_shape))
          mask2 = random.bernoulli(key2, p=0.4, shape=x2.shape)
          x2 = jnp.where(mask2, mask_constant, x2)
  
      other_shape = [1, 3, 5, 7, 9, 11, 13, 15][:n]
      for i in contracting_dims + batch_dims:
          other_shape[i] = x_shape[i]
      other = random.normal(key3, other_shape)
      other = jnp.arange(jnp.size(other)).reshape(other_shape)
  
      other_t = jnp.transpose(other, r_permutation)
      r_c_dims = tuple(r_permutation.index(c) for c in c_dims)
      r_b_dims = tuple(r_permutation.index(b) for b in b_dims)
  
      if is_rhs:
          lhs, rhs = None, other_t
          dn = ((c_dims, r_c_dims), (b_dims, r_b_dims))
      else:
          lhs, rhs = other_t, None
          dn = ((r_c_dims, c_dims), (r_b_dims, b_dims))
  
      lhs_ndim = None if lhs is None else lhs.ndim
      init_fn, apply_fn, kernel_fn = stax.DotGeneral(
          lhs=lhs, rhs=rhs, dimension_numbers=dn, batch_axis=batch_axis
      )
  
      def get_exact():
          return kernel_fn(
              x1,
              x2,
              diagonal_spatial=diagonal_spatial,
              diagonal_batch=diagonal_batch,
              batch_axis=batch_axis,
              channel_axis=channel_axis,
              mask_constant=mask_constant,
          )
  
      if (
          [i for i in c_dims if i not in (batch_axis, channel_axis)]
          and diagonal_spatial
      ) or (batch_axis in c_dims and diagonal_batch):
          self.assertRaises(ValueError, get_exact)
  
      else:
          exact = get_exact()
  
          out_c_axis = utils.axis_after_dot(
              channel_axis, c_dims, b_dims, lhs_ndim
          )
          out_b_axis = utils.axis_after_dot(
              batch_axis, c_dims, b_dims, lhs_ndim
          )
  
          def get_empirical(get):
              def get_diagonal_axes():
                  axes = ()
                  if (
                      get in ("cov1", "cov2")
                      and diagonal_batch
                      and batch_axis not in c_dims
                  ):
                      axes += (out_b_axis,)
  
                  if diagonal_spatial:
                      axes += tuple(
                          utils.axis_after_dot(
                              i, c_dims, b_dims, lhs_ndim
                          )
                          for i in range(n)
                          if i
                          not in c_dims + (batch_axis, channel_axis)
                      )
                      rhs_ndim = None if rhs is None else rhs.ndim
                      axes += tuple(
                          utils.axis_after_dot(
                              i, r_c_dims, r_b_dims, rhs_ndim
                          )
                          for i in range(n)
                          if i not in r_c_dims
                          and not (
                              i in r_b_dims
                              and b_dims[r_b_dims.index(i)]
                              == batch_axis
                          )
                      )
                  return axes
  
              def batch_axes():
                  if batch_axis in contracting_dims:
                      return (), ()
  
                  axis = out_b_axis
                  if out_c_axis < axis:
                      axis -= 1
                  if not diagonal_spatial:
                      axis *= 2
  
                  if get in ("cov1", "cov2") and diagonal_batch:
                      return (axis,), (0,)
                  return (axis, axis + 1), (0, 1)
  
              kernel_fn_mc = nt.monte_carlo_kernel_fn(
                  init_fn=init_fn,
                  apply_fn=stax.unmask_fn(apply_fn),
                  key=key1,
                  n_samples=1,
                  trace_axes=(out_c_axis,),
                  diagonal_axes=get_diagonal_axes(),
                  device_count=-1
                  if (
                      get == "nngp"
                      and batch_axis == out_b_axis == 0
                      and 0 not in c_dims + b_dims
                  )
                  else 0,
                  implementation=_DEFAULT_TESTING_NTK_IMPLEMENTATION,
              )
  
              empirical = kernel_fn_mc(
                  x1=x2 if get == "cov2" else x1,
                  x2=x2 if get == "nngp" else None,
                  get="nngp",
                  batch_axis=batch_axis,
                  channel_axis=channel_axis,
                  mask_constant=mask_constant,
              )
              empirical = jnp.moveaxis(empirical, *batch_axes())
              return empirical
  
          for get in ("nngp", "cov1", "cov2"):
              if get == "cov2" and same_inputs:
                  continue
  
              with self.subTest(get=get):
                  test_utils.assert_close_matrices(
                      self,
                      get_empirical(get),
                      getattr(exact, get),
                      0.01,
                      atol,
                  )
  
imports: import itertools
  import random
  import string
  import time
  from absl.testing import absltest
  from jax import default_backend
  from jax import jit
  from jax import lax
  from jax import random
  from jax import vjp
  from jax import config
  import jax.numpy
  import more_itertools
  import neural_tangents
  from neural_tangents import stax
  from neural_tangents._src.empirical import _DEFAULT_TESTING_NTK_IMPLEMENTATION
  from neural_tangents._src.utils import utils
  from tests import test_utils
  import numpy
label_desc: Use image node_id 1 for calling the DotGeneralTest obj's underlying member method code with example usage: obj.test_dot_general(same_inputs, n, batch_dims, contracting_dims, c_dims, b_dims, r_permutation, channel_axis, is_rhs, diagonal_spatial, diagonal_batch, batch_axis) and returns: kernel_fn, empirical, axes, axis,  unknown,  int,  int, ,  , axis,  int