code: def test_periodic_kernel(
      x1, x2, amplitude, length_scale, exact
  ) -> None:
      tol = 1e-5
      batch_size = amplitude.shape[0]
      history_length_1 = x1.shape[0]
      history_length_2 = x2.shape[0]
      num_features = x1.shape[1]
      if batch_size > 1:
          x1 = nd.tile(x1, reps=(batch_size, 1, 1))
          x2 = nd.tile(x2, reps=(batch_size, 1, 1))
          for i in range(1, batch_size):
              x1[i, :, :] = (i + 1) * x1[i, :, :]
              x2[i, :, :] = (i - 3) * x2[i, :, :]
      else:
          x1 = x1.reshape(batch_size, history_length_1, num_features)
          x2 = x2.reshape(batch_size, history_length_2, num_features)
      amplitude = amplitude.reshape(batch_size, 1, 1)
      length_scale = length_scale.reshape(batch_size, 1, 1)
      frequency = 1 / 24 * nd.ones_like(length_scale)
      periodic = PeriodicKernel(amplitude, length_scale, frequency)
  
      exact = amplitude * nd.exp(
          -2
          * nd.sin(frequency * math.pi * nd.sqrt(exact)) ** 2
          / length_scale**2
      )
  
      res = periodic.kernel_matrix(x1, x2)
      assert nd.norm(exact - res) < tol
  
imports: import math
  import pytest
  from mxnet import nd
  from gluonts.mx.kernels import PeriodicKernel
label_desc: Use image node_id 1 for calling a global function with example usage: test_periodic_kernel(x1, x2, amplitude, length_scale, exact) without return types