code: def test_matern_kernel(num_gps, nu):
      mk = MaternKernel(
          nu=nu,
          num_gps=num_gps,
          length_scale_init=0.1 + torch.rand(num_gps),
      )
  
      dt = torch.rand(1).item()
      forward = mk.transition_matrix(dt)
      backward = mk.transition_matrix(-dt)
      forward_backward = torch.matmul(forward, backward)
  
      # going forward dt in time and then backward dt in time should bring us back to the identity
      eye = (
          torch.eye(mk.state_dim)
          .unsqueeze(0)
          .expand(num_gps, mk.state_dim, mk.state_dim)
      )
      assert_equal(forward_backward, eye)
  
      # let's just check that these are PSD
      torch.linalg.cholesky(mk.stationary_covariance())
      torch.linalg.cholesky(mk.process_covariance(forward))
  
      # evolving forward infinitesimally should yield the identity
      nudge = mk.transition_matrix(torch.tensor([1.0e-9]))
      assert_equal(nudge, eye)
  
imports: import pytest
  import torch
  from pyro.ops.ssm_gp import MaternKernel
  from tests.common import assert_equal
label_desc: Use image node_id 1 for calling a global function with example usage: test_matern_kernel(num_gps, nu) without return types