text: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  from __future__ import unicode_literals
  
  from math import exp, pi
  
  import os
  import random
  import torch
  import unittest
  import gpytorch
  from torch import optim
  from torch.autograd import Variable
  
  from gpytorch.kernels import RBFKernel, GridInterpolationKernel
  from gpytorch.likelihoods import GaussianLikelihood
  from gpytorch.means import ConstantMean
  from gpytorch.priors import SmoothedBoxPrior
  from gpytorch.random_variables import GaussianRandomVariable
  
  # Simple training data: let's try to learn a sine function,
  # but with KISS-GP let's use 100 training examples.
  n = 40
  train_x = torch.zeros(pow(n, 2), 2)
  for i in range(n):
      for j in range(n):
          train_x[i * n + j][0] = float(i) / (n - 1)
          train_x[i * n + j][1] = float(j) / (n - 1)
  train_x = Variable(train_x)
  train_y = Variable(torch.sin(((train_x.data[:, 0] + train_x.data[:, 1]) * (2 * pi))))
  
  m = 10
  test_x = torch.zeros(pow(m, 2), 2)
  for i in range(m):
      for j in range(m):
          test_x[i * m + j][0] = float(i) / (m - 1)
          test_x[i * m + j][1] = float(j) / (m - 1)
  test_x = Variable(test_x)
  test_y = Variable(torch.sin((test_x.data[:, 0] + test_x.data[:, 1]) * (2 * pi)))
  
  
  # All tests that pass with the exact kernel should pass with the interpolated kernel.
  class GPRegressionModel(gpytorch.models.ExactGP):
      def __init__(self, train_x, train_y, likelihood):
          super(GPRegressionModel, self).__init__(train_x, train_y, likelihood)
          self.mean_module = ConstantMean(prior=SmoothedBoxPrior(-1, 1))
          self.base_covar_module = RBFKernel(
              log_lengthscale_prior=SmoothedBoxPrior(exp(-3), exp(3), sigma=0.1, log_transform=True)
          )
          self.covar_module = GridInterpolationKernel(self.base_covar_module, grid_size=64, grid_bounds=[(0, 1), (0, 1)])
  
      def forward(self, x):
          mean_x = self.mean_module(x)
          covar_x = self.covar_module(x)
          return GaussianRandomVariable(mean_x, covar_x)
  
  
  class TestKissGPKroneckerProductRegression(unittest.TestCase):
      def setUp(self):
          if os.getenv("UNLOCK_SEED") is None or os.getenv("UNLOCK_SEED").lower() == "false":
              self.rng_state = torch.get_rng_state()
              torch.manual_seed(0)
              if torch.cuda.is_available():
                  torch.cuda.manual_seed_all(0)
              random.seed(0)
  
      def tearDown(self):
          if hasattr(self, "rng_state"):
              torch.set_rng_state(self.rng_state)
  
      def test_kissgp_gp_mean_abs_error(self):
          likelihood = GaussianLikelihood()
          gp_model = GPRegressionModel(train_x.data, train_y.data, likelihood)
          mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, gp_model)
  
          # Optimize the model
          gp_model.train()
          likelihood.train()
  
          with gpytorch.settings.max_preconditioner_size(5):
              optimizer = optim.Adam(list(gp_model.parameters()) + list(likelihood.parameters()), lr=0.1)
              optimizer.n_iter = 0
              for _ in range(10):
                  optimizer.zero_grad()
                  output = gp_model(train_x)
                  loss = -mll(output, train_y)
                  loss.backward()
                  optimizer.n_iter += 1
                  optimizer.step()
  
              for param in gp_model.parameters():
                  self.assertTrue(param.grad is not None)
                  self.assertGreater(param.grad.norm().item(), 0)
              for param in likelihood.parameters():
                  self.assertTrue(param.grad is not None)
                  self.assertGreater(param.grad.norm().item(), 0)
  
              # Test the model
              gp_model.eval()
              likelihood.eval()
  
              test_preds = likelihood(gp_model(test_x)).mean()
              mean_abs_error = torch.mean(torch.abs(test_y - test_preds))
              self.assertLess(mean_abs_error.data.squeeze().item(), 0.1)
  
  
  if __name__ == "__main__":
      unittest.main()
  