new_contents: import math
  
  import torch
  
  import pytest
  from pyro.contrib.oed.eig import EwmaLog
  from tests.common import assert_equal
  
  
  @pytest.mark.parametrize("alpha", [0.5, 0.9, 0.99])
  def test_ewma(alpha, NS=10000, D=1):
      ewma_log = EwmaLog(alpha=alpha)
      sigma = torch.tensor(1.0, requires_grad=True)
  
      for k in range(1000):
          exponent = torch.randn(NS, D) * sigma
          s, _ = torch.max(exponent, dim=0)
          log_eT = s + ewma_log((exponent - s).exp().mean(dim=0), s)
          log_eT.backward()
          sigma_grad = sigma.grad.clone().data.numpy()
          sigma.grad.zero_()
          if k % 100 == 0:
              error = math.fabs(sigma_grad - 1.0)
              assert error < 0.07
  
  
  def test_ewma_log():
      ewma_log = EwmaLog(alpha=0.5)
      input1 = torch.tensor(2.)
      ewma_log(input1, torch.tensor(0.))
      assert_equal(ewma_log.ewma, input1)
      input2 = torch.tensor(3.)
      ewma_log(input2, torch.tensor(0.))
      assert_equal(ewma_log.ewma, torch.tensor(8./3))
  
  
  def test_ewma_log_with_s():
      ewma_log = EwmaLog(alpha=0.5)
      input1 = torch.tensor(-1.)
      s1 = torch.tensor(210.)
      ewma_log(input1, s1)
      assert_equal(ewma_log.ewma, input1)
      input2 = torch.tensor(-1.)
      s2 = torch.tensor(210.5)
      ewma_log(input2, s2)
      true_ewma = (1./3)*(torch.exp(s1 - s2)*input1 + 2*input2)
      assert_equal(ewma_log.ewma, true_ewma)
  
subject: add basic ewmalog tests (#1312)