code: def test_newton_step_converges(trust_radius, dims):
      batch_size = 100
      batch_shape = torch.Size((batch_size,))
      mode = (
          random_inside_unit_circle(
              batch_shape + (dims,), requires_grad=True
          )
          - 1
      )
      x = (
          random_inside_unit_circle(
              batch_shape + (dims,), requires_grad=True
          )
          + 1
      )
  
      # create a quadratic loss function
      noise = torch.randn(batch_size, dims, 1)
      hessian = noise.matmul(
          noise.transpose(-1, -2)
      ) + 0.01 * torch.eye(dims)
  
      def loss_fn(x):
          diff = (x - mode).unsqueeze(-2)
          return (
              0.5 * diff.bmm(hessian).bmm(diff.transpose(-1, -2)).sum()
          )
  
      # check convergence
      for i in range(100):
          x = x.detach()
          x.requires_grad = True
          loss = loss_fn(x)
          x, cov = newton_step(loss, x, trust_radius=trust_radius)
          if ((x - mode).pow(2).sum(-1) < 1e-4).all():
              logger.debug(
                  "Newton iteration converged after {} steps".format(
                      2 + i
                  )
              )
              return
      pytest.fail("Newton iteration did not converge")
  
file_path: pyro/tests/ops/test_newton.py
imports: import itertools
  import logging
  import pytest
  import torch
  from torch.autograd import grad
  from pyro.ops.newton import newton_step
  from tests.common import assert_equal
label_desc: Use image node_id 4 for calling a global function with example usage: test_newton_step_converges(trust_radius, dims) and returns: unknown