docstr: Test special cases where bvnu admits closed-form solutions.
  
  Note: inf should not be passed to _bvnu as bounds, use big numbers instead.
docstr_tok: ["Test","special","cases","where","bvnu","admits","closed-form","solutions",".","Note",":","inf","should","not","be","passed","to","_bvnu","as","bounds",",","use","big","numbers","instead","."]
code: def test_bvnu_taylor(self) -> None:
      r"""Test special cases where bvnu admits closed-form solutions.
  
      Note: inf should not be passed to _bvnu as bounds, use big numbers instead.
      """
      use_taylor = self.correlations.abs() >= 0.925
      r = self.correlations[use_taylor]
      xl = self.xl[..., use_taylor]
      yl = self.yl[..., use_taylor]
      with self.subTest(msg="exact_unconstrained"):
          prob = _bvnu_taylor(
              r, torch.full_like(r, -1e16), torch.full_like(r, -1e16)
          )
          self.assertAllClose(prob, torch.ones_like(prob))
  
      with self.subTest(msg="exact_marginal"):
          prob = _bvnu_taylor(
              r.expand_as(yl),
              torch.full_like(xl, -1e16),
              yl,
          )
          test = Phi(-yl)  # same as: 1 - P(y < yl)
          self.assertAllClose(prob, test)
  
      with self.subTest(msg="exact_independent"):
          prob = _bvnu_polar(torch.zeros_like(xl), xl, yl)
          test = Phi(-xl) * Phi(-yl)
          self.assertAllClose(prob, test)
  
imports: from __future__ import annotations
  from itertools import count
  from typing import Any, Callable, Dict, Optional, Tuple, Union
  import torch
  from botorch.exceptions import UnsupportedError
  from botorch.utils.probability.bvn import _bvnu_polar, _bvnu_taylor, bvn, bvnmom, bvnu, Phi
  from botorch.utils.testing import BotorchTestCase
  from torch import Tensor
label_desc: Use image node_id 8 for calling the TestBVN obj's underlying member method code with example usage: obj.test_bvnu_taylor() without return types