code: def test_find_interior_point(self):
      # basic problem: 1 <= x_1 <= 2, 2 <= x_2 <= 3
      A = np.concatenate([np.eye(2), -np.eye(2)], axis=0)
      b = np.array([2.0, 3.0, -1.0, -2.0])
      x = find_interior_point(A=A, b=b)
      self.assertTrue(np.allclose(x, np.array([1.5, 2.5])))
      # problem w/ negatives variables: -2 <= x_1 <= -1, -3 <= x_2 <= -2
      b = np.array([-1.0, -2.0, 2.0, 3.0])
      x = find_interior_point(A=A, b=b)
      self.assertTrue(np.allclose(x, np.array([-1.5, -2.5])))
      # problem with bound on a single variable: x_1 <= 0
      A = np.array([[1.0, 0.0]])
      b = np.zeros(1)
      x = find_interior_point(A=A, b=b)
      self.assertLessEqual(x[0].item(), 0.0)
      # unbounded problem: x >= 3
      A = np.array([[-1.0]])
      b = np.array([-3.0])
      x = find_interior_point(A=A, b=b)
      self.assertAlmostEqual(x.item(), 5.0, places=4)
  
imports: from __future__ import annotations
  import itertools
  import warnings
  from typing import Any, Dict, Type
  from unittest import mock
  import numpy
  import torch
  from botorch.exceptions.errors import BotorchError
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.sampling.pathwise import draw_matheron_paths
  from botorch.utils.sampling import _convert_bounds_to_inequality_constraints, batched_multinomial, DelaunayPolytopeSampler, draw_sobol_samples, find_interior_point, get_polytope_samples, HitAndRunPolytopeSampler, manual_seed, normalize_linear_constraints, optimize_posterior_samples, PolytopeSampler, sample_hypersphere, sample_simplex, sparse_to_dense_constraints
  from botorch.utils.testing import BotorchTestCase
label_desc: Use image node_id 9 for calling the TestSampleUtils obj's underlying member method code with example usage: obj.test_find_interior_point() without return types