code: def test_2d_sphere_constraints_line_intersections(self):
      # Interior initial point
      ta, tb, intersect = sphere_intersections(
          [0, 0], [1, 0], 0.5, entire_line=True
      )
      assert_array_almost_equal([ta, tb], [-0.5, 0.5])
      assert_equal(intersect, True)
  
      # No intersection between line and circle
      ta, tb, intersect = sphere_intersections(
          [2, 0], [0, 1], 1, entire_line=True
      )
      assert_equal(intersect, False)
  
      # Outside initial point pointing toward outside the circle
      ta, tb, intersect = sphere_intersections(
          [2, 0], [1, 0], 1, entire_line=True
      )
      assert_array_almost_equal([ta, tb], [-3, -1])
      assert_equal(intersect, True)
  
      # Outside initial point pointing toward inside the circle
      ta, tb, intersect = sphere_intersections(
          [2, 0], [-1, 0], 1.5, entire_line=True
      )
      assert_array_almost_equal([ta, tb], [0.5, 3.5])
      assert_equal(intersect, True)
  
      # Initial point on the boundary
      ta, tb, intersect = sphere_intersections(
          [2, 0], [1, 0], 2, entire_line=True
      )
      assert_array_almost_equal([ta, tb], [-4, 0])
      assert_equal(intersect, True)
  
imports: import numpy
  from scipy.sparse import csc_matrix
  from scipy.optimize._trustregion_constr.qp_subproblem import eqp_kktfact, projected_cg, box_intersections, sphere_intersections, box_sphere_intersections, modified_dogleg
  from scipy.optimize._trustregion_constr.projections import projections
  from numpy.testing import TestCase, assert_array_almost_equal, assert_equal
  import pytest
label_desc: Use image node_id 2 for calling the TestSphericalBoundariesIntersections obj's underlying member method code with example usage: obj.test_2d_sphere_constraints_line_intersections() without return types