code: def box_sphere_intersections(
      z, d, lb, ub, trust_radius, entire_line=False, extra_info=False
  ):
      """Find the intersection between segment (or line) and box/sphere constraints.
  
      Find the intersection between the segment (or line) defined by the
      parametric  equation ``x(t) = z + t*d``, the rectangular box
      ``lb <= x <= ub`` and the ball ``||x|| <= trust_radius``.
  
      Parameters
      ----------
      z : array_like, shape (n,)
          Initial point.
      d : array_like, shape (n,)
          Direction.
      lb : array_like, shape (n,)
          Lower bounds to each one of the components of ``x``. Used
          to delimit the rectangular box.
      ub : array_like, shape (n, )
          Upper bounds to each one of the components of ``x``. Used
          to delimit the rectangular box.
      trust_radius : float
          Ball radius.
      entire_line : bool, optional
          When ``True``, the function returns the intersection between the line
          ``x(t) = z + t*d`` (``t`` can assume any value) and the constraints.
          When ``False``, the function returns the intersection between the segment
          ``x(t) = z + t*d``, ``0 <= t <= 1`` and the constraints.
      extra_info : bool, optional
          When ``True``, the function returns ``intersect_sphere`` and ``intersect_box``.
  
      Returns
      -------
      ta, tb : float
          The line/segment ``x(t) = z + t*d`` is inside the rectangular box and
          inside the ball for for ``ta <= t <= tb``.
      intersect : bool
          When ``True``, there is a intersection between the line (or segment)
          and both constraints. On the other hand, when ``False``, there is no
          intersection.
      sphere_info : dict, optional
          Dictionary ``{ta, tb, intersect}`` containing the interval ``[ta, tb]``
          for which the line intercepts the ball. And a boolean value indicating
          whether the sphere is intersected by the line.
      box_info : dict, optional
          Dictionary ``{ta, tb, intersect}`` containing the interval ``[ta, tb]``
          for which the line intercepts the box. And a boolean value indicating
          whether the box is intersected by the line.
      """
      ta_b, tb_b, intersect_b = box_intersections(
          z, d, lb, ub, entire_line
      )
      ta_s, tb_s, intersect_s = sphere_intersections(
          z, d, trust_radius, entire_line
      )
      ta = np.maximum(ta_b, ta_s)
      tb = np.minimum(tb_b, tb_s)
      if intersect_b and intersect_s and ta <= tb:
          intersect = True
      else:
          intersect = False
  
      if extra_info:
          sphere_info = {
              "ta": ta_s,
              "tb": tb_s,
              "intersect": intersect_s,
          }
          box_info = {"ta": ta_b, "tb": tb_b, "intersect": intersect_b}
          return ta, tb, intersect, sphere_info, box_info
      else:
          return ta, tb, intersect
  
file_path: catboost/contrib/python/scipy/py3/scipy/optimize/_trustregion_constr/qp_subproblem.py
imports: from scipy.sparse import linalg, bmat, csc_matrix
  from math import copysign
  import numpy
  from numpy.linalg import norm
label_desc: Use image node_id 4 for calling a global function with example usage: box_sphere_intersections(z, d, lb, ub, trust_radius, entire_line, extra_info) and returns: ta,  tb,  intersect,  sphere_info,  box_info, ta,  tb,  intersect