`scipy.optimize._trustregion_constr.qp_subproblem:box_sphere_intersections`

source: /scipy/optimize/_trustregion_constr/qp_subproblem.py :236

Signature

   def     box_sphere_intersections (    z    ,    d    ,    lb    ,    ub    ,    trust_radius    ,    entire_line    =  False   ,    extra_info    =  False     )

Summary

Find the intersection between segment (or line) and box/sphere constraints.

Extended Summary

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 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.

Aliases

scipy.optimize._trustregion_constr.qp_subproblem.box_sphere_intersections