sphere_intersections(z, d, trust_radius, entire_line=False)

Find the intersection between the segment (or line) defined by the parametric equation x(t) = z + t*d and the ball ||x|| <= trust_radius .

Parameters

z : array_like, shape (n,)

Initial point.

d : array_like, shape (n,)

Direction.

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 ball ||x|| <= trust_radius . When False , the function returns the intersection between the segment x(t) = z + t*d , 0 <= t <= 1 , and the ball.

Returns

ta, tb : float

The line/segment x(t) = z + t*d is inside the ball for for ta <= t <= tb .

intersect : bool

When True , there is a intersection between the line/segment and the sphere. On the other hand, when False , there is no intersection.

Find the intersection between segment (or line) and spherical constraints.

Examples

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

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GitHub : /scipy/optimize/_trustregion_constr/qp_subproblem.py#65
type: <class 'function'>
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