httk.analyse.generic.lower_hull
===============================

.. py:module:: httk.analyse.generic.lower_hull

.. autoapi-nested-parse::

   Generic lower convex-hull analysis for finite point-and-value collections.



Classes
-------

.. autoapisummary::

   httk.analyse.generic.lower_hull.LowerConvexHull


Module Contents
---------------

.. py:class:: LowerConvexHull(points, values, *, tolerance = 1e-08)

   The lower convex hull of scalar values over arbitrary finite coordinates.

   A point belongs to the hull when its value is no greater than the cheapest
   leave-one-out convex mixture at the same coordinates, within ``tolerance``.
   The input order is retained throughout, including for tied duplicate points.

   Coordinates and values are converted through ``numpy.float64`` and exposed as
   ordinary :class:`float` values. Every coordinate equality is retained in the
   mixture LP, together with the affine ``sum(weights) == 1`` equality.

   :param points: Coordinate rows for the input points.
   :param values: Scalar values corresponding to ``points``.
   :param tolerance: Maximum value excess treated as on the lower hull.
   :raises ValueError: If the points, values, or tolerance are invalid.


   .. py:property:: points
      :type: tuple[tuple[float, Ellipsis], Ellipsis]


      Return input coordinates in their original order as float tuples.

      :return: The immutable input coordinate rows.


   .. py:property:: values
      :type: tuple[float, Ellipsis]


      Return input scalar values in the same order as :attr:`points`.

      :return: The immutable input values.


   .. py:property:: hull_indices
      :type: tuple[int, Ellipsis]


      Return indices of points on the lower hull in input order.

      :return: The immutable lower-hull indices.


   .. py:property:: value_above_hull
      :type: tuple[float, Ellipsis]


      Return non-negative leave-one-out value excesses for every input point.

      :return: The immutable value excesses in input order.


   .. py:property:: supported_segments
      :type: tuple[tuple[int, int], Ellipsis]


      Return midpoint-supported pairs of distinct lower-hull points.

      :return: The immutable supported index pairs in input order.


   .. py:method:: decomposition(index)

      Return lower-hull mixture ``(index, weight)`` pairs, or ``None`` on hull.

      :param index: Input point index.
      :return: The stable-point mixture, or ``None`` when the point is on the hull.



   .. py:method:: is_on_hull(index)

      Return whether ``index`` belongs to :attr:`hull_indices`.

      :param index: Input point index.
      :return: Whether the point is on the lower hull.