pyuncertainnumber.calibration.data_peeling.scenario
===================================================

.. py:module:: pyuncertainnumber.calibration.data_peeling.scenario

.. autoapi-nested-parse::

   Solution to the scenario optimization problem for enclosing sets.

   A scenario optimization inputs (1) a table of observations i.e. an (nxd) array, and (2) a shape.

   In general, a scenario program should output three data structures:

   (1) A list of integers pointing to the support vectors in the data set;
   (2) A data structure representing the set if parametric, e.g. a box, a circle, an ellipse.
   (3) A function or object representing the optimal set. For example, the function/method returns true if evaluated inside the set and false otherwise.



Attributes
----------

.. autoapisummary::

   pyuncertainnumber.calibration.data_peeling.scenario.bet


Functions
---------

.. autoapisummary::

   pyuncertainnumber.calibration.data_peeling.scenario.minimal_enclosing_hyperbox
   pyuncertainnumber.calibration.data_peeling.scenario.is_inside_box
   pyuncertainnumber.calibration.data_peeling.scenario.epsLU


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

.. py:function:: minimal_enclosing_hyperbox(x)

   Inputs
   x: (nxd) array, where n is the size of the data, and d is the number of dimensions of the box

   Outputs
   active_scenarios: list[int], a list of integers pointing to the corresponding active scenarios in the dataset
   box: 2xd array, an enclosing box of dimension d.


.. py:function:: is_inside_box(x, abox)

   x:    (nxd) array
   abox: (dx2) array, or list[list[2 float]] ex.: [[0,1],[3,8],[1,9]] <- a.k.a. interval iterable


.. py:function:: epsLU(k, N, bet)

   Port of the MATLAB code provided by the Authors.

   %% Reference Article
   % Title Risk and complexity in scenario optimization
   % Authors S. Garatti and ·M. C. Campi
   % Journal Mathematical Programming
   % DOI https://doi.org/10.1007/s10107-019-01446-4

   % This function provide the lower and upper reliability parameter for a
   % convex program as defined in Eq (14) of the refernced paper

   % N= number of samples
   % k = Number of scenarios \delta_i for which \zeta_i \geq 0, i.e.  f(x,\delta_i) \geq 0
   % beta = confidence parameter (e.g. very high confidence beta=10^-8)



.. py:data:: bet
   :value: 0.1