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Define an empty MultiIndexSet instance.

Damar Wicaksono requested to merge dev-132 into dev

An empty MultiIndexSet instance has an empty array as its exponents. It can be created by passing an empty two-dimensional array to the default constructor. Such a set has an lp-degree that is defined during construction; its spatial dimension, however, may be 0.

The properties of such a set are as follows:

  • exponents: a two-dimensional empty array as specified.
  • lp_degree: as specified during construction (float).
  • poly_degree: None (it cannot be computed).
  • spatial_dimension: according to the value of the second dimension of the given empty array (may be 0, int).
  • is_complete: False a priori.
  • is_downward_closed: False a priori.
  • __len__(): 0 (i.e., zero cardinality).

Empty sets are defined to support further set operations involving MultiIndexSet. Such a set cannot be used to construct polynomials or Grid instances.

This MR should resolve Issue #132 (closed).

Several additional changes:

  • A safeguard is introduced to the constructors of polynomials, Grid, and OrdinaryRegression not to accept an empty set.
  • The test suite for MultiIndexSet is refactored to uniformly use class-based grouping for organization purposes.
  • The same test suite is updated with testing the behavior of all methods involving an empty set.
  • The test suites for polynomials, Grid (newly added), and OrdinaryRegression are updated with testing the construction using an empty set.
Edited by Damar Wicaksono

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