2. Toy Examples

2.1. Univariate Polynomials

class popcor.examples.Poly4Lifter(poly_type='A')

Bases: PolyLifter

Fourth-degree polynomial examples.

Two types are provided:

• poly_type=”A”: one global minimum, one local minimum

• poly_type=”B”: two global minima

Simple univariate polynomial lifter, mostly for testing and pedagogical purposes.

Poly4Lifter Type A

Poly4Lifter Type B

class popcor.examples.Poly6Lifter(poly_type='A')

Bases: PolyLifter

Sixth-degree polynomial examples.

Two types are provided:

• poly_type=”A”: one global minimum, two local minima, 2 local maxima

• poly_type=”B”: one global minimum, one local minimum, one local maximum

Simple univariate polynomial lifter, mostly for testing and pedagogical purposes.

Poly6Lifter Type A

Poly6Lifter Type B

2.2. Other Toy Examples

class popcor.examples.Stereo1DLifter(n_landmarks, param_level='no')

Bases: StateLifter

Toy example for stereo localization in 1D. We minimize the following cost function:

\[f(\theta) = \sum_{j=0}^{N-1} (u_j - 1 / (\theta - a_j))^2\]

where \(a_j\) are the landmarks and \(u_j\) are the measurements.

This is the pedagogical running example of this paper. and also used in the Quick Start Guide.