2. Toy Examples

2.1. Univariate Polynomials

The below plots are generated by calling the following lines of code. You can find the full code in the __main__ section of the corresponding module.

lifter = Poly4Lifter.create_example(example_type="A")  # choose A or B
lifter.plot_cost()

class popcor.examples.Poly4Lifter

Bases: PolyLifter

Fourth-degree polynomial lifter.

Two example types are provided and selected with create_example(example_type=…).

• example_type=”A”: one global minimum at -1, one local minimum at 2.

• example_type=”B”: two global minima at 1 and 3.

Poly4Lifter Type A

Poly4Lifter Type B

class popcor.examples.Poly6Lifter

Bases: PolyLifter

Sixth-degree polynomial examples.

Two example types are provided and selected with create_example(example_type=…).

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

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

Poly6Lifter Type A

Poly6Lifter Type B

2.2. Other Toy Examples

class popcor.examples.Stereo1DLifter(n_landmarks: int, param_level: str = '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.