A Gravity Model probability distribution implementation in Java. The GravityModelDistribution is initialized by providing one or more bodies to consider. A body has an item which it represents, a mass, and a spatial location in N-Dimensional space. Given a reference body at some location, the GravityModelDistribution implements a categorical probability distribution over the bodies, where the weights for each body are determined by the amount of gravitational force they exert on the reference body. If the reference point has an identical location to a body in the distribution (or if it simply is one of the bodies in the distribution), the body has a probability of 0 of being selected.
The bodies need not represent physical bodies such as planetary bodies, but can represent any object that has a location in real or abstract space, and some abstract concept of "mass". For example, the motivation for this code was selecting a random city where the "mass" is a city's population.
GravityModelDistribution is a totally standalone Java application with no dependencies.
This repository includes basic implementations of 1D, 2D, and 3D bodies, as well as a GIS body type that uses the Haversine formula for precise distances along the earth's surface at the cost of increased computational demands. For each of these, there is also a convenience class called Simple[X]GravityModelDistribution to reduce the number of type parameters compared to raw use of the class. It also has two separate implementations of the GravityModelDistribution interface described below:
SimpleGravityModelDistribution is a simple O(N) computation over all bodies, parallelized with Streams for quick execution. This implementation could be easily extended by implementing a new Body type for your use case, such as computing the gravity model in higher dimensions.
QuadtreeGravityModelDistribution uses a Quadtree and a variation on the Barnes-Hut algorithm to approximate the distribution and perform better with a large number of bodies. Due to the nature of Quadtrees, this implementation only works in 2D space. So far, test results have been disappointing and it has served as a poor approximation of the distribution unless the parameter theta is effectively zero. The performance tends to be far worse than SimpleGravityModelDistribution in all cases tested, and it is highly recommended to avoid this implementation.
This code creates bodies on each corner of a square centred on (0, 0) with side length 10 with values of 0, 1, 2, and 3; and masses of 0, 100, 200, and 300, respectively. It then queries the distribution for a point at the centre (0, 0). The resulting distribution is a categorical distribution with probabilities [0, 1/6, 1/3, 1/2], but will change if queried for a different point.
public static void main(String[] args) {
List<Body2D<Integer>> bodies = List.of(
new Body2D<>(0, -10, 10, 0),
new Body2D<>(100, 10, -10, 1),
new Body2D<>(200, 10, 10, 2),
new Body2D<>(300, -10, -10, 3)
);
Body2D<Integer> ref = new Body2D<>(1.0, 0, 0, null);
Simple2DGravityModelDistribution<Integer> dist = new Simple2DGravityModelDistribution<>(bodies);
Body2D<Integer> rand = dist.getRandomBody(ref);
}