# Point processes in Rust
[](https://crates.io/crates/point_process)
[](https://docs.rs/point_process)
[](https://raw.githubusercontent.com/ManifoldFR/point-process-rust/master/LICENSE)
Point processes are stochastic processes with a wide range of applications in seismology, epidemiology, or financial mathematics. They are utilized to model the arrival of random events as a function of time.
This crate provides functions to simulate point processes in [Rust](https://rust-lang.org).
## Time-dependent processes
The following time-dependent point processes have been implemented within the `timedependent` module:
* Poisson point process (homogeneous and inhomogeneous, with custom function)
* Hawkes processes, with the exponential kernel (refer to Dassios and Zhao's 2013 paper [(1)]) 
The API returns the process trajectories as a vector of a `struct` named `Events`, which has the following fields: a timestamp, the current process intensity and a vector holding any children events (for processes with this property, *coming soon*).
## n-dimensional processes
The `generalized` module provides functions for higher-dimensional processes, using [`ndarray`](https://github.com/bluss/ndarray).
For now, only Poisson processes have been implemented.
```rust
fn poisson_process(lambda: f64, domain: &T)
where T: Set -> ndarray::Array<f64, Ix2> {
...
}
fn variable_poisson<F, T>(lambda: F,max_lambda: f64,domain: &T) -> Array2<f64>
where F: Fn(&Array1<f64>) -> f64,
T: Set
{
...
}
```
which takes a reference to a _domain_, that is a subset of n-dimensional space implemented with the `Set` trait (see API docs), and returns a 2-dimensional array which is a set of point events in d-dimensional space falling into the domain.
## Examples
Some examples require milliams' [plotlib](https://github.com/milliams/plotlib) graphing library. To compile them, you'll need to checkout plotlib locally:
```bash
git clone https://github.com/milliams/plotlib
cargo build --example 2d_poisson
```
To run the examples, do for instance
```bash
cargo run --example variable_poisson
```
Some will produce SVG image files in the `examples` directory.
The examples show how to use the API.
[(1)]: http://eprints.lse.ac.uk/51370/1/Dassios_exact_simulation_hawkes.pdf "Exact simulation of Hawkes process with exponentially decaying intensity"
