This repository is the source code accompanying the following papers.
- [An O(n) algorithm for generating uniform random vectors in n-dimensional cones](https://arxiv.org/abs/2101.00936)
- [An algorithm for estimating volumes and other integrals in n dimensions](https://arxiv.org/abs/2007.06808)
  
However, most of the code for [An O(n) algorithm for generating
uniform random vectors in n-dimensional
cones](https://arxiv.org/abs/2101.00936) has been released as a
separate library—sambal. See [PyPI
page](https://pypi.org/project/sambal/) and
[source](https://git.systemreboot.net/sambal).

# Dependencies

The code depends on the following dependencies. Please install them
before running the scripts. A python virtual environment may be an
easy way to do this.

- Python 3
- matplotlib
- numpy
- scipy
- sambal

# Run

The core functions are in `nsmc.py`. The experiments are in the
scripts `distribution-volumes.py`, `distribution-integrals.py` and
`spheroid.py`. Run those scripts as
```
$ python3 distribution-volumes.py
$ python3 distribution-integrals.py
$ python3 spheroid.py
```
Plots of the number of samples versus the dimension get written to the
current directory. Play around with the number of trials, dimensions,
and relative error tolerances in the scripts.