Update examples readmes

examples/README.md

@@ -1,6 +1,10 @@
 # Examples
 
-You will find two Jupyter notebooks in this folder:
+You will find three Jupyter notebooks in this folder:
 
+- `associative_scan.ipynb` plots the speedup of the associative scan algorithm implemented in `thermox` using a GPU.
 - `diffrax_comparison.ipynb` runs a simple OU process using `thermox` and [`diffrax`](https://github.com/patrick-kidger/diffrax) and compares runtimes (showing a large benefit from using `thermox` for long simulation times)
-- `thermodynamic_linear_algebra.ipynb` is a small tutorial on how to use functions from the `thermox.linalg` module.
+- `thermodynamic_linear_algebra.ipynb` is a small tutorial on how to use functions from the `thermox.linalg` module.
+
+Additionally the `matrix_exponentials` folder contains code for reproducing the simulations 
+in the [thermodynamic matrix exponentials paper](https://arxiv.org/abs/2311.12759).

examples/matrix_exponentials/README.md

@@ -0,0 +1,17 @@
+# Thermodynamic Matrix Exponentials Simulations
+
+This folder contains code to replicate the convergence time simulations in the
+[thermodynamic matrix exponentials paper](https://arxiv.org/abs/2311.12759).
+
+The script `run.py` contains the code to run the simulations and can be executed with 
+e.g. the following command from the root of the repository:
+```bash
+PYTHONPATH=. python examples/matrix_exponentials/run.py --n_repeats=10 --matrix_type=orthogonal --alpha=1.1   
+```
+where `--matrix_type` represents a function in `matrix_generation.py`.
+
+The script `plot.py` contains the code to plot the results of the simulations and can be executed with e.g. the following command from the root of the repository:
+```bash
+PYTHONPATH=. python  examples/matrix_exponentials/plot.py --save_dir=examples/matrix_exponentials/results_orthogonal.pkl
+```
+