instructions added to run the algorithms

README.md

@@ -1,8 +1,36 @@
 # ShfitedPowGMRES
 
-Work in progress. In the actual version, the `main.py` works but only for the Algorithm 1 of the paper. It's suggested to use the first database.
+> Relation of the project: [view](https://github.com/lukefleed/ShfitedPowGMRES/blob/main/tex/main.pdf) / [download](https://github.com/lukefleed/ShfitedPowGMRES/raw/main/tex/main.pdf)
 
-### TO DO:
+This repository contains the code of my attempt to replicate the results obtained in `[1]`. The scripts are all written in python and are heavily build around the libraries SciPy and NumPy. To install all the required packages with `pip` run the following command in terminal
 
-- [ ] Add the other algorithms
-- [ ] Use argparse to make the code more flexible in `load_data()`
+```bash
+pip install -r requirements.txt
+```
+
+At the moment, the standard and shifted power method to compute the PageRank with multiple damping factors are fully implemented (as described in `[1]`). To run the program, go into the folder `src/` and execute the `./main.py` file. It takes as input two arguments:
+
+- `--dataset`: the options are `BerkStan` and `Stanford`. This commands selects the web-graph to run the algorithms on. 
+- `--algo`: the options are `power`, `shifted`, `both`. If you choose the last option, it will first run the standard power method and then the shifted one. 
+
+Here an example of what's described above.
+
+```bash
+cd src
+sudo chmod +x main.py
+```
+
+Now we can run the program
+
+```bash
+./main.py --dataset Stanford --algo both
+```
+
+## Under development 
+
+In the `testing/` folder there are two python notebook that contains the attempt on replicating the results obtained in `[1]` for the shifted GMRES method. The implementation of the Arnoldi process is fully working. On the other hand, there are several problems on the shifted GMRES algorithm that I can't figure out.  
+
+
+## References
+
+`[1]` _Zhao-Li Shen, Meng Su, Bruno Carpentieri, and Chun Wen. Shifted power-gmres method accelerated by extrapolation for solving pagerank with multiple damping factors. Applied Mathematics and Computation, 420:126799, 2022_