# Parallel matrix multiplication

Performance tests for parallel matrix multiplication algorithms.

## Usage

1. Install the required python libraries, found in `requirements.txt`. The following command shows how to do it using `pip`, but `conda` or any package manager can also be used.

```shell
pip install -r requirements.txt
```

2. Build the matrix multiplication executables using `make`.

```shell
cd MatMult
make
```

3. Run the experiments using the launcher.

```shell
cd ..
python launcher.py experiments.csv
```

4. Generate the graphics, using the results of the experiments from every machine.

```shell
python graphics.py experiments1.csv experiments2.csv experiments3.csv -o img/
```

## Results

The experimentation results are summarized in the following figures.

![Matrix size vs Time line plot](img/size-time.png)
![Threads vs Time line plot](img/threads-time.png)
![Matrix size vs Threads heatmap](img/size-threads-time.png)
![Matrix size vs Threads heatmap](img/distribution.png)

In this case, the experiments were run in 3 different machines:

- A ml.c5.9xlarge AWS instance, with 36 vCPUs and 72 GiB RAM.
- A ml.m5.8xlarge AWS instance, with 32 vCPUs and 128 GiB RAM.
- A ml.r5.8xlarge AWS instance, with 32 vCPUs and 128 GiB RAM.

Every matrix size - number of threads combination was executed 30 times, in order to make the experiments statistically significant. The values in the graphics represent the mean values of those 30 repetitions.

### Metrics

The following metrics summarize the experimentation results, regarding the algorithms performance for different number of threads:

- Speed up: $$Sp = \frac{t_{serial}}{t_{parallel}}$$

![SpeedUp](img/speedup.png)

- Efficiency: $$Ep = \frac{Sp}{p}$$

![Efficiency](img/efficiency.png)