HPC.ParallelMatrixInversion

In this project, we implemented a parallel matrix inversion algorithm using OpenMP and MPI as part of the High-Performance Computing course at the University of Trento.

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Prerequisites

To run this project, ensure the following packages and tools are installed:

System Packages

• C Compiler: gcc or mpicc with support for C99 or later.
• MPI Library: OpenMPI.
• Python: Python 3.x for Jupyter Notebook.

Install Necessary Packages

Ubuntu/Debian:

sudo apt update
sudo apt install build-essential libopenmpi-dev python3 python3-pip

Fedora:

sudo dnf install gcc openmpi openmpi-devel python3 python3-pip

Arch Linux:

sudo pacman -S gcc openmpi python python-pip

Python Packages for Jupyter Notebook

The Jupyter Notebook (matrix_generator.ipynb) requires the following Python packages:

• numpy
• matplotlib
• jupyter

Install them using pip:

pip install numpy matplotlib jupyter

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Description of Implementations

This project includes three implementations of the matrix inversion algorithm:

1. OpenMP Implementation

   • Main File: main.c
   • Utilizes OpenMP for parallel computation.

2. MPI Implementation

   • Main File: mpi_inverse_main.c
   • Leverages MPI for distributed-memory parallelism.

3. Serial Implementation

   • Main File: main_serial.c
   • Provides a baseline for performance comparison.

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Compiling the Files

1. OpenMP Execution (Main File: main.c)

   mpicc -std=c99 -g -Wall -I./helpers -o main_program ./helpers/common.c ./helpers/file_reader.c matrix_inversion_parallel.c matrix_inversion.c main.c -lm

2. MPI Execution (Main File: mpi_inverse_main.c)

   mpicc -std=c99 -g -Wall -I./helpers -o main_program ./helpers/common.c ./helpers/file_reader.c matrix_inversion_parallel.c matrix_inversion.c mpi_inverse_main.c -lm

3. Serial Execution (Main File: main_serial.c)

   mpicc -std=c99 -g -Wall -fopenmp -I./helpers -o main_program ./helpers/common.c ./helpers/file_reader.c matrix_inversion_parallel.c matrix_inversion.c main_serial.c -lm -pg

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Submitting Jobs to a Cluster

The matrix_inversion.sh script is configured with different values for ncpus as needed. To submit the script to a cluster, use:

qsub matrix_inversion.sh

This command returns a task ID. The resulting output and errors can be found in:

• matrix_inversion.sh.o[task_id]
• matrix_inversion.sh.e[task_id]

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Generating Test Matrices and Performance Metrics

• Copy paste the logs and rename them based on the naming specified in the jupiter notebook
• Matrix Generator: Use the matrix_generator.ipynb notebook to generate test matrices.
• Performance Metrics: Metrics are automatically saved in the Metrics folder after code execution.

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Folder Structure

• Source Files:
  • main.c: OpenMP implementation.
  • mpi_inverse_main.c: MPI implementation.
  • main_serial.c: Serial implementation.
  • helpers/: Contains utility files (common.c, file_reader.c).
• Jupyter Notebook: matrix_generator.ipynb for generating test matrices.
• Metrics Folder: Stores performance metrics.
• Shell Script: matrix_inversion.sh for submitting cluster jobs.

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License

This project is licensed under the MIT License. See the LICENSE file for details.

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