Matrix Multiplication

This project provides a collection of C++ implementations for matrix multiplication, exploring different parallelization strategies and algorithms.

Implementations

The project includes the following implementations:

• Serial: A naive matrix multiplication implementation with loop blocking and SIMD optimizations.
• OpenMP: A parallel version of the naive implementation using OpenMP for shared-memory parallelism.
• MPI: A parallel version of the naive implementation using MPI for distributed-memory parallelism.
• Hybrid (MPI + OpenMP): A hybrid version combining MPI and OpenMP for parallelism.
• Strassen's Algorithm: A serial implementation of Strassen's algorithm, a recursive method for faster matrix multiplication.
• Strassen's Algorithm with OpenMP: A parallel version of Strassen's algorithm using OpenMP.
• Strassen's Algorithm with MPI: A parallel version of Strassen's algorithm using MPI.
• Strassen's Algorithm with Hybrid (MPI + OpenMP): A hybrid version of Strassen's algorithm combining MPI and OpenMP.

Prerequisites

• A C++23 compatible compiler (e.g., g++-15 or newer)
• OpenMP
• An MPI implementation (e.g., Open MPI)
• Eigen3 library (for testing)

How to Build

First install Eigen3 lib, and add the lib to Makefile, or export as environment variable

export EIGEN=path-to-lib

To build all the test executables, run:

make all

This will create the following executables in the bin/ directory:

• test_serial
• test_omp
• test_mpi
• test_hybrid

How to Run

You can run the tests using the make command. The default matrix size is 1000x1000, but you can change it by passing the N variable.

• Serial:

  make run_test_serial N=2000

• OpenMP:

  make run_test_omp N=2000

• MPI:

  make run_test_mpi N=2000

  This will run with 4 MPI processes by default.

• Hybrid (MPI + OpenMP):

  make run_test_hybrid N=2000

  This will run with 4 MPI processes by default.

How to Test

To run all the tests with a specific matrix size:

make test N=500