Matrix-Vector Multiplication with MPI

This repository is part of the features2 module in the matvet-team-10 project. It implements matrix-vector multiplication using MPI (Message Passing Interface) to parallelize the computation, enhancing performance and scalability.

What It Does

Initialization

• A random matrix (A) and vector (x) are created on the main process (rank 0).
• The matrix and vector are distributed to all processes using MPI_Bcast.

Parallel Computation

• Matrix rows are split among the processes.
• Each process computes the dot products for its assigned rows with the vector.

Gathering Results

• Results from all processes are combined using MPI_Reduce.

Testing

• Both row-major and column-major layouts are tested for performance and correctness.
• Computation times for each layout are measured.

Why Use MPI?

• Scalability: Supports larger matrices by leveraging multiple processes and machines.
• Efficiency: Parallel computation reduces processing time.
• Optimization: Minimizes inter-process communication delays with MPI.

Repository Structure

• src/main_Pmatrix.cpp: The main program that implements matrix-vector multiplication.
• src/MatrixTest.hpp: Header file defining the MatrixTest class.
• examples/: Directory for sample test cases and outputs.
• Makefile: Simplifies the compilation process.

Compilation

To compile the program, use:

make

Running the Program

Default execution:

./main_Pmatrix --dense

Specify the number of MPI processes:

mpirun -n <number_of_processes> ./main_Pmatrix --dense

Example:

mpirun -n 4 ./main_Pmatrix --dense

Example Output

Row-Major Test:

Final result vector y: [290, 321, 308, ...]
Computation time: 7.851e-06 seconds

Column-Major Test:

Final result vector y: [290, 321, 308, ...]
Computation time: 5.579e-06 seconds

Performance Notes

• Correctness: Both row-major and column-major tests produce identical results.
• Computation Time: Column-major layout demonstrates slightly better performance, potentially due to better cache utilization.

How It Works

• The MatrixTest class handles matrix initialization, computation, and testing.
• Parallelism is achieved through MPI functions like MPI_Bcast and MPI_Reduce.