CUDA Implementation and Optimization for PCA

I have an existing project that requires a clear implementation of my algorithm (PCA for Image Compression). The project already contains source code for Pthreads, MPI, and serial. Your task will be to maintain the structure of the project while implementing CUDA, CUDA + MPI, and conducting an overall correctness check for all the existing code.

Key Responsibilities:
- Implement the algorithm using CUDA and CUDA + MPI
- Ensure a high level of performance optimization
- Maintain code readability and comments throughout the implementation
- Conduct correctness checks

The primary goal of this project is to leverage parallel processing capabilities of CUDA to enhance the performance of the algorithm.

Ideal Skills:
- Extensive experience with CUDA and CUDA + MPI
- Proficiency in performance optimization techniques
- Ability to maintain code readability and comments
- Experience with Pthreads and MPI

Please note, while performance optimization is the highest priority, code readability and thorough commenting are also important to maintain the integrity of the project structure. Your ability to balance these aspects will be crucial for the success of this project.