Project 1: Matrix Addition And Multiplication Task 1 Ba

Project 1 Matrix Addition And Matrix Multiplicationtask 1 Basic M

This assignment involves developing CUDA programs to perform matrix addition and matrix multiplication for two-dimensional matrices. The task requires implementing both GPU-based and CPU-based computations, then comparing their results to ensure correctness. Specifically, you will write CUDA kernels to add and multiply matrices in parallel on the GPU, transfer the results back to the CPU, and verify that the GPU results match those computed on the CPU. Successful verification results in a "Test PASSED" message. Additionally, students must initialize matrices according to given pseudo code, select specified matrix sizes and thread block configurations for testing, and prepare comprehensive documentation including source codes, a README, and a report detailing functionalities and execution evidence. The project emphasizes proper environment setup on the provided UNIX server, code submission via specified channels, and adherence to academic integrity standards.

Paper For Above instruction

Matrix operations are fundamental in computational mathematics and are extensively used in scientific computing, machine learning, computer graphics, and data analysis. The efficient implementation of matrix addition and multiplication on parallel architectures like GPUs accelerates computational workloads dramatically. This paper discusses the development of CUDA-based programs to perform matrix addition and multiplication, alongside CPU implementations, with a focus on correctness verification, optimized parallel execution, and systematic testing.

Matrix addition is a straightforward operation, involving element-wise summation of two matrices. The CUDA implementation involves launching a kernel where each thread computes the sum for one element of the result matrix. Properly configuring grid and block dimensions ensures that all elements are processed efficiently, while boundary checks prevent memory access violations. The provided pseudo code for the GPU kernel demonstrates this approach: each thread calculates its row and column indices based on thread and block IDs, then adds corresponding elements if indices are within bounds.

Similarly, matrix multiplication is more complex due to the nested loop structure requiring summing the product of respective row and column elements. The CUDA kernel for multiplication assigns each thread to compute one element of the product matrix, iterating over the corresponding row and column to perform dot product calculations. Ensuring correct synchronization and efficient memory access patterns is critical for optimal performance. The pseudo code outlines the kernel’s logic, emphasizing boundary checks and the accumulation process.

Matrix initialization follows a pseudo code that fills matrices with values derived from modular arithmetic and scaling, producing deterministic yet varied data for testing. The choice of matrix sizes—such as 128x128—along with thread block configurations like 8x8 or 16x16, influences execution efficiency and debugging ease. These configurations are crucial, as they impact the kernel’s parallelism, occupancy, and overall runtime.

Practical implementation demands familiarity with the CUDA programming environment and remote server setup. Students are instructed to connect to the Unix server fry.cs.wright.edu via SSH, using secure clients like PuTTY or through campus Wi-Fi. After editing code locally with tools like Notepad++, files are transferred securely using WinSCP. Compilation employs the NVIDIA CUDA compiler (nvcc), and execution is managed on GPU nodes accessed via specific srun commands. This systematic workflow ensures that code execution and testing are conducted in a standardized production environment.

Verification of GPU results involves comparing the output matrices with CPU-computed counterparts. The CPU implementations are straightforward, utilizing nested loops to calculate the same operations sequentially. For addition, the pseudo code iterates over each element, summing corresponding elements from matrices A and B. For multiplication, a triple-nested loop computes the dot products, filling the product matrix P. Correctness is asserted if all elements match, triggering confirmation messages. Discrepancies highlight potential coding errors or boundary violations, requiring debugging.

Thorough documentation encompasses source code files, a README clarifying compilation and execution steps, and a detailed report evaluating functionality, efficiency, and any unimplemented features. Screenshots and output logs substantiate successful operation. Proper formatting, inclusion of course details, personal identifiers, and adherence to submission guidelines are mandatory, with penalties for omissions.

In conclusion, CUDA programming for matrix operations offers significant performance gains but demands precision in kernel design, memory management, and environment setup. This project integrates theoretical knowledge with practical skills, preparing students for real-world high-performance computing challenges inherent in scientific software development. Mastery of this material enables scalable solutions to computationally intensive problems, underpinning advances across numerous technological domains.

References

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• NVIDIA Corporation. (2020). CUDA C Programming Guide. NVIDIA. Retrieved from https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html
• Glaser, S., & Mueller, S. (2019). Parallel Programming with CUDA. IEEE Computing in Science & Engineering, 21(6), 85-95.
• Zhao, J., & Lee, J. (2018). Efficient GPU-based Matrix Multiplication. Journal of Parallel and Distributed Computing, 119, 1-11.
• Sanders, J., & Kandrot, E. (2010). CUDA by Example: An Introduction to General-Purpose GPU Programming. Addison-Wesley.
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• Booth, R., & Lee, H. (2017). CUDA Programming for High-Performance Scientific Computing. CRC Press.
• Fang, H., & Madduri, K. (2020). Parallel Sparse Matrix-Vector Multiplication for GPUs. IEEE Transactions on Parallel and Distributed Systems, 31(4), 929-943.
• Williams, S., et al. (2009). Analyzing the Parallel Performance of CUDA Kernels. Proceedings of the ACM International Conference on Supercomputing, 101-110.