Suppose You Have A Matrix X With N Rows And N Columns

Question

Suppose You Have A Matrix X With N Rows And N Columns And Another Matr Suppose you have a matrix X with n rows and n columns and another matrix Y with n rows and n columns. Each element in X or Y is a random integer number between 0 and 255. Please write a simple program to compute XY+X (Method 1). Then, please write a parallel computing program defined by yourself using multi-thread CPU to compute XY+X (Method 2). Then, please write another parallel computing program defined by yourself (e.g., using GPU CUDA, or any methods you defined, etc.) to compute X*Y+X (Method 3). Please do the following experiments: When n=24, the running time of Method 1, Method 2 and Method 3. When n=25, the running time of Method 1, Method 2 and Method 3. When n=26, the running time of Method 1, Method 2 and Method 3. ... When n=219, the running time of Method 1, Method 2 and Method 3. When n=220, the running time of Method 1, Method 2 and Method 3. Please make a table and draw the changes of log2 n and the running time of different methods for this experiment. You can use any language (C, C++, JAVA, Python, etc.) to implement the program. The running time does not include the time to generate the random numbers. Final report: >=3 pages, not including the references. In the report, please explain the algorithm flow and implementation details of the three methods, experimental results and your findings. Final submission: source code + report + presentation file.

Dr. Jack HW Helper · Accepted Answer

The task involves implementing three computational methods to multiply and add matrices, and then conducting performance experiments across varying matrix sizes. The three methods include a basic sequential approach, a multi-threaded CPU approach, and a GPU-accelerated approach. This paper delineates the algorithmic flow, implementation nuances, and experimental results, highlighting their comparative efficiencies. Introduction Matrix multiplication is a fundamental operation in numerous fields such as computer graphics, machine learning, and scientific computing. Depending on implementation and hardware utilization, the computation can significantly differ in performance. This study explores three methods—sequential, multi-threaded CPU, and GPU-accelerated—to compute the expression X * Y + X, where X and Y are square matrices populated with random integers between 0 and 255. The primary goal is assessing the computational efficiency across increasing matrix sizes, especially within the range of n=24 to n=220. Methodology Method 1: Sequential Computation The sequential approach involves straightforward execution of matrix multiplication followed by addition. For matrices X and Y, each of size n x n, the calculation implements the classical triple-nested loop approach. The algorithm iterates over each element of the resulting matrix C, computed as C = X * Y + X. Specifically, for each element C[i][j], it computes: C[i][j] = Σ_{k=0}^{n-1} X[i][k] * Y[k][j] + X[i][j] The implementation uses three nested loops over i, j, and k, resulting in a complexity of O(n^3). This method serves as a baseline for measurement. Method 2: Multi-threaded CPU Computation The parallel approach leverages multi-core CPU architectures. Implementation utilizes threading libraries such as OpenMP in C++ or multiprocessing in Python. The common strategy partitions the matrix rows among threads, where each thread computes a subset of the matrix independently. Key points include minimizing thread

Suppose You Have A Matrix X With N Rows And N Columns

Suppose You Have A Matrix X With N Rows And N Columns And Another Matr

Paper For Above instruction

Introduction

Methodology

Method 1: Sequential Computation

Method 2: Multi-threaded CPU Computation

Method 3: GPU-Accelerated Computation

Experimental Design

Results and Analysis

Discussion

Conclusion

References