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通过并行计算进行大规模矩阵计算
假设您有一个 n 行 n 列的矩阵 X 和另一个 n 行 n 列的矩阵 Y。 X 或 Y 中的每个元素都是 0 到 255 之间的随机整数。请编写一个简单的程序来计算 X*X + X*XT + 4*Y*Y（方法 1）。 然后，请编写一个自己定义的并行计算程序来计算X*X + X*XT + 4*Y*Y（方法2）。 请做以下实验：
当n=23时，Method 1和Met ...
Task
Large-scale matrix computation by parallel computing
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 X*X + X*XT + 4*Y*Y (Method 1). Then, please write a parallel computing program defined by yourself to compute X*X + X*XT + 4*Y*Y (Method 2). Please do the following experiments:
When n=23, the running time of Method 1 and Method 2.
When n=24, the running time of Method 1 and Method 2.
When n=25, the running time of Method 1 and Method 2.
When n=214, the running time of Method 1 and Method 2.
When n=215, the running time of Method 1 and Method 2.
XT means the transposed matrix of X, and you can see the following link for the detailed definition: https://mathinsight.org/matrix_transpose
Please make a simple 1-page report (WORD or PDF), including your idea for the parallel computing and a table to show detailed running time of two methods and a figure to show the changes of log2n and the running time of two methods for this experiment. You can use C++ or JAVA or Python programming to implement the source code. The running time does not include the time to generate the random numbers. A video demo is required to show the correctness of your program and your video demo should be less than 40MB.
Final submission: A single zipped file including source code + video demo + report (idea + table + figure).
Grading rubrics:
Hard coding will receive 0 points.
Highly similar code will be considered as plagiarism, which will receive the severe penalty of -200 points. We will use an automatic software to compare the similarity of submitted code for this assignment. So, please do not share your code with any others.
If you are a student from an English-speaking country, please feel free to contact us at [email protected] and we will provide you with an excellent writing service.
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