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# 计算机代写|基础编程代写Fundamental of Programming代考|ECE217 Analysis Benchmarks Group A

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## 计算机代写|基础编程代写Fundamental of Programming代考|Analysis Benchmarks Group A

test_A_01 $y=2.5 \cdot \operatorname{mean}\left(\boldsymbol{v}_1\right)$
V: $100 \% \mathrm{~A}: 100 \% \mathrm{U}: 12 \%$
This very simple benchmark is designed as a proof of concept for vectorial GP, which could be solved by the vector variant and the pre-aggregated variant easily. However, the unrolled variant has to perform the mean aggregation manually by summing all individual variables and dividing by the number of variables. Since for the benchmarks the vectors contain 20 values, 20 individual variables have to be summed, which is already difficult for standard GP, hence the low success rate of $12 \%$.
test_A_02 $y=\operatorname{std}\left(\boldsymbol{v}_1\right)-2$
V: $100 \% \mathrm{~A}: 100 \% \mathrm{U}: 0 \%$
Complexity-wise, this instance is similar to the previous one, but using the standard deviation for aggregation. This is still easily solvable with the vector variant by using the standard deviation aggregation function or with the pre-aggregated variant by using the already pre-calculated standard deviation. However, the equation for calculating the standard deviation of 20 values manually is quite challenging for GP. For this calculation, the deviation of each value to the mean is required first, meaning that the mean of the 20 values has to be calculated beforehand, and since the treebased models cannot store the mean for multiple use, it has to be recalculated 20 times. Therefore, the unrolled variant was not able to solve this benchmark.

## 计算机代写|基础编程代写Fundamental of Programming代考|Analysis Benchmarks Group B

test_B_01 $y=x_1 \cdot \operatorname{mean}\left(\boldsymbol{v}{\mathbf{1}}+\boldsymbol{v}{\mathbf{2}}\right)$
V: $100 \%$ A: $100 \% \mathrm{U}: 0 \%$
This instance requires a mean aggregation of the sum of two vectors. Because, the expected value of the sum of two random variables is the sum of the expected values, i.e. $E[X+Y]=E[X]+E[Y]$, this instance can both be solved by the vector variant and the aggregated variant. The vector variant can either calculate the sum of the vectors first, and then calculate the mean, or calculate the mean of the vector separately and them sum the means. The pre-aggregated variant always can simply add the pre-calculated means of the vectors. With sufficiently sized trees, the unrolled variant should also be able to solve this, however, would require considerable more resources and would result in a very large model.
test_B_02 $y=x_1 \cdot \operatorname{mean}\left(\boldsymbol{v}_1 \cdot \boldsymbol{v}_2\right)$
V: $100 \%$ A: $0 \% \mathrm{U}: 0 \%$
This instance is similar to the previous test_B_01, however the mean of the product of two vectors is used. In general, the expected value of the product of two random variables is not equal the product of the expected value, i.e. $E[X \cdot Y] \neq E[X] \cdot E[Y]$, thus, the pre-aggregated variant is not able to solve this instance completely because multiplying the pre-calculated means does not yield the correct result. In cases where the two vectors are completely independent from each other, the expected value of the product would be equal to the product of the expected value. Although the data for the benchmarks is generated randomly, there is still some very small, random correlation, i.e. $|\operatorname{Cov}[X, Y]|>0$, therefore the instance could not be solved according to the defined success-threshold of $N M S E<10^{-4}$. For real-world application, however, it is to be expected that measured signals of a system are connected and therefore will rarely be complete independent from each other, meaning that pre-aggregating vector data into scalars would not be able to maintain the relevant information to solve such a case.

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MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。