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# 统计代写|R语言代写r project代考|STA518 Defining functions and operators

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## 统计代写|R语言代写r project代考|Defining functions and operators

Abstraction can be defined as separating the fundamental properties from the accidental ones. Say obtaining the mean from a given vector of numbers is an actual operation. There can be many such operations on different numeric vectors, each one a specific case. When we describe an algorithm for computing the mean from any numeric vector we have created the abstraction of mean. In the same way, each time we separate operations from specific data we create a new abstraction. In this sense, functions are abstractions of operations or actions; they are like “verbs” describing actions separately from actors.

The main role of functions is that of providing an abstraction allowing us to avoid repeating blocks of code (groups of statements) applying the same operations on different data. The reasons to avoid repetition of similar blocks of code statements are that 1) if the algorithm or implementation needs to be revisede.g., to fix a bug or error-it is best to make edits in a single place; 2) sooner or later pieces of repeated code can become different leading to inconsistencies and hard-to-track bugs; 3) abstraction and division of a problem into smaller chunks, greatly helps with keeping the code understandable to humans; 4) textual repetition makes the script file longer, and this makes debugging, commenting, etc., more tedious, and error prone.

How do we, in practice, avoid repeating bits of code? We write a function containing the statements that we would need to repeat, and later we call (“use”) the function in their place. We have been calling R functions or operators in almost every example in this book; what we will next tackle is how to define new functions of our own.

New functions and operators are defined using function function(), and saved like any other object in $\mathrm{R}$ by assignment to a variable name. In the example below, $\mathrm{x}$ and $\mathrm{y}$ are both formal parameters, or names used within the function for objects that will be supplied as arguments when the function is called. One can think of parameter names as placeholders for actual values to be supplied as arguments when calling the function.

## 统计代写|R语言代写r project代考|Ordinary functions

After the toy examples above, we will define a small but useful function: a function for calculating the standard error of the mean from a numeric vector. The standard error is given by $S_{\hat{x}}=\sqrt{S^2 / n}$. We can translate this into the definition of an $\mathrm{R}$ function called SEM.
$$\text { SEM <- function }(x){\operatorname{sqrt}(\operatorname{var}(\mathrm{x}) / \text { length }(\mathrm{x}))}$$
We can test our function.
a <- $c(1,2,3,-5)$
a.na <- c(a, NA)
SEM $(X=a)$
# [1] $1.796988$

SEM(a)
## [1] 1.796988
SEM(a.na)
## [1] NA
For example in SEM(a) we are calling function SEM() with a as an argument. The function we defined above will always give the correct answer because NA values in the input will always result in an NA being returned. The problem is that unlike R’s functions like var(), there is no option to omit na values in the function we defined.

This could be implemented by adding a second parameter na.omit to the definition of our function and passing its argument to the call to var() within the body of SEM(). However, to avoid returning wrong values we need to make sure na values are also removed before counting the number of observations with length().

A readable way of implementing this in code is to define the function as follows.
sem $<-$ function $(x$, na. omit $=$ FALSE)
if $($ na.omit)
$\quad x<-\operatorname{na} \cdot$ omit $(x)$
}
sqrt $(\operatorname{var}(x) /$ length $(x))$
$\operatorname{sem}(x=a)$
$# #[1] 1.796988$
$\operatorname{sem}(x=a \cdot n a)$
$# #[1]$ NA
sem(x = a.na, na.omit $=$ TRUE)
# [1] 1.796988

## 统计代写|R语言代写r project代考|Ordinary functions

$$\text { SEM }<-\text { function }(x) \operatorname{sqrt}(\operatorname{var}(\mathrm{x}) / \text { length }(\mathrm{x}))$$

\begin{aligned} & \text { 一个<-c }(1,2,3,-5) \ & \text { a.na }<-c(a, \text { NA }) \ & \text { SEM }(X=a) \ & #[1] 1.796988 \ & \text { SEM(a) } \ & # #[1] 1.796988 \ & \text { SEM(a.na) } \ & # #[1] \text { NA } \end{aligned}

\begin{aligned} & \quad x<-\mathrm{na} \cdot \text { 忽略 }(x) \ & } \ & \text { 开方 }(\operatorname{var}(x) / \text { 长度 }(x)) \ & \operatorname{sem}(x=a) \end{aligned}

$\operatorname{sem}(x=a \cdot n a)$

$\operatorname{sem}(x=a$. and ， and . 省略 $=$ 真 $)$
# [1] $1.796988$

## MATLAB代写

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。