R Data Types - Part 1: Basis, Vectors, Matrices & Lists

参照 R Programming slides on cousera (pdf)，作总结。

部分更新来自 R Cookbook。

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1. Data Type 基础

1.1 Atomic Classes

R has 5 atomic classes

• character
• numeric (real numbers，实数，双精度 double)
  • Inf represents infinity; e.g. 1 / 0;
  • Inf can be used in ordinary calculations; e.g. 1 / Inf == 0
  • NaN represents an undefined value (“not a number”); e.g. 0 / 0
• integer（整数）
  • 1 默认是 numeric
  • 1L 才是 integer（L 应该是指 long）
• complex（复数）
  • 比如 2+4i
• logical (boolean; TRUE & FALSE，可以简写成 T & F; 另外还有 NA 值)

1.2 Basic Objects

• The most basic object is a vector
  • A vector can only contain objects of the same class
• list is represented as a vector, but can contain objects of different classes
  • Technically, lists are vectors. 因为 is.vector(list()) == TRUE。但 is.list(vector()) == FALSE

1.3 Attributes

R objects can have attributes：

• names, dimnames
• dimensions (e.g. matrices, arrays)
• class
• length
• other user-defined attributes/metadata

Attributes of an object can be accessed using the attributes() function.

2. Vectors

2.1 Creating Vectors

• Empty vectors can be created with the vector() function.
• x <- vector("numeric", length = 10) 产生 10 个 0
  • 或者用 x <- rep(0, times = 10) 也可以
• x <- 9:29 产生 [9, 29] 的整数序列
  • 其实也可以产生实数序列，比如: pi:10 产生 3.141593 4.141593 5.141593 6.141593 7.141593 8.141593 9.141593
• x <- c(xxx, yyy, zzz, ...) 接收变长参数列表填到 vector

2.2 Vector Element Coercion

When different objects are mixed in a vector, coercion occurs so that every element in the vector is of the same class. e.g. y <- c(1.7, "a") ## class(y) 得到的是 character

Explicit Coercion 可以理解为强制类型转换，比如 as.numeric(x)、as.logical(x)、as.character(x)、as.complex(x)

2.3 Element Index

• x[1:10] 返回前 10 个 元素
• x[!is.na(x)] 返回所有不是 NA 的元素
• x[x>0] 返回所有大于 0 的元素
• x[c(-2, -10)] 或者 x[-c(2, 10)] gives us all elements of x EXCEPT for the 2nd and 10 elements
• x["bar"] 获取 name 为 bar 的元素

3. Matrices [‘meɪtrɪsi:z] (matrix [ˈmeɪtrɪks])

Matrices are vectors with a dimension attribute.

3.1 直接创建 matrix

m <- matrix(nrow = 2, ncol = 3) 产生一个 2 行 3 列的矩阵，初始值都是 NA。矩阵的记法是 “行” 在前 “列” 在后，所以 2 行 3 列记作 2x3 矩阵，英文叫 2 by 3 matrix。

dim(m) 返回一个 c(nrow, ncol)

Matrices are constructed column-wise, so entries scan be thought of starting in the “upper left” corner and running down the columns.

> m <- matrix(1:6, nrow = 2, ncol = 3)
> m
	 [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6

Observe that the matrix was filled column by column, not row by row. 不过可以指定 byrow=TRUE:

> m <- matrix(1:6, nrow = 2, ncol = 3, byrow = TRUE) 
> m
	 [,1] [,2] [,3]
[1,]    1    2    3
[2,]    4    5    6

If the first argument of matrix is a single value, then R will apply the Recycling Rule and automatically replicate the value to fill the entire matrix:

> matrix(0, 2, 3) # Create an all-zeros matrix
	 [,1] [,2] [,3]
[1,]    0    0    0
[2,]    0    0    0

3.2 间接创建 matrix

Matrices can also be created directly from vectors by adding a dimension attribute.

> m <- 1:10 
> m
[1] 1 2 3 4 5 6 7 8 9 10 
> dim(m) <- c(2, 5) ## 改成一个 2x5 矩阵
> m
	 [,1] [,2] [,3] [,4] [,5]
[1,]    1    3    5    7    9
[2,]    2    4    6    8   10

Matrices can be created by column-binding or row-binding with cbind() and rbind().

> x <- 1:3
> y <- 10:12
> cbind(x, y) ## 可以理解为 bind by column
	 x y 
[1,] 1 10 
[2,] 2 11 
[3,] 3 12
> rbind(x, y) ## 可以理解为 bind by row
  [,1] [,2] [,3]
x    1    2    3
y   10   11   12

但是要注意一点：R will repeat the shorter column or row to make the matrix:

> rbind(x=1:6, y=10:12)
  [,1] [,2] [,3] [,4] [,5] [,6]
x    1    2    3    4    5    6
y   10   11   12   10   11   12

> cbind(x=1:3, y=4:5)
	 x y
[1,] 1 4
[2,] 2 5
[3,] 3 4

3.3 Matrix Operations

• A * B: Element-wise multiplication
• A %*% B: Matrix multiplication of $ A $ and $ B $
• t(A): Transposition of $ A $, i.e. $ A^t $
• solve(A): Inverse of $ A $, i.e. $ A^{-1} $, where $ A $ is a square matrix
• det(A): Determinant of $ A $
• matA <- qr(A); matA$rank: Rank of $ A $
• diag(n): An n-by-n diagonal (identity) matrix

• a <- c(1,2,3); A <- matrix(a): 把 vector $ a $ 转成一个 matrix
  • 严格来说，vector 应该看做是 nx1，虽然我总是看成 1xn
  • 但是不管你看成 nx1 还是 nx1，你什么参数都不加，直接把 vector 转成 matrix 一定会是一个 nx1，所以你也就不用费力气去加个 t() 操作了
• a <- as.vector(A): 把 matrix $ A $ 转成一个 vector
  • 从 column 1 开始扫描，逐个元素填到 vector；然后扫描 column 2、column 3……
  • 如果你想从 row 1 开始扫描，可以用 as.vector(t(A))

更多请参考：

• Matrix Operations in R
• Quick-R: Matrix Algebra

4. Lists

x <- list(1, "a", TRUE, 1 + 4i) 创建一个 list。注意：

• x[[1]] == 1 ## 获取第一个元素
• x[1] == list(1) ## returns a list of the selected elements

在使用 column name 来 access 的时候也有同样的问题，比如我们定义 x <- list(first=1, second=2)，有

• x[["first"]] == 1 ## 获取第一个元素
• x["first"] == list(1) ## returns a list of the selected elements

4.1 Using unlist to Flatten a List into a Vector

There are many contexts that require a vector. Basic statistical function, say, mean, works on vectors but not on lists, for example. Instead, we must flatten the list into a vector using unlist and then compute the mean of the result:

grade = list(88,92,96)

mean(grade)
[1] NA
Warning message:
In mean.default(grade) : argument is not numeric or logical: returning NA

mean(unlist(grade))
[1] 92

4.2 Removing NULL Elements from a List

有点高端的写法：

lst[sapply(lst, is.null)] <- NULL

4.3 Removing Elements Whose abs < 1

The simplest solution is flattening the list into a vector by calling unlist and then testing the vector:

lst[abs(unlist(lst)) < 1] <- NULL

A more elegant solution uses lapply to apply the function to every element of the list:

lst[lapply(lst,abs) < 1] <- NULL