R01_2 vector.Rmd

---
title: "Basic vector"
author: "Jilung Hsieh"
date: "2018/7/3"
output: 
  html_document: 
    number_sections: true
    highlight: textmate
    theme: spacelab
    toc: yes
editor_options: 
  chunk_output_type: inline
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

# Language

## Assignment

* 將右邊的算式或數值指派給左邊的變數，`<-`可以用`=`單等號來取代，但為了避免混淆，在R中一般都用`<-`。

* 在幾乎所有程式語言中，單等號`=`指的是assignment，把右方的算式、值或物件指給左方的變數。而比較兩者相不相等，則用雙等號`==`，例如`1==3-2`。

```{r}
a <- 1
b <- c(1, 2, 3, 4)
c <- c("1", "2", "3", "4")
d <- c(b, a)
e <- "abcd"
```


## comments 註解

* 在程式碼區塊若前面有`#`字號後面跟著空白的話，那代表那行被標示為註解，程式執行時會自動跳過註解不執行。
* 在RStudio中的快速鍵為選取該行程式碼後打`cmd(ctrl)-shift-c`。

```{r}
# df <- data.frame(a = c(1, 2, 3), b = c(3, 4, 5))
```





# Vector

注意事項：
1. `a <- a[a %% 2 == 0]`當要篩選合乎條件的a時，如果要改變原本的a，就要用assign覆蓋之。
2. `a <- sort(a)`排序後的結果如果要改變原本的a，亦要覆蓋之。
3. 要篩選一個vector中的數值有兩種做法，直接用索引直接指定你要哪幾個，另一個方法是用一個等長的logical vector（TRUE or FALSE）就可以把TRUE的部分選出來。
4. `sort(a)`傳回的是a的數值排序後的結果，`order(a)`傳回的是a由小到大分別在哪幾個位置。



## V1: Creating a Vector

* 資料來源：[台灣出口進口貿易資料查詢](http://cus93.trade.gov.tw/FSC3040F/FSC3040F?menuURL=FSC3040F)

* 在程式碼中，只要是文字必用成對的雙引號或單引號包含其中，以區隔「文字」、「變數」和「數字」。如果看到沒有雙引號的「英文字母」必定是變數名稱，或函式名稱。如果看到有雙引號的數字，那也是文字。

```{r}
country <- c("CN", "US", "JP", "HK", "KR", "SG", "DE", "MY", "VN", "PH", "TH", "AU", "NL", "SA", "ID", "GB", "IN", "FR", "IT", "AE")
p.import <- c(26.142, 12.008, 7.032, 13.646, 4.589, 5.768, 2.131, 2.802, 3.428, 3.019, 1.976, 1.118, 1.624, 0.449, 0.983, 1.302, 1.027, 0.553, 0.670, 0.455)
p.export <- c(22.987, 12.204, 11.837, 7.739, 5.381, 4.610, 2.866, 2.784, 2.414, 2.092, 1.839, 1.788, 1.665, 1.409, 1.391, 1.075, 0.974, 0.899, 0.800, 0.728)
```


```{r}
a <- seq(11, 99, 11)
b <- 11:20
# create by distribution
x <- runif(1000, 1, 10) # uniform dist, n=1000
x <- rnorm(10000000, 1, 10) # normal dist, n=1000
```


## V2: Plotting
```{r}
plot(density(x))
```



## V3: Viewing

只要直接打該變數名稱，該變數的內容就會被列印出來。例如`df`或者是做完數學操作（如加減乘除），而沒有把他assign給新的變數，那就會被列印出來。

```{r}
country
p.import
head(country)
tail(country)
length(country)
# View(country)
```


## V4: Subsetting, slicing

```{r}
country[c(5, 3, 1)] # how about country[c(1, 3, 5)]
country[3:6] # is it equal to country[c(3, 4, 5, 6)]
a <- 11:19
a[3:length(a)]
a[length(a):3]
```



## V5: Deleting
Without assignment, deletion won't change original vectors
實際上像下面這樣只是用負號來篩掉不要的項目，原本變數沒變，要被覆蓋掉才變。

```{r}
b <- 11:20
b[-(3:5)]
b[-c(1, 3, 5)]
b
```




* (V) Deletion with assignment to replace original vector
（重要）當用負號篩選掉不要的那些項目後，必須要Assign以覆蓋掉原本的變數，不然原本的變數不會有所改變。

```{r}
b <- b[-(3:5)]
b

a <- seq(11, 99, 11)
a <- a[-c(1, 3, 5)]
a

```


## V6: Concatinating
```{r}
a <- 1:10
a <- c(a, 11)
a
b
a <- c(a, b)
a
a <- c(a, a, b)
a
```



## V7: Arithmetic operations

* `a <- a %% 2`除以二取餘數
* `a <- a %/% 2`除以二取商

```{r}
a <- 11:19
a + 3
a / 2

a %% 2
a %/% 2
a <- a %% 2 	# modular arithmetic, get the reminder
a <- a %/% 2 	# Quotient

```




## V8: Logic comparisons
```{r}
a %% 2 == 0 	# deteting odd/even number
a %% 2 != 0
a[a%%2==0]
a > b
p.import > mean(p.import)
p.import > p.export

TRUE == T 		# == equal to,
TRUE != F    	# != Not equal to

any(a>11) # is there any element larger than 1
all(a>11) # are all elements larger than 1

```


## V9: Subsetting by logic comparisons
* two methods to filter data from vectors, by index vector or a logical vector with equal length.
* `a%% 2 == 0`意味在判斷a除以2會不會等於0。計算後的結果會變成TRUE和FALSE，因為邏輯判斷所產生的就是TRUE或FALSE。所以他會產生一整個TRUE或FALSE的Vector。把這樣的Vector塞給a後，它會留下TRUE的部分，FALSE的部分則不會留下。


```{r}
a <- seq(11, 55, 11)
a[c(T, F, T, F, T)]
a[a%%2==1]
a%%2
a%%2==1
a <- c("你好","你好棒棒","你好棒","你真的好棒")
a[nchar(a)>3]

# which will return "index-of"
a <- seq(11, 55, 11)
a[which(a%%2==1)]
which(a%%2==1)
```


## V10: Sorting

* 排序`sort(x)`的結果必須用`<-`覆蓋原本的`x`，此時的`x`才會是排序的結果。

* `order(x)`函式會傳回`x`數值由小到大的**索引**。這個例子的結果是`5, 4, 3, 6, 1, 2`，也就是`5`位置的那個數最小、`4`那個位置的數次小、接下來`3, 6, 1, 2`。

* `x[order(x)]`把`order(x)`結果（也就是`c(5, 4, 3, 6, 1, 2)`）傳給原本的`x`便會使得原本的`x`重新排序。通常`order()`的用途是，我們可以將兩個等長的variables例如var1和var2，依據var2來重新排序var1，例如var1[order(var2)]。

```{r}
x <- c(33, 55, 22, 13, 4, 24)
sort(x)
x <- sort(x) # assign to replace original x
order(x) 
x[order(x)]
```


## V11: Using built-in math functions
```{r}
a <- 11:19
min(a); max(a); mean(a); median(a); sd(a)
log2(a)
log1p(a)
?log1p
```


## V12: Checking data type
```{r}
mode(country)				# character
mode(p.import)					# numeric
mode(p.import > mean(p.import))	# logical

p.importc <- c("26.142", "12.008", "7.032", "13.646", "4.589")
mode(p.importc)				# character

```


## V13: Converting data type

* numeric vector可以用`as.character(x)`轉成`charcter`；logical vector可以用`as.numeric(x)`轉為`numeric`。概念上可以說是`character > numeric > logical`。

* 如果硬是在logical vector後附加一個numeric element的話，那就會整個vector被轉為numeric vector；相仿地，如果numeric vector後附加一個character element的話那整個vector就會被轉為character vector。

* 可以用`sum()`函式來計算logical vector有幾個`TRUE`值。例如`sum(a%%2==1)`就是計算`a`中有幾個奇數。`TRUE`可視為`1`、`FALSE`可視為`0`，所以加總起來就是`TRUE`有幾個。

```{r}
p.importc <- as.character(p.import)
p.importn <- as.numeric(p.importc)

a <- seq(11, 99, 11)
a <- c(a, "100")

a <- seq(11, 99, 11)
sum(a%%2==1)

```



## V14: Character operations
```{r}
a <- seq(11, 55, 11)
paste("A", a)		# concatenate
paste0("A", a)		# concatenate

```





# Practice
## Filtering data
```{r}
x.a <- rnorm(1000, 1, 10)

# 1.1 Filter out extreme values out of two standard deviations

# 1.2 Plotting the distribution of the remaining vector x.a

# 1.3 Calculate the 25% 50% and 75% quantile of vector x.a. You may google "quantile r"

# 1.4 Get the number between 25% to 75% and assign to x.a1

# 1.5 Plotting x.a1

```



## Practice II: Accessing characters
```{r}
x.b <- c("a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k")

# 2.1 Get only elements at odd positions and assign to x.b1

# 2.2 Truncate the first 2 elements and the last 2 elements and assign to x.b2

```