a5.basic-functions.R

# Basic functions

## Environment functions
search()

x <- 1
y <- 1

objects()
remove(x)
rm(y)
rm(list=objects())

getwd()
setwd("d:/")

getOption("digits")
1e10 + 0.5
options(digits=15)
1e10 + 0.5

## Package functions
require(graphics)
library(graphics)
library(fUnitRoots)
install.packages(c("dplyr","plyr","lubridate"))

## Object functions

### Object typing
x <- 1
class(x)
typeof(x)
str(x)

x <- c(1,2,3)
class(x)
typeof(x)
str(x)

x <- c("a","b")
class(x)
typeof(x)
str(x)

x <- list(a=1,b=2)
class(x)
typeof(x)
str(x)

x <- data.frame(a=1,b=2)
class(x)
typeof(x)
str(x)

### Object dimensions
df <- data.frame(a=c(1,2,3),b=c(2,3,4))
m1 <- matrix(c(1,2,3,2,3,4,3,4,5),ncol = 3)
a1 <- array(1:48,dim = c(2,8,3))
dim(df)
dim(m1)
dim(a1)
ncol(df)
nrow(df)
ncol(m1)
nrow(m1)
ncol(a1)
nrow(a1)

## Logical functions
a1 <- c(TRUE, TRUE, FALSE)
a2 <- c(TRUE, FALSE, FALSE)
a1 & a2
a1 | a2
!a1

x <- c(-2,-3,2,3,1,0,0,1,2)
any(x > 1)
all(x <= 1)

which(x >= 1.5)
x[x>=1.5]

x <- 1 %in% c(1,2,3)

## Character functions: cat(), message(), print(), sprintf(), paste(), paste0()
cat("Hello, world!")
message("Hello, world!")
print("Hello, world!")
cat("A new line\nA tab\t")
message("A new line\nA tab\t")
sprintf("Hello, %s! Your number is %d., and your score is %.2f","Jack",50,35.618)
paste("Hello","world")
paste("Hello","world",sep="-")
paste0("Hello","world")
tolower("Hello")
toupper("Hello")
nchar("Hello")
ch1 <- "Hello"
substr(ch1,1,3)
substr(ch1,1,3) <- "abc"
strsplit("a,bb,ccc",split = ",")
strsplit(c("Ken,24,Finance","James,25,Economics"),split = ",")

## Math funcitons
sin(1)
cos(1)
tan(1)
exp(-1)
sinh(1)
cosh(1)
tanh(1)
factorial(5)
ceiling(10.6)
floor(9.5)
trunc(1.5)
round(pi,3)
signif(pi,3)

polyroot(c(1,2,1,-1))
f <- deriv(y~sin(cos(x)*y),c("x","y"),func=T)
f(1,2)

l <- uniroot(function(x) x^3-x+1,c(-5,5))


## Statistical functions
x.norm <- rnorm(20)
mean(x.norm)
sd(x.norm)
median(x.norm)
quantile(x.norm,probs = c(0.5,0.8))
max(x.norm)
min(x.norm)
pmax(c(1,2,3),c(2,3,1))
pmin(c(1,2,3),c(2,3,1),c(3,2,1))
summary(x.norm)


set.seed(100)
sample(c(1,2,3),size = 2,replace = FALSE)
sample(c("a","b","z"),size = 10, replace = TRUE)
rnorm(20,mean = 10,sd = 2)
rbinom(20,size = 10,prob = 0.6)
runif(20)
runif(20,min = 10,max = 20)
rgamma(20,shape = 0.5)

plot(dnorm,xlim=c(-3,3))
plot(pnorm,xlim=c(-3,3))
qnorm(c(0.01,0.99))

table(sample(letters[1:3],100,T))
table(sample(letters[1:3],100,T),sample(LETTERS[1:4],100,T))


## Data manipulation

### Data read
EURUSD5 <- read.csv("data/EURUSD5.csv",header=FALSE,
  col.names=c("Date","Time","Open","High","Low","Close","Volume"))

idx <- read.csv("data/sh000300.csv",header = T,
  col.names=c("date","open","high","low","close","volume","tradeVolume"),
  colClasses=c("Date","numeric","numeric","numeric","numeric","numeric","numeric"))
us.cpi <- read.csv("data/us-cpi.csv",header = T,
  col.names=c("year","month","cpi"),
  colClasses=c("integer","integer","numeric"))
us.gdp <- read.csv("data/us-gdp.csv",header = T,
  col.names=c("year","month","gdp"),
  colClasses=c("integer","integer","numeric"))
us <- merge(us.gdp,us.cpi,by = c("year","month"))

### Transformation
EURUSD5$DateTime <- strptime(paste(EURUSD5$Date,EURUSD5$Time),
  format="%Y.%m.%d %H:%M")
EURUSD5 <- EURUSD5[c("DateTime","Open","High","Low","Close","Volume")]

EURUSD5a <- transform(EURUSD5, Medium=(High+Low)/2)

EURUSD5b <- within(EURUSD5, Median <- (High+Low)/2)

### Data write
write.csv(EURUSD5a,"output/EURUSD5a.local.csv",row.names=FALSE)
write.table(EURUSD5a,"output/EURUSD5a.local.txt",row.names=FALSE,sep="\t")

#### Read/Write via RSQLite
##### Write data.frame to SQLite database
require(RSQLite)
conn <- dbConnect(SQLite(),"data/example.local.sqlite")
n <- 1000000
products.df <- data.frame(i=1:n,type=sample(LETTERS,n,T),
  class=sample(LETTERS[1:3],n,T),x=rnorm(n,6,2),y=rbinom(n,10,0.6))
dbWriteTable(conn,"products",products.df)
dbDisconnect(conn)

##### Read data.frame from SQLite database
require(RSQLite)
conn <- dbConnect(SQLite(),"data/example.local.sqlite")
products.A <- dbGetQuery(conn,"SELECT * FROM products WHERE type='A'")
products.subset <- dbGetQuery(conn,"SELECT i,class,x+y AS z FROM products WHERE type='A' AND x>=8")
dbDisconnect(conn)

## Higher-order functions

### Example: passing a function as an argument
add <- function(x,y,z=3) {
    x+y+z
}
product <- function(x,y,z) {
    x*y*z
}
aggregate <- function(x,y,z,fun) {
    fun(x,y,z)
}

### Example: using lapply()
result <- list()
for(i in seq_along(x)) {
    result[[i]] <- f(x[i])
}

result <- lapply(1:10, function(i) {
  c(a=i,b=i+1,c=i^2)
})

### Example: using closure
add <- function(x,y) {
    x+y
}
result <- lapply(1:10, add)

add <- function(y) {
    function(x) {
        x+y
    }
}
result <- lapply(1:10,add(3))
result <- sapply(1:10,add(30))

## Optimization functions
f <- function(x) x^4+3*x^2+x-1
optimize(f,c(-6,6))

f <- function(x) x^4+3*x^2+x-1
nlm(f, 0)

f <- function(x) sum((x-1:length(x))^2)
nlm(f, c(10,10))

## Anonymous functions

lapply(1:10,function(i) {
  c(a=i,b=i*2,c=i*(i-1))
})

sapply(1:5,function(i,x) {
  i+x
},x=2)


## Meta-functions

### get
f1 <- function(x,y) {
  (x+y)*(x-y)
}

f2 <- function(x,y) {
  (x^2+y^2)/(x^4+y^4+1)
}

f <- get("f1")
f(1,2)

f <- get("f2")
f(1,2)

f <- function(i) {
  f <- get(paste0("f",i))
  function(x,y) {
    f(x,y)
  }
}

f(1)(1,2)
f(2)(1,2)

fs <- lapply(1:2,f)
fs[[1]](1,2)
fs[[2]](1,2)


### do.call
f1 <- function(x,y) {
  (x+y)*(x-y)
}

do.call("f1",list(x=1,y=2))

do.call(f1,list(x=1,y=2))

data.frame(do.call(rbind,lapply(1:10,function(i) {
  c(a=i,b=i*2,c=i*(i-1))
})))

do.call(cbind,lapply(1:10,function(i) {
  c(a=i,b=i*2)
}))

### system.time
system.time(result <- lapply(1:2000,function(i) {
  x <- rnorm(1000)
  y <- rnorm(1000)
  mean(x)+mean(y)
}))

## Plot functions

### Basic plots
x <- rnorm(100)
y <- 2*x + rnorm(100)*0.1
plot(x)
plot(x,y)
plot(x^2,main="Graph 1")
plot(x,type="l")
plot(y,type="l",col="red")

plot(x)
lines(y,col="red")

plot(y,type="l",main="y",ylim=c(-8,8))
points(x,pch=10,col="red")

plot(sin,xlim=c(-3,3),main="Sin(x)",ylab="sin(x)")

par(mfrow=c(1,2))
plot(x,main="x")
hist(x)

data(airquality)
View(airquality)
oz <- airquality$Ozone
tbl <- table(LETTERS[ceiling(oz/20)])
barplot(tbl,main="Air quality (bar chart)")
pie(tbl,main="Air quality (pie chart)")