###############################################################################
### Introduction to R
### see also www.cran.r-project.org/doc/manuals/R-intro.pdf
###############################################################################

###----------------------------------------------------------------------------
### Basic operations
###----------------------------------------------------------------------------

## Scaler operation
## i have a dream
a <- 3 
b <- 4
c <- a+b
d <- a^2+b
e <- a/b
f <- a^b
a*b
class(a) # check type of the data

## Vectors
## In R,  a vector does not have dimension attributed
x <- c(10.4, 5.6, 3.1, 6.4, 21.7)
x^2
x + 4
x*2
x/3
exp(x)
leght(x) # length of x

## Random numbers
A <- rnorm(n = 100, mean = 0, sd = 1)
mean(A)
sd(A)

B <- runif(n = 100, max = 1,min = 0)

mean(B)
sd(B)

## Matrics
Z <- matrix(runif(24), 4, 6)
Z
dim(Z)
nrow(Z)
ncol(Z)

length(Z)

Z^2
D <- log(Z)
D
dim(D)

Z + D
D-D
Z*D


cbind(1, Z) # column-bind two vectors or matrices
rbind(1, Z) # row-bind


TZ <- t(Z) # transpose of Z, 6x4 matrix
TZ
dim(TZ)

Q <- Z %*% TZ # matrix multiplication, 4x4
dim(Q)

all.equal(t(Q),  Q) # is Q symmetric?

solve(Q) # inverse of Q


## Indices for vectors
x[1]
x[-1]
x[-c(2, 4)]
x[2:4]
x[c(1, 3, 4)]
x[length(x)]


## Indices for matrices
K <- Z[, 1] # extract the first column, don't forget the comma
Z[1, ] # extract the first row
M <- Z[, 1:3]
Z[2:4, ]

dim(M)
dim(K) # the dimension will be dropped if only one row or column is selected
K1 <- Z[, 1, drop = FALSE] # prevent dropping dimensions
dim(K1)



D[1:3] # what will get for this?

## Help in R
?matrix # get help for a function
help("matrix")
example(matrix) # learn how to use the function.


###----------------------------------------------------------------------------
### The working environment
###----------------------------------------------------------------------------

ls() # list all user created variables in R
A
rm(A) # remove variable "A" in R
rm(list = ls()) # remove all user created variables in R

getwd() # your current working directory
setwd("") # set your working directory
getwd() # check your working directory again


save.image(file = "myRWorkSpace.Rdata") # Save all the variables into your hard disk
q() # quit R

# start R again
load(file = "myRWorkSpace.Rdata") # Load your previous working space into R

###----------------------------------------------------------------------------
### Import data into R
###----------------------------------------------------------------------------

## clean your data before you input it
## Put your data in the same folder as your working directory
## R can only read txt,  csv format data.
## Keep your data file name simple(without space)

DataRaw <- read.table("Table_1_1.csv", header = TRUE)
DataRaw

Y <- DataRaw[, 2, drop = TRUE] # obtain Y
X1 <- DataRaw[, 4]
X2 <- DataRaw[, 5]
X <- cbind(1, X1, X2) # add an intercept

###----------------------------------------------------------------------------
### Simple plot
###----------------------------------------------------------------------------

## Scatter plot
plot(X1, Y)
plot(X1, Y, col = "blue")
plot(X1, Y, xlab = "This X", ylab = "This Y", main = "My first R plot")

## Histogram
hist(Y)
hist(Y, breaks = 20)
hist(Y, breaks = 20, freq = FALSE)

## Boxplot
boxplot(X1)
boxplot(cbind(X1, X2)) # boxplot of two matrices