###introduction to R####################

##R package can be downloaded from website for free http://www.r-project.org##

##use "help" to know the functions##

help(sqrt) #r will tell you the usage of sqrt function and give you exmaples how to use the function

## or use help.search("***")

## Using a '#' comments out any text afterwards on a line


#########Random Number Generators####################################
##Seed
##A pseudo random number generator is an algorithm based on a starting point called "seed".
##If you want to perform an exact replication of your program, you have to specify the seed 
##using the function set.seed(). The argument of set.seed has to be an integer.
set.seed(1)
runif(10)

x <- rnorm(10,mean=0,sd=1)
y <- rnorm(n=10)                ## default generates N(0,1)

## plotting.  
plot(x,y)

##Sampling in a vector
##Toss 10 coins

sample(0:1,10,replace=T)

#Roll 10 dice

sample(1:6,10,replace=T)
 

##play lottery (6 random numbers out of 49 without replacement)

sample(1:49,6,replace=F) ##replace=F is the default
 
##select a simple random sample

a<-c(1,3,5,7,9,11,13,15,17,19)
b<-sample(1:10,5)
b
a[b]

#or 
srs.sample<-a[sample(1:10, 5, replace=F)]

##illustrate simple random sampling (from Yihui XIE)
x = cbind(rep(1:10, 10), gl(10, 10))
par(mar = rep(0.1, 4))
for (i in 1:10) {
    plot(x, pch = 19, col = "blue", axes = F, ann = F)
    points(x[sample(100, 15), ], col = "red", cex = 3, lwd = 2)
    Sys.sleep(1)
}

###### Matrix Algebra #########


######### Vectors ###########

## Concatenate function 'c' to create a vector
u <- c(1,2,3,4)

## print u
print(u)

##just typing u also prints
u

u <- 1:4  ## makes the same vector as above
u
v <- seq(0,1.5,by=.5)
v
v <- seq(0,1.5,length=4) ## same thing
w <- rep(u, times=2)
w

## Scalar mult
2*u

## Vector Addition
u+v

## square every element of u
u^2

## multiply each element of u by the corresponding elements of v
u*v

## sum up every element of u
sum(u)

## subsetting
v[1]        ## get the first element of v
v[1:3]      ## get the first 3 elements of v
v[c(2,4)]   ## get the 2nd and 4th elements of v
v[-4]       ## get all but the 4th element of v

######### Matrices ##########

A <- rbind(u,v)
A
B <- cbind(u,v)
B

## subsetting
A[1,1]         ## get the (1,1) element of A
A[1:2,1:3]     ## get the first 3 rows of A with the first three columns
A[,1:2]        ## get the 1st and 2nd columns of A (with all rows)
B[-3,]         ## get all but the 3rd row of B (with all columns)
               ## (e.g. eliminate he 3rd observation)

## transpose
t(A)

## Matrix multiplication
C <- A%*%B
C
A%*%C  ## doesn't work b.c. A is (2x4) and C is (2x2)
C%*%A  ## does work

## Element by element multiplication
C*C   ## is not the same as C%*%C
C%*%C
A*C   ## doesn't work, A and C must have the same dimensions

## Matrix Inverse
C.inv <- solve(C)
C.inv
C%*%C.inv

## Note: C^(-1) does NOT work
C%*%C^(-1)    ## does not equal the identity


#########read data####################################
## Data frames are basically the same as matrices

## Turn a matrix B into a data frame
B.data <- as.data.frame(B)

## read data into a data frame from a webpage
ex.data <- read.table(file="http://www.stat.unm.edu/**/**.txt", header=T)
ex.data

## Read data from a local file
ex.data <- read.table(file="W:/teaching/stat445545anova/CH16PR07.txt")
ex.data