#############
# Section 2
#############

#Accessing built-in data sets
data()

help(state)

data(state)

state.name

# Checking type of vector:

is.character(state.name)   

# extracting elements of a vector using square brackets:

state.name[40]

# Assignment operator <- :

my.state<-state.name[40]

my.state

# A single equals sign also works as an assignment operator:

my.state = state.name[40]

#Reading a labeled numeric vector

data(precip)

precip

names(precip)

help(precip)

# Various simple functions that work on vectors:

length(precip)

sum(precip)

mean(precip)

sd(precip)

var(precip)

## 
# Recall previous question about indices:
# Try this:
##

as.vector(precip)

#Creating a numeric vector

blastoff = c(5,4,3,2,1)

(blastoff) = c(5,4,3,2,1)  # gives error

(blastoff = c(5,4,3,2,1) )  

# Surrounding an assignment code in parentheses causes it to print to the screen.

# Creating simple sequences

1:100

x=3:6

10:-100

5:1

seq.length=length(seq(-10,10,0.1)); seq.length

seq(-10,10,0.1)

rep(1,10)

scan()
1 3 5 7 2
21 3

mydata=scan()
1 3 5 7 2
21 3

# Checking what "type" or "mode" a vector is:

mode(precip)
is.integer(precip)
is.double(precip)
is(precip)


mode(blastoff)
is.integer(blastoff)  
# Doesn't check whether elements are whole numbers! is.integer pertains more to storage than appearance.
is.double(blastoff)

# Writing a function to check whether elements are whole numbers:

is.wholenumber <-
    function(x, tol = .Machine$double.eps^0.5)  abs(x - round(x)) < tol

is.wholenumber(blastoff)
all(is.wholenumber(blastoff))
is(blastoff)

# Coercing the vector to be a certain type:

as.integer(blastoff)

is.integer(as.integer(blastoff))


state.region

is(state.region)  # not too informative

attributes(state.region) # more accurate

# More coercing:

regions.cvec=as.character(state.region)

regions.fvec=as.factor(regions.cvec)


#2.3 Matrices

data(USPersonalExpenditure)
is.matrix(USPersonalExpenditure)
ls()
USPersonalExpenditure

#Studying attributes of a matrix

# A named matrix.

attributes(USPersonalExpenditure)
dim(USPersonalExpenditure)  # Checking dimensions (rows by columns) of a matrix

nrow(USPersonalExpenditure)

ncol(USPersonalExpenditure)

# Dimension names of this named matrix:

dimnames(USPersonalExpenditure)
dimnames(USPersonalExpenditure)[[2]]
dimnames(USPersonalExpenditure)[[2]][3]


#Extracting elements, rows and columns of a matrix
USPersonalExpenditure[3,1]
USPersonalExpenditure[3,]
USPersonalExpenditure[,1]
USPersonalExpenditure[,-4]  #every column EXCEPT 4th column.
USPersonalExpenditure[c(1,2,4),]
USPersonalExpenditure[2:4,]
USPersonalExpenditure[,"1955"]  # can also pick rows or columns by their names.
USPersonalExpenditure[,c("1960","1940")]
USPersonalExpenditure["Private Education",]


help(state)

# More examples of working with a named matrix.
state.x77

attributes(state.x77)

dim(state.x77)

length(state.x77)

dim(state.x77)[1]

dim(state.x77)[2]

state.x77[3,5]

state.x77[3,]

state.x77[,5]

state.x77[3,c(1,5,7)]

state.x77[,"Murder"]

state.x77[,"murder"]

# R is case sensitive!


# 2.4 Data Frames

# Creating a data frame:

state.dfr <- data.frame(state.name,state.region,state.abb,state.x77)

state.dfr

# Aspects of data frames:

attributes(state.dfr)

names(state.dfr)

row.names(state.dfr)

# referencing data frame columns:

Population

state.dfr$Population

is.character(state.dfr$state.name)

is.factor(state.dfr$state.name)

state.dfr<- data.frame( I(state.name), state.region, I(state.abb), state.x77)

# Repeat previous two lines of code ...


# 2.5 Lists

# Studying attributes of a list

attlist.state.dfr<-attributes(state.dfr)

attlist.state.dfr


# Function outputs can be lists

A <- state.x77[1:3,1:3]

elistA <- eigen(A)

elistA

elistA[[1]]

elistA[[1]][1]

elistA$values

# Functions:  look at vecnorm.txt

source("vecnorm.txt")  # after changing to the correct directory...

my.vec <- c(1,5,-3)

vecnorm(my.vec)

vecnorm(my.vec,3)


###
###
# Combining vectors into matrices using 'cbind' and 'rbind':
###
###

vec1 <- c(4,5,6)
vec2 <- c(40,50,60)

my.mat.3by2 <- cbind(vec1,vec2); my.mat.3by2

my.mat.2by3 <- rbind(vec1,vec2); my.mat.2by3

# The 'matrix' function also can create matrices; we will see more examples of this in the Section 5 notes.

matrix(c(vec1,vec2), nrow=3, ncol=2, byrow=F)

matrix(c(vec1,vec2), nrow=2, ncol=3, byrow=T)

# Section 2.6

# Generating sequences with "by" and "length" arguments

seq(from=-2.0, to=2.0, by=0.5)

seq(from=-2.0, to=2.0, length=9)

# Be careful about omitting argument names if you don't know the correct default order:

seq(-2.0, 2.0, 0.5)

seq(-2.0, 2.0, 9)

seq(-2.0, 2.0, length=9)


#Studying the "pretty" command

seq(-2.0,2.0,length=10)

pretty(seq(-2.0,2.0,length=10))

pretty(seq(-2.0,2.0,length=10),10)

seq(-2.0, 2.0, 0.5)

# a function that does different things, depending on what is input:

A

diag(A)

diag(my.vec)