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#
# INTRODUCTION TO R
#
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# calculator
(50 + 1.45)/12.5


# assignment operators
x = 945
y <- sin(0.47)^2 * sqrt(5) #Used the most by R users
y^2 -> z


# to inspect the value of a variable simply type its name
x
y
z


# listing and deleting objects
ls()
rm(y)
rm(x,z)

# remove everything in the working environment
rm(list=ls())


#
# Vectors (the most basic data objects in R)
#

# creating vectors
v <- c(14,7,23.5,76.2)
v

# generating a regular sequence of numbers
v <- 1:10
v

v <- seq(from=5, to=10, by=2)
v

w <- rep(v, times = 2)
w


# scalars are vectors with a single element
w <- 45.0
w

# vectors can be created using other vectors
z <- c(v, 2.5, w)
z




###############################################################################
#
# PROBLEMS:
#
# - construct a vector that contains elements: 1,2,3,...,19,20
#
# - construct a vector that contains elements: 1,2,3,...,19,20,19,...,3,2,1
#
# - construct a vector that contains elements: 1,3,5,1,3,5,...,1,3,5 
#   where there are 10 occurrences of element 5
#
###############################################################################

###############################################################################
#
# SOLUTIONS:
#
###############################################################################
v <- 1:20
v

v <- c(1:20,19:1)
v

v <- rep(c(1,3,5), times = 10)
v

###############################################################################


v <- c(8, 4, 2, 3, 6, 9, 1)

# some useful vector functions
length(v)
max(v)
min(v)
which.min(v)
sum(v)
mean(v)
sd(v)
rev(v)
sort(v)
sort(v, decreasing=T)
order(v)


# types of vectors
mode(v)

# logical vector - has logical constants as elements 
b <- c(TRUE, FALSE, F, T)
b
mode(b)

x <- 5 > 3
x
mode(x)


# string vector - has strings as elements
s <- c("character", "logical", "numeric", "complex")
mode(s)


# type coercion (all elements must be of the same type)
x <- c(F, T, 34.56, 'aaa')
x


#
# Vectorization
#

# vector arithmetic (operations are performed element-wise)
v1 <- c(10,20,30,40)
v2 <- 1:4
v1 + v2
v1 * v2


# functions operate directly on each element of a vector
v1^2
sqrt(v1)
exp(v1)
log2(v1)

# the recycling rule (if lengths are different the elements of the shorter vector are repeated)
v1 * 10
v1 + 1
v1 + c(100, 200)





###############################################################################
#
# PROBLEMS:
#
# - calculate the values of sin(x) at 0, 0.1, 0.2, 0.3, ..., 1.0
#
# - Suppose we measure the height and weight of ten individuals:
#
#   #the vector of heights in 'cm'
#   height <- c(179, 185, 183, 172, 174, 185, 193, 169, 173, 168)
#
#   # the vector of weights in 'kg'
#   weight <- c(95, 89, 70, 80, 92, 86, 100, 63, 72, 70)
#
#   Calculate the body mass index (bmi) for each individual using the formula:
#   bmi = weight_in_kg / (height_in_m)^2
#
#   HINT: first convert heights from 'cm' to 'm', then use the formula above.   
#
###############################################################################

###############################################################################
#
# SOLUTIONS:
#
###############################################################################

v <- c(0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0)
# or
v <- (0:10)/10
# or
v <- seq(from=0, to=1, by=0.1)

sin(v)


height <- c(179, 185, 183, 172, 174, 185, 193, 169, 173, 168)
weight <- c(95, 89, 70, 80, 92, 86, 100, 63, 72, 70)

bmi = weight / (height / 100)^2
bmi

###############################################################################



#
# Indexing
#

x <- c(-10,20,-30,40,-50,60,-70,80)
x


# individual elements can be addressed using an integer index vector
# (indexing starts with 1)
x[3]
x[c(1,4,5)]
x[1:3]
x[]

# negative integer indices address all elements but those stated
x[-1]
x[-c(4,6)]
x[-(1:3)]


# vector elements can be addressed using logical vectors
# (elements corresponding to constants TRUE are selected)

# logical vector
x > 0

# logical vector indexing
x[x>0]
x[x <= -20 | x > 50]
x[x > 40 & x < 100]

# equality operator is ==
# inequality operator is !=


# the which() function returns indices corresponding to constants TRUE
which(x > 0)



# character string index vector
point <- c(4.7, 3.6, 2.5)
names(point) <- c('x', 'y', 'z')
point

point['x']
point[c('x','z')]

# empty indices
point[] <- 0
point

# not the same as
point <- 0
point


#
# Vector editing
#

x <- c("a", "b", "c", "d")

# replacing an element
x[2] <- "BBBBB"
x

x[c(1,3)] <- c("AAAAA", "CCCCC")
x

# adding new element
x[length(x)+1] = "EEEEE"
x

# what happens if we do not define all elements in the vector?
x[10] <- "FFFFF"
x

# which elements are not defined
is.na(x)


# removing elements
x <- x[-c(1,3)]
x

x <- c(x[2],x[3])
x



###############################################################################
#
# PROBLEM:
#
# - given a vector: 
#   x <- c(1, -2, 3, -4, 5, -6, 7, -8)
#   
#   Edit the vector x as follows. Replace all elements with a negative value 
#   with 0. Multiply the elements with a positive value by 10. 
# 
###############################################################################

###############################################################################
#
# SOLUTION:
#
###############################################################################

x <- c(1, -2, 3, -4, 5, -6, 7, -8)


x[x < 0] <- 0
x[x > 0] <- x[x > 0] * 10
x

###############################################################################




#
# Factors
#

gender <- c("f","m","m","m","f","m","f")
gender

# factors are useful when modelling nominal variables
gender <- factor(gender)
gender

# argument "levels" defines all possible elements' values
dir <- factor(c('left','left','up'), levels = c('left','right','up','down'))
dir

# all possible elements' values
levels(dir)

# if no match is found
dir[1] <- "diagonal"
dir

# valid assignment
dir[1] <- "down"
dir

# frequency tables for factors 
table(gender)
table(dir)



#
# Lists (an ordered collection of objects - components)
#

# creating a list
student <- list(id=12345,name="Marko",marks=c(10,9,10,9,8,10))
student

# extracting elements of a list (using named components)
student$id
student$name
student$marks

# extracting elements of a list (using indexing)
student[[1]]
student[[2]]
student[[3]]

# extending lists
student$parents <- c("Ana", "Tomaz")
student


#
# Data frames
#
 
# creating a data frame
height <- c(179, 185, 183, 172, 174, 185, 193, 169, 173, 168)
weight <- c(95, 89, 70, 80, 92, 86, 100, 63, 72, 70)
gender <- factor(c("f","m","m","m","f","m","f","f","m","f"))
student <- c(T, T, F, F, T, T, F, F, F, T)

df <- data.frame(gender, height, weight, student)
df

# some important functions
summary(df)
names(df)
nrow(df)
ncol(df)

# accessing elements of data frames
df[5,]
df[1:5,]
df[,1]
df[,c(1,3,4)]
df[1,3]
df[1,-3]

df$height

df[df$height < 180,]
df[df$gender == "m",]


# adding columns to a data frame
df <- cbind(df, age = c(20, 21, 30, 25, 27, 19, 24, 27, 28, 24))
df

df$name = c("Joan","Tom","John","Mike","Anna","Bill","Tina","Beth","Steve","Kim")
df

summary(df)


###############################################################################
#
# PROBLEMS:
#
#
# - calculate the average age of persons in our dataset. 
#   (HINT: use the meann function)
#
# - are there more males or females in our dataset? 
#   (HINT: use table function)
#
# - write out persons that are also students. 
#
# - write out persons who are between 1.8 to 1.9 m of height (inclusive). 
#
# - write out students who are over the average height 
#   (calculated on the whole dataset).
#
# - arrange persons by their age. (HINT: use the order function)
#
###############################################################################

###############################################################################
#
# SOLUTIONS:
#
###############################################################################

mean(df$age)

table(df$gender)

df[df$student,]

selection <- df$height >= 180 & df$height <= 190
df[selection,]
# or directly
df[df$height >= 180 & df$height <= 190,]

df[df$student & df$height > mean(df$height),]

df[order(df$age),]

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