#################################################################
###                  Introduction to R                        ###
#################################################################


# Download R:   http://www.r-project.org/

# R is an interpreted language => you do not need to define all the object you use
# It is possible:
#  - to write directly on the console (EX: make a simple sum between 2 numbers)
#  - (better) to write the code in a separate script (like this text editor) and run it

# To run the code from the editor to the console:
#  - Cut and Paste the selected lines from the editor to the console (not efficient)
#  - R       : ctrl + r or selection of rows and |->| button 
#  - R studio: ctrl + enter
#  - R and RStudio: source ("file.R")

1
test <- 1

# Comments: anything after '#' is a comment, i.e., it is not executed by the R console
# DO NOT FORGET TO COMMENT YOUR CODE!!!!



#######################
#    Preliminaries    #
#######################

# IMPORTANT: as Matlab, SAS and many other programs, R needs a working directory


#--- To select the working directory: ---#

#  - if RStudio
#   > select "Session" -> 'Set working Directory' -> 'Choose Directory',
#  - if R
#   > select "File" -> 'Change working Directory'
#  - line command
#   > setwd("path of the folder where data are contained and files have to be saved")

setwd('your/working/directory/')


#--- To show the actual working path: ---#

getwd()


#--- To SAVE objects ---#

# From the workspace (R and RStudio):
# - Select the script/editor windows, then click 'File' -> 'Save' or 'Save as'

# From the console (R and RStudio):
# - To save the whole workspace (.RData file)
save.image("prove fino a qui.RData")

# - You may also save only some objects:
save(object1, object2, file="file name.RData")  # not the best option
# - if objects are vectors, tables, matrices or data:
write.table(object, 'object name.txt')   # save in .txt format (the easiest to be loaded)


#--- To LOAD objects ---#

# To load RData files:

load("work_so_far.RData")


#--- To LIST objects ---#

# To list the object defined and saved in the workspace:
ls()

# To list the objects contained in the working directory:
dir()

# To list the last n command executed
history(5)


#--- To REMOVE objects ---#

#rm(list of objects to be removed)
rm(list=ls(all=TRUE))  # Remove ALL the objects

# Note: it is important to clean the memory. Since in R you don't need to declare variables nor delete them once used,
#       it is a safe habit to clean the shell regularly, to save memory and to avoid overscript 



##########
## HELP ##
##########

#--- To recall the info associated to a command ---#

# help(name of the command) or ?nameofthecommand
help(hist)
?hist

# More in general
help.start()    




#############
## LIBRARY ##
#############

# What are R packages?

# In general, they are archives of .R files (or files from other languages) and data,
# which enable the definition of particular kind of functions or the execution of
# complex functions for specific analyses.

#--- To INSTALL a package ---#

# R       : 'Packages' -> 'Install Packages' -> ... select a city (usually Italy(Padua)) and then the name of the package 
# R Studio: 'Tools' -> 'Install Packages'  (much easier and helpful)

# From the CRAN it is also possible to download the .zip version of a package.
# You have to put it in your R package folder and then ask for installation from .zip file


#--- To LOAD a package ---#

# In order to use packages, you must load them 
library(MASS)   # now all the functions and data contained in the MASS package are available to your workspace




########################
## Data Import/Export ##  
########################

# Import the file "record.txt"
record <- read.table('record.txt', header=T)

# Note:
# - "header=TRUE" specifies that the first line of the file contains columns titles
# - if needed, sep="\t" indicates that different entries are divided by a tabular
# - if needed, dec="," indicates that the comma is used to define decimals

# Dimensions and variables names
dim(record)
dimnames(record)

# Show the first lines
head(record)
str(record)
record[1:5,]

# Name rows using labels contained in the 8th column
record <- data.frame(record[,1:7], row.names=record[,8]) 

# Name columns
var.names <- c("m100","m200","m400","m800","m1500","m3000","Marathon")
dimnames(record)[[2]] <- var.names

head(record)

# Save the modified version
write.table(record, file = 'record_mod.txt')

# Read the saved file
record <- read.table('record_mod.txt', header=T)


### EX1: see the assigments ###



##################
## Algebra in R ##
##################

# The R console may be used as a simple calculator

# - sum:
2+2
# - product:
2*3
# - subtraction and division:
(5-2)/3
# - power:
17^(1/3)
4^2

# others:

sqrt(9)
log(10)
exp(1)



##################
## OBJECTS IN R ##
##################

# You may assign values using <- or =


#--- scalars ---#

a <- 1
a
a = 2
a

b <- 3
b

4 -> c
c

a <- b
a
b


#--- logical operators ---#

# < (<=)    less (or equal)
# > (>=)    greater (or equal)
# ==        equal to
# !=        different from
# &         and
# |         or

1 < 3
5 > 7
sqrt(9) == 3
sqrt(3)*sqrt(3)-3 == 0   # !!!!! mind the approximations !!!!!
sqrt(3)*sqrt(3)-3
sqrt(4)*sqrt(4)-4 == 0  
4 != 9



#--- vectors ---#

# c() : function concatenating elements

# numeric vecotrs
v <- c(2,7,3,10)
v

t(v)  # transpose

# character vectors
vv <- c("mother","father","son")

vvv <- c(v,vv)
vvv               # note that all the items are now char

# extract the second element
v[2]
# extract more elements
v[2:3]
v[c(1,3)]
# extract everything but the first
v[-1] 
# extract everything but the last
v[-length(v)] 


# Operations on vectors
min(v)
max(v)
sum(v)
mean(v)
median(v)
range(v)    # EX: extract the minimum (maximum) only
sd(v)
var(v)
sort(v)
order(v)
v^2        # Note: element by element


# which()
# useful to search elements whithin a vector. A logical condition is required. The index o the element is returned
which(v==7)


# other particular options for building vectors

# seq
u <- seq(0,0.5,0.1)  # seq(from, to, by)
u

length(u)

u <- seq(0,0.5,len=9)  # seq(from, to, length)
u

u1 <- seq(0.5,0,-0.1)   # decreasing sequence
u1

u2 <- 1:5     # default: unit lag
u2


# rep
w <- rep(1,10)  # repat 'first argument' 'second argument' times 
w

# you may also repeat sequences
w1 <- rep(c(1,2,3,4),3)
# QUIZ: which is the length of w1?
w1


# you can also combine commands
w2 <- rep(1:8,rep(3,8))
w2

w3 <- rep(seq(0,10,len=6),1:6)
w3

w4 <- rep(c(5,9,1,3),c(1,4,2,0))
w4



#--- factors ---#

age <- c(16,72,33,46,90,1,28)
sex <- as.factor(c("M","M","M","F","M","M","F"))
levels(sex)

tapply(age,sex,mean)




#--- matrices & arrays ---#

dati <- c(1,2,3,4,5,6,7,8,9,10,11,12)
W <- matrix(data = dati, nrow = 4, ncol = 3, byrow = F)
w
# or
w <- array (data = dati, dim=c(4,3))
W
# or
W <- rbind(c(1,5,9),c(2,6,10),c(3,7,11),c(4,8,12))   # built joining rows
W
# or
W <- cbind(1:4,5:8,9:12)                             # built joining columns
W


# Extract elements from the matrix

W
dim(W)

W[2,3]
W[2:4,1]
W[4,c(1,3)]


# Extract rows and/or columns
W[3,]
W[,2]

# Extraxt sub-matrices
W[c(1,3,4),2:3]



#--- lists ---#

exam <- list (course = 'Statistics',
                 date.exam = '30/06/2010',
                 num_students = 25,
                 stu_ID = as.character(c(45020,45679,46789,43126,42345,47568,45674)),
                 marks = c(30,19,29,21,25,26,27))

exam
exam$marks
# or
exam[[5]] 

# list may also concatenate objects of different size (ex: dataframe and vectors)



#--- data frame ---#

# Data frames are matrices where each column may differ in nature from others

iris # basic dataset in R

head(iris)  # shows the first lines of the dataframe
str(iris)   # specifies the type of each variable
names(iris)
Sepal.Lenght[1:5]

iris$Sepal.Length[1:5]

attach(iris)
Sepal.Length[1:5]
detach(iris)

Sepal.Length[1:5]



##################
## Algebra in R ##
##################

# NB: the default option in R is to execute operations component by component

a <- 1
b <- 2
c <- c(2,3,4)
d <- c(10,10,10)
e <- c(1,2,3,4)
f <- 1:6
W    # dimensioni 4x3 da prima
Z <- rbind(rep(0,3),1:3,rep(10,3),c(4,7,1))
Z    # Z ha le stesse dimensioni di W


#--- algebra on scalars and vectors ---#

a+b    # scalar + scalar
c+d    # vector + vector 
a*b    # scalar * scalar
c*d    # vector * vector 
c+a    # vettore + scalare
c^2    # power
exp(c) 

# MIND THE RECYCLING!!! 
# when operations are carried out on vector with different size, R gives results, but they are not consistent.

c
e
c+e # warning, not error!

# The two vectors have different lenght, but R computes their sum anyway.
# How it is possible?
# The component by component sum is carried out up to the end of the shorter element.
# then R recycles!

c
f
c+f # recycling happens with no warning, since the length of f vector is multiple of the one of c vector


#--- algebra on matrices ---#

Z
W

Z+W   

colSums(Z)
rowSums(Z)

Z*W     # mind the size of the 2 matrices

Z%*%t(W) # 4x3 * 3x4 = 4x4


# inverse of a matrix

C <- 3*diag(4,3)
solve(C)  

solve(W)   # error! it is not a squared matrix

library(MASS)
ginv(C)   # generalized inverse




####################
## Functions in R ##
####################

# Functions are the only object in R that needs to be defined (and run) before being used.

# Specify in parentheses data and parameters to be provided to the function and give name to the function

std.err <- function( vector ) {    
              std.dev <- sd( vector )
              n          <- length( vector )
              std.err  <- std.dev/sqrt(n)
            }

mytrial <- std.err(v)
mytrial

# Note: objects defined inside the function do not need to be declared and exist only during the execution.
#       Their content will be deleted at the end of the run.
#       The only object returned is the one associated to the function name