numeric(5)#vector with 5 zeros
logical(7)
x<-c(1.2,1.3,1.5)
x
is.numeric(x) #gives a true or false value
as.numeric(x) 
as.character(x) #converts x to a character vector
y=1:10 #vector for 1 to 10 with step=1
as.logical(-1:1)#zero is false and the other numbers true
mode(x)#shows the type of the object
x1=3
x2=x1<3
x2 #this gives false value
x1="stelios" #character
#define a complex number
x=complex(real=5,imaginary=6)
x
typeof(x) #similar with mode but gives more explanations specifically on storage issues
y=1.5:4 #increases by 1 at each step
y

#NA value means missing data and NaN means not a number usually rises in arithmetic calculations
#NaN implies NA but not the inverse
# calculations
x=3*sqrt(5)+5*cos(1)
x

#calculations
x=3
y=5
x*y
x/y
y%%x #this gives the residual of the division
x%/%y #this gives the floor value
#comparison operators
x=3
y=4
x==y
x<y
x!=y
(3<5)>(4==5) #checks that 3<5 then gives false to 4=5 but overall true>false(1>0)

#we can define step functions 
x=3
xnew=(x<1)*10+(x>=1)*5

#more general
x=-5:10
y=(x<1)
y2=1-y
xnew=y*10+(1-y)*5 #we omit the comparisons by store them


x=1:5
y=-1:3
x<y #the must have the same length


#logical operators

x=1:5
(x<4) & (x>5)
(x<4) | (x>5)


#mathematical functions
#binomial coefficient 
choose(5,2)
lchoose(5,2) #log of choose
hepl(lchoose)
factorial(30)
pi
#the rm() delete something that is previously defined
#to avoid overflow fist we log and then we take the e

#vectors where stands for combine
x=c(1,2)
y=c(1,x)
length(x) 
names(x)=c("banana","apple") #give names on each value
#abbreviation of seq
1:10
10:1
-3:-5
-1.3:-5.3
1.1:-2.5

seq(from=1,to=10,by=2)
seq(from=1,by=10,length=15)
x=1:5
seq(from=1,by=10,along=x) #this is used instead of length(length of x)
rep(x,times=2) #repeat the vector one more time
rep(x,times=2,each=2) #at first it duplicates each element and then duplicates the whole vector
rep(x,times=1:5) #each element is repeated as many times as the corresponding vector in times

#operations with vectors
#recycling
x=1:5
y=rep(1,3) 
x+y #the length of this vector is the maximum length of x and y so inevitably the y is recycled(it begins again)
x+2
x/2
x*2
y1=2:6
x*y1 #same length here
#logical calculations
height=c(1.47,1.50,1.65,1.80)
height<1.5
height<1.5|height>1.7

logical(3)
x=c(T,F)
is.na(x) #cheks for missing values

#subsets of vectors

height[1]#the interior defines the position
height[c(1,2)]
height[height<1.5]
height[-c(1,2)] #skips the first 2 elements

#common arithmetic functions

mean(height)
var(height)
prod(height)

#classification of vectors

sort(height)
sort(height,decreasing = T)
rev(sort(height))#it means reverse the same thing as above exactly

x=c(1,3,2,5,8)
rank(x) #the number of observations that is smaller or equal with each element in increasing order

y=c(1,2,2,3,4,5,6) #ties the default option takes the mean of the ranks of the 2 ties in icreasing order
rank(y)

y1=c(9,2,4,3)
order(y1) #this indicates the potition of each element in ascending order

any(y1>8)
all(y1<5)


#examples
#gcd
a=10
b=12
c=max(a,b)
test=1:c
y1=a%% test==0 #find the divisors of a with test
y2=b%% test==0 #find the divisors of b with test
y3=y1&y2 #common divisors of a and b
max(test[y3]) #the gcd
#in function form
gcd=function(a,b){
  c=min(a,b)
  test=1:c
  y1=a%% test==0 #find the divisors of a with test
  y2=b%% test==0 #find the divisors of b with test
  y3=y1&y2 #common divisors of a and b
  d=max(test[y3]) #the gcd,the test[y3] returns thete values of y3 which have true positions
  return(d)}
#this is also contained in a package 

#trimmed mean
x=c(51,46,58,30,41,43,28,29,28,50,61,39,48,32,45,69,34,48,49,44,59,68)
#let's say that the trim=0.05(5 percent)
#first method 
sort(x)
y=length(x)
y_new=trunc(y*0.05)
trim=mean(x[(y_new+1):(y-y_new)])

#with the Rfunction 
mean(x,trim = 0.05)
#same result

#another way with rank
r=rank(x)
y=length(x)
y_new=trunc(y*0.05)
trim=mean(x[(r>y_new)&(r<=(y-y_new))])

#median
#with Rfunction
median(x)
#another method,just for practice
med=NULL
y=sort(x)
n=length(x)
artios=(n%% 2==0)
if(n==artios){med=(y[n/2]+y[n/2+1])/2 #if the division gives positive resial then R takes the intger part
}else{ med=y[(n+1)/2]}

#character vectors 
#combine 2 words
x=c("MITSOS")
y=c("Giannakos")
paste(x,y)

#seperate characters
x=c("Mpamphs")
y=c("Giota")
z=c("love forever")

paste(paste(x,y,sep="+"),z,sep="=")

#combine the characters of vectors
x=c("apple,bananas")
paste(x,collapse=",")
date()
paste("TODAY IS",date())

paste("A",1:3,sep="")

#matrices

x=c(1:3,11:13,21:23,31:33)
y=matrix(x,ncol=3)#the row index moves faster
y=matrix(x,nrow=3)#fills the columns by default from left to right
y=matrix(x,nrow=3,byrow=T) #fills the rows from left to right
z=matrix(c(1,2,3,4),ncol=2)
dimnames(z)=list(c("row1","row2"),c("col1","col2"))
#we can name them also inside the matrix(list=)

#dimension
dim(z)
#make a vector matrix
x=1:10
dim(x)=c(2,5)
x

#make 2 vectors matrix

x=1:5
y=rep(1,5)
z=cbind(x,y) #column
rbind(x,y) #row

#diagonal matrix
diag(x)
diag(2)#identity matrix with dimesion 2

#calculations
z^2
sqrt(x)
z==5 #logical matrix

#submatrices
x=matrix(1:12,ncol=3,byrow=T)
x[1,3] #(1,3) element
x[1,] #first row
x[,3]#third column
x[1,c(1,3)] #vector
x[c(1,2),c(2,3)] #matrix
x[x<5]

#matrix operations
x=matrix(1:4,ncol=2,byrow=T)
y=matrix(1:4,ncol=2)
x%*%y
solve(x) #inverse
t(x)#transpose
z=c(1,2)
z%*%x #z as row matrix

#ARRAYS
#set of matrices(twodimensional) (multidiamensional )
x=1:24
y=array(x,dim=c(3,4,2)) #2 3x4 matrices

#subarrays
dim(x)=c(3,4,2)
x
x[1,2,2] #from the second matrix the (1,2) element

x[,2,2] #all row elements from the second column of the second matrix


# categorical variables
#factors for nominal data
x=c(0,1,2)
y=as.factor(x)
factor(c("0","1","2"),levels=c("1","0","2")) #specify exactly the levels
ordered(x)#ordinal data
#split the data
x=rnorm(1000) #1000 random observations from normal distribution
#we can also set the set.seed of something to take the same values each time
x_cut=cut(x,c(-Inf,-2,-1,0,1,2,Inf))#split the continuous population
table(x_cut) #contingency table
#the split function
#basically it allow us to spit the data into sub populations
x=1:10
y=c(1,1,1,1,2,2,2,2,3,3)
z=split(x,y)
mean(z$"1")

## data frames
#2 dimensional matrix but it allows for different types of elements in different columns
#so you can formulate a data matrix
height=seq(from=1.45,to=1.80,by=0.05)
id=1:length(height)
sex=c(rep("M",3),rep("F",5))
data.frame(id,height,sex)#the id is not necessary here
data=data.frame(ypsos=height,fylo=sex) #give your own names
data.frame(height,sex,row.names=c("MPAMPHS","KOSTAS","NIKOS","ALEX","GEORGE","STEFANOS","STELIOS","NIKH")) #GIVE NAMES IN ROWS
#subelements
data[1,2]
data[1,]
data[,"fylo"] #the columns of sex
data[-1,]#delete the first row
data$ypsos
#lists
#is like an array but allows different structures
x=1:5
y=list(data=data,x=x) #data frame and a vector
y$x
y[[1]] #the frist "matrix" of the list
y[[2]] #the second "matrix of the list
y[[1]][,2] #the second column of the first "matrix"

z=list(ames=data,vec=x) #give different names


#IMPORT DATA
#R's data editor
x=data.frame() #NULL
x
edit(x) # OPENS THE EDITOR(pop up window)
#AT THIS STEP IF WE WRITE SOME VALUES THEIR NOT SAVED
x=edit(x) #we have to name the editor first
x #now the data are saved

#for a list
x2=list(x1=1:10,x2=matrix(1:4,2,2))
x2=edit(x2) #we can edit our current list

#another method that imports the data directly

x=scan(n=10)#we can put the values in a vector by using the keyboard
x3=scan(n=3,what=character())#we specify the type we want to use

#similar function readline
#comment, you can use brackets in R to write a set of commands as a single argument
#this function is used to create questionnaires
options=menu(c("YES","NO"),title="Do you like basketball?")

#THIS CREATES A POP UP MENU
options=menu(c("YES","NO"),title="Do you like basketball?",graphics = T)

#FOR MORE OPTIONS

select.list(c("car","motorcycle","bisycle","TV"),title="Which of the following products do you prefer to own ? ",multiple = T,graphics = T)

##files and directories
#This command shows the place of the working directory
getwd()
#change the working place(now everything is saved here)
setwd("C:/Users/steli/Desktop/R")
getwd()
#we can use paste to create paths
drive="C:"
path1="Users"
path2="steli"
path3="Desktop"
path4="R"
paste(drive,path1,path2,path3,path4,sep="/")

#command that allow us to search the file 

file.choose()
#we can save the file on x
x=file.choose()

#import data from txt,excel,etc
x=scan("scan_example.txt" )
#this command returns a vector
#if the file was not in the working directory 
#then we had to determine the full path
#combine the scan with the file.choose
y=file.choose()
matrix(scan(y),length(y))
#this command returns a data.frame instead of a vector
read.table("C:/Users/steli/Desktop/R/A numerical illustration.dat",header = T)      
#we also use the header to recognize the first row as names of the columns
#we can skip lines with skip=
#stringsAsFactors transform the characters to factors

###we can write code in text and call it with source()

#we can save workplace variables in a text fie
x=1:4
y=2:5
z=cbind(x,y)
save(x,z,file="scan_example.txt")
rm(z)#delete
load(file="scan_example.txt")#then we bring it back
#save.image() saves the whole workspace

#other ways of saving things
#this command creates a txt in working directory that saves the results of sumand length
sink("output_example.txt")
x=rnorm(100)
length(x)
sum(x)
sink()


#packages for better results(including images)
#R2wd for word,Sweave for exporting in latex etc
#import files from excel
install.packages("gdata")
library(gdata)
readxl::read_xlsx("C:/Users/steli/Desktop/developer/ΠΡΟΓΡΑΜΜΑΤΙΣΜΟΣ ΜΑΘΗΜΑΤΩΝ.xlsx",sheet=1,header=T)

#CSV TYPE (MSDOS SAVE IN EXCEL)

read.csv2("C:/Users/steli/Desktop/developer/EXAMPLE.csv",header = T)

#from spss
library(foreign)
read.spss("C:/Users/steli/Downloads/ATTICA Study 10 yr FU  NEO !.sav",to.data.frame = T)

#similar from sas with the read.xport("path")

#histogram
#random sample with replacement from 0 to 100 with sample size 200
x=sample(0:100,size=200,replace=T) #discrete uniform
hist(x) #the number of intervals is [logn]+1 

hist(x,nclass = 20) #we define the number of classes
#we say to R which are the breaks
hist(x,breaks=c(0,20,50,100))
#if we set prob=T the range of each class is multiplied with the height such as the sum of all bars will be 1
#so this gives an estimation of the probability distribution of our data
hist(x,probability = T)
#we set colours for the bars with col=number
#if plot=F the output gives the breaks and the heights(counts) of the hist,but not the graphical representation
#the main= gives our own title to the plot
#also xlab and ylab set our own names for the axis
hist(x,main="Plot of discrete dist" )

#xlim and ylim gives the desire range for x's and y's
#e.g ylim=c(0,20)


###boxplots
boxplot(x,col=5)#2 ways for using colours
boxplot(x,col="cyan")
#outlier
x[1]=180
y=x
boxplot(y) #whiskies q3+1.5*IQR,q1-1.5*IQR
Y=sample(50:200,size=200,replace=T)
#2 boxplots in the same picture
boxplot(x,Y,col=c("red","green"),names=c("y","Y"))

#scatter plot
x=sample(0:100,size=200,replace=T)
#200 random normal dists with mean=0 and sd=10
e=rnorm(200,0,10)
plot(x,e) #independency
#now we set a linear relationship
#the e can be considered the noise-error
y=2*x+e
plot(x,y)#positive correlation

#insert a line
#verical line,lwy,lwd also possible options
abline(v=100,col="blue")
#horizontial line
abline(h=200,col="red")
#line with intercept=0 and slope=2
#the width of the line with lwd
abline(0,2,col="magenta",lwd=4)

#type= argument
#p for dots,l for lines,s for step functions,n doesn't show anything
#make a graph with lines or plot
#normal dist
x1=seq(-4,4,length=1000)
plot(x1,dnorm(x1,0,0.5),type="l")
#to use lines,you have to sketch one plot first
lines(x1,dnorm(x1,0,1),col="red")
lines(x1,dnorm(x1,0,2),col="green")
lines(x1,dnorm(x1,0,3),col="blue")

#plot lnx
x2=seq(0.01,1000,length=10000)
y=log(x2)
plot(x2,y,type="l")

#plot x^4-x^3+x^2
x4=seq(-10000,10000,length=100000)
y1=x4^4-x4^3+x^2
plot(x4,y1,type="l")


#add more information to scatter plots

weight=c(rnorm(100,70,12),rnorm(100,55,7))
height=c(rnorm(100,175,14),rnorm(100,158,10))
sex=rep(c("M","F"),each=100)#seperate the weight and height in M and F
plot(height,weight,type="p")
#colour the males,pch represents the dots in different shapes
points(height[sex=="M"],weight[sex=="M"],col="red")
points(height[sex=="F"],weight[sex=="F"],col="green")
#instead of colours you can use characters with labels=

#multiple scatter plots

e=rnorm(200,0,15)
z=30-3*x1+e
matrix1=cbind(x1,y,z)
dimnames(matrix1)=list(NULL,c("X","Y","Z"))
pairs(matrix1)#all different scatter plots


#legend() adds more information to the diagram



legend("topright",pch=c(1,3),legend=c("Males","Females"),col=c("red","green"))
legend(locator((1)),pch=c(1,3),legend=c("Males","Females"),col=c("red","green"))
#change the size of the box
windows(height=7,width=3.5)

#multiple diagrams in one output(same box)
plot(height[sex=="M"],weight[sex=="M"],xlim = c(120,230),ylim = c(20,130),col="red")
par(new=T) #this adds the second data for females
plot(height[sex=="F"],weight[sex=="F"],xlim = c(120,230),ylim = c(20,130),col="green")

#multiple plots in one output (different boxes)
#this command is giving us 2*2=4 plots
par(mfrow=c(2,2))
x=rnorm(100,0,1)
hist(x)
y=rnorm(100,0,2)
hist(y)
boxplot(x)
boxplot(y)
#similar comman split.screen
hist(x)
lines(x)
dev.off() #to shut down the process
graphics.off()#similar command
#set a line in histogram
x=rnorm(100,0,1)
hist(x,probability=T)
lines(density(x=x,col="red"))
#ggplot package
library("tidyverse")
#this works with data.frame
x=rnorm(100,0,1)
y=rnorm(100,0,2)
z=rep(c("F","M"),each=50)
data=data.frame(x=x,y=y,z=z)
ggplot(data,mapping=aes(x,y))+geom_point(alpha=0.5,col="red")
#geom_point(scatter),geom_boxplot,geom_line

##if statement
x=5
y=4
if(x>=5) y=0 #the value of y gets zero
y

c(x,y)
if(x<5)y=10
y #y stays the same 

if(x<=5){
  y=10
  x=x^2
}
#or
if(x<=5){y=10 ;x=x^2}
#x and y change

if(x>0)print("positive number")
#this procedure prints a phrase
#in general we try to avoid comparisons
#2 conditions or more
x=4
y=5
if(x<5){
  y=0
  x=x^2
}else{
  x=0
  y=10
}
c(x,y) #the first condition is true
#this argument can be made also in one line
#the if statement doesn't use vectors
#if the test uses a vector then only the first element is cheked

#first solution if we wand to something that involves the chek of a vector
#boolean expressions
u=1:10
t=(u<5)*(-1)+(u>=5)*1
t
#faster than the if's so we use them when we can

#multiple if's
x=5
if(x==10){print("same")
}else if (x>1){
  print("bigger")
}else {print("smaller")}

#second choice for comparisons with vectors,but also for matices and arrays
x=1:10
ifelse(x<5,1,2)#second element yes ,third no
ifelse(x<5,1:5,1:3) #first it takes the first element of yes etc



##loops
#for
x=1:5
y=seq(10,18,by=2)
for(i in x)y[i]=-y[i]
y#the opposites of y
z=c(1,2,3)
for(i in 1:2)z[i]=2*i
z

for(i in 1:5){
  x[i]=x[i]^2
  y[i]=y[i]*2+1}

#we don't have to use the indices
for(i in 1:5){x=x^2} #at first step it squares the x and so on


#for's are slow and we have to use another method if we can
#for example
x=rnorm(10000,0,1)
x=x+1
for(i in 1:length(x))x[i]=x[i]+1

#loops of for
#this algorithm produces the opposite matrix of x
x=matrix(1:16,4,4)
for(i in 1:4){
  for(j in 1:4){
    x[i,j]<- -x[i,j]
  }
}  

x

#calculate sums with loops
#6.1 example sum
x=c(3,4,6,7,8,1,7,4,9,0,4,5,6,12,17,19,35,45,20,18)
ex_sum=function(n){
  sum1=0
  for(i in 1:n){
    for(j in 1:n){
      sum1=sum1+(x[i]-x[j])^2
    }
    print(sum1) #print each result 
  }
  
  return(sum1/(2*length(x)^2))}

#the first output is in the previous loops
sum_first=NULL
for(i in 1:length(x))sum_first[i]=(x[i]-x[1])^2
sum(sum_first) #the first result
#we can calculate the previous sum without loops
((length(x)-1)/length(x))*var(x) 

#the control variable e.g i,is preferable to stay constant
#for example

for(i in 1:5){
  i=i+10
  print(i)}
#as we the commands are repeated 5 times and it doesn't matter that we change the i
#other languages have problem with that change

# the while again creates loops but according to some logical condition 
#as long as the condition is true the command-commands will be repeated
i=1
while(i<100){
  print(i)
  i=i+1}
#we have to be careful in order to not create endless loops

#another example,we want to solve the equation pnorm(x)=0.7
#show we want to find the quantile (lower) of the normal dist
#non-linear non-linear equation
t=-1 #initial value
while(pnorm(t,0,1)<=0.7)t=t+0.001
qnorm(0.7)#same result

while(c(1,2)<2) print("kalhmera") #endless loop it cheks only the first element


#in order to avoid loops we use apply
#faster method
#it uses arrays or matrices
x=matrix(1:16,4,4)
apply(x,2,mean) #the means of columns
apply(x,1,mean)#the mean of rows
#we can set also our own function
y=array(1:16,dim = c(2,2,4))
apply(y,1,sum) #sums of the rows of all matrices
apply(y,c(1,2),sum) #sum of the rows and columns of all matrices



##functions
#multiple benefits such as better management of the memory,because each variable inside is local
#we don't have to run the same commands again and again
#easy to fix problems inside the function
#helps others to understand the program better
#the argument here is a vector
#make the range
range_ours=function(x){
  range=max(x)-min(x)
  return(range)}
y=rnorm(100)
range_ours(y)

#or 
z=range(y)
z[2]-z[1]#range

E=matrix(1:4,2,2)
#the argument here is a matrix
square_matrix=function(A){ B=A^2
return(B)} #we don't have to use the return necessarily

#In contrast with other programs we don't have to define the arguments 

# the  input variable each time we call the function must be of the same type with the argument mus
#it is a good practice to set initial values inside the function in order to avoid confusion with other variables that are used elsewhere(non-local)
#and in general it is better to not use global variables inside of functions
#if we have more outputs we use the list()

examp=function(x,y){x=x^2;y=y^3;list(x=x,y=y)}
examp(y=1,x=2)#this shows that we don't have to use a specific order if we use the names of the arguments
#the output can be presented also in a vector form with return(c(x,y)) or print

#as an example we write a function of a sort of like trimmed mean

trimmedmean=function(x){
  meanvalue=mean(x)
  n=length(x)
  std=sd(x)
  sum1=0 #sum of the values
  id=0# #how many values were included
  for(i in 1:n){
    if(abs((x[i]-meanvalue)/std)<=2){#we include those values of at most 2 standar deviations
      
      sum1=sum1+x[i]
      id=id+1
    }
  }
  sum1/id#trimmed mean
}

x=rnorm(1000,1,2)
trimmedmean(x)    
y=rgamma(150,shape=1,rate=1)   #gamma dist
trimmedmean(y) 

#multiple outcomes
#in former code we ask for the id also
trimmedmean1=function(x){
  meanvalue=mean(x)
  n=length(x)
  std=sd(x)
  sum1=0 #sum of the values
  id=0# #how many values wher included
  for(i in 1:n){
    if(abs((x[i]-meanvalue)/std)<=2){#we include those values of at most 2 standar deviations
      
      sum1=sum1+x[i]
      id=id+1
    }
  }
  list(trimmed=sum1/id,number_obs=id)#trimmed mean
}

trimmedmean1(x)
trimmedmean1(x)$trimmed #call a specific output with $

#of course we can set default values in functions
#e.g
eg=function(x,l=2){k=x^2;s=l*2
list(k=k,s=s)}
eg(5)#we didn't use the l at all

#we can define functions inside of other functions
#but this is debatable,the only use is when we don't want to bind more memory

#inside of functions it is not necessary to take any specific result,e.g the function can include only a plot
plotnormal=function(m=0,s=1){
  lowerbound=qnorm(0.001)
  upperbound=qnorm(0.999)
  x=seq(lowerbound,upperbound,length=1000)
  plot(x,dnorm(x,m,s),ylab="density",type="l")
}
plotnormal() 

#books grolemund