# http://biecek.pl/R/Rwydanie2.pdf
# 
# http://r.meteo.uni.wroc.pl/
# 
# https://www.rstudio.com/
# 
# https://www.rstudio.com/products/RStudio/
# 
# https://cran.r-project.org/web/views/Finance.html

setwd("")

############## Podstawy R ########################
#Podstawowe operacje arytmetyczne
1+2
1/2
log(1)
log(exp(1))
log(exp(10^9))
exp(10^9)
sin(pi/2)
factorial(4)
?factorial
##################################################
#Pomoc
help.start()
help.search("integral")
?integrate
?seq 
?factorial
seq(1, 60, by = 2)
seq(0, 1, length.out=11)
seq(17)
##################################################
#Podstawowe operacje na wektorach
x=c(1,2,3,4)
x
x<-c(2,4,5)
x
y<-1:4
y
is.vector(y)
y<-seq(1,3)
y
(y<-seq(1,3))
y+2  
(y+1)/100	
y^2
x+y
3*(x-y)+x*y
x<-c(10,-2,30,-4)
x[2]	
x[c(1,3)] 
x>0	
x[x>0]

seq(-1,3,by=.2)
rep(c(1,3),5)
seq(1,3,len=10)
?seq


x<-c(2,4,5); y<-c(1,3,2)
x+y; x*y+2

notowania<-c(10,11,9,6,8)
notowania
names(notowania)<-c("PN","WT","SR","CZW","PT")
notowania
notowania["PN"]

w<-c(1,2,1,3,1,2,4,3,2); w
wfact<-factor(w); wfact
summary(wfact)
plot(wfact)
table(w)
summary(wfact)

##################################################
#Podstawowe statystyki
help(sum)
sum(y)

length(y) 
mean(y)
? mean 
var(y) 
?var
sum((y-mean(y))^2/(length(y)-1))

sd(y) 
median(y)
table(y)
zakres<-max(y)-min(y);zakres	
IQR(y) 
?IQR
summary(y)

##################################################
v<-vector("double",10)
v<-v+10
v[3]<-5
v
2->v[4]
v
#Podstawowe operacje na macierzach
m<-matrix(c(1,2,3,11,12,13))
m
dim(m)
m <- matrix(c(1,2,3,4,5,6), nrow = 2, ncol=3, byrow=TRUE,
            dimnames = list(c("w1", "w2"),
                            c("c1", "c2", "c3")))
m
dim(m)
dim(m)<-c(3,2)
m <- matrix(c(1,2,3,4,5,6), nrow = 2, ncol=3, byrow=FALSE,
            dimnames = list(c("w1", "w2"),
                            c("c1", "c2", "c3")));m
crossprod(m)#c1*c1,c1*c2 itd
sum(m)	
sum(m[,2])	
m["w1",2]
m[2,3] 
100+m	
w<-c(1:10);w
dim(w)<-c(5,2);w
nw<-cbind(w,100);nw
nw<-rbind(nw,-12);nw

###########################################
#Rysujemy i wyrabiamy intuicj?
demo(graphics)


?dnorm
postscript("NormalDensity.ps",width=6,height=6,horizontal=FALSE)
par(mfrow=c(1,1))
curve(dnorm(x,mean=0.5,sd=0.5), from = -5, to = 5, col = "red", lwd = 2,main = "NormalDensity")
curve(dnorm(x,mean=-0.5,sd=2), from = -5, to = 5, col = "slategray", lwd = 2,main = "",add=TRUE)
curve(dnorm, from = -5, to = 5, col = "blue", lwd = 3,main = "",add=T)
text(-5, 0.4, expression("N(0.5,0.5)"), adj = 0)
text(-5, 0.3, expression("N(-0.5,2)"), adj = 0)
text(-5, 0.5, expression("N(0,1)"), adj = 0)
text(-5, 0.7, expression(f(x)==frac(1,sigma*sqrt(2*pi))*e^{-frac((x-mu)^2,2*sigma^2)}), adj = 0)
dev.off()


postscript("NormalDensity.ps",width=6,height=6,horizontal=FALSE)
curve(dnorm(x,mean=0.5,sd=0.5), from = -5, to = 5, col = "red", lwd = 2,main = "NormalDensity")
curve(dnorm(x,mean=-0.5,sd=2), from = -5, to = 5, col = "slategray", lwd = 2,main = "",add=TRUE)
curve(dnorm, from = -5, to = 5, col = "slategray", lwd = 3,main = "",add=T)
text(-5, 0.4, expression("N(0.5,0.5)"), adj = 0)
text(-5, 0.3, expression("N(-0.5,2)"), adj = 0)
text(-5, 0.5, expression("N(0,1)"), adj = 0)
text(-5, 0.7, expression(f(x)==frac(1,sigma*sqrt(2*pi))*e^{-frac((x-mu)^2,2*sigma^2)}), adj = 0)
dev.off()


postscript("Skosnosc.ps",width=6,height=6,horizontal=FALSE)
mi<-0
ni<-3
par(mfrow=c(1,1))
curve(dnorm(x,mean=mi,sd=1), from = -5, to = 9, col = "slategray", lwd = 3,main = "",add=F,ann=T)
curve(dchisq(x,df=ni), from = -5, to = 9, col = "red", lwd = 3,main = "",add=T)
text(-5, 0.32, expression("N(0,1)"), adj = 0)
text(-5, 0.2, expression(chi^{2}*(3)), adj = 0,col="red")
abline(v=mi,lty="dashed",lwd = 2,col = "slategray")
abline(v=ni,lty="dashed",col="red",lwd = 2)
abline(h=0.1,lty="dashed",col="green",lwd = 4)
dev.off()

postscript("Leptokurtoza.ps",width=6,height=6,horizontal=FALSE)
mi<-0
ni<-1
par(mfrow=c(1,1))
curve(dnorm(x,mean=mi,sd=1), from = -6, to = 6, col = "slategray", lwd = 3,main = "",add=F,ann=F)
curve(dnorm(x,mean=mi,sd=2), from = -6, to = 6, col = "blue", lwd = 3,main = "",add=T,ann=F)
curve(dt(x,df=ni), from = -6, to = 6, col = "red", lwd = 3,main = "",add=T)
text(-5, 0.33, expression("N(0,1)"), adj = 0,col = "slategray")
text(-5, 0.30, expression("N(0,2)"), adj = 0,col="blue")
text(-5, 0.27, expression(t(5)), adj = 0,col="red")
dev.off()

#################################################
#W?asne Funkcje
mnozenie<-function(a,b){
  a*b
}
mnozenie(2,3)


test<-function(a){3*a}
test(2)
curve(test)

alfa<-function(a){2*a+5*cos(a)}
alfa(3)
curve(alfa,xlim=c(2,20),col="green")

for (i in 1:14){ #Przyk?ad p?tli
  print(i)
}

for(i in 1:15) print(i:(2*i))

i<-0
for(j in c(7,13,18,120)) {
  print(1:(2*i))
  i<-i+j
}
#Zad6 Tworzenie funkcji w praktyce - generowanie z wielowymioarowego r.normalnego
#http://mst.mimuw.edu.pl/lecture.php?lecture=sst&part=Ch5
rnorm(10)
set.seed(2023)
plot(rnorm(100),col="purple")

# II spos?b# I spos?b
sigma1 <- 5
sigma2 <- 3
ro <- 0.6

X1 <- rnorm(1,0,1)
X2 <- rnorm(1,0,1)

X1 <- sigma1*X1
X2 <- ro*(sigma2/sigma1)*X1+sigma2*((1-ro^2)^(0.5))*X2

X1
X2
# A teraz jak wy?ej ale w postaci funkcji
#generowanie rozk?adu normalnego
rbivariate <- function(mean.x = 70, sd.x=3, mean.y=162, sd.y=14, r=.50, iter=100) {
  z1 <- rnorm(iter)
  z2 <- rnorm(iter)
  x <- sqrt(1-r^2)*sd.x*z1 + r*sd.x*z2 + mean.x
  y <- sd.y*z2 + mean.y
  return(list(x,y))
}
data <- rbivariate(iter=1000,r=0)
mean(data[[1]])
sd(data[[1]])
mean(data[[2]])
sd(data[[2]])
plot(data[[1]],data[[2]])

# III spos?b
# Gotowe rozwi?zania
#a) mvrnorm()
#b)rmvnorm

#Ada)

install.packages("MASS")
library("MASS")
Sigma <- matrix(c(10,3,3,2),2,2)
Sigma
?mvrnorm
var(mvrnorm(n=1000, rep(0, 2), Sigma))
var(mvrnorm(n=1000, rep(0, 2), Sigma, empirical = TRUE))
Sigma<-diag(2)
Sigma
Sigma<-matrix(c(1,0,0,2),2,2)
Sigma
mvrnorm(n=1000,rep(0,2),Sigma)
plot(mvrnorm(n=1000,rep(0,2),Sigma))

#Ad b)
#install.packages("MASS")
?rmvnorm
install.packages("mvtnorm")
library(mvtnorm)
mu=c(0,1)
sigma=matrix(c(5,0,0,5),2,2)
z=rmvnorm(300,mu,sigma)
z
plot(z)

#Implementacja wzoru na opcj? w modelu BS
BS<-function(S,X,r,t,sigma){
  values<-c(2)
  dp<-(log(S/X)+(r+sigma^2/2)*t)/(sigma*sqrt(t))
  dm<-(log(S/X)+(r-sigma^2/2)*t)/(sigma*sqrt(t))
  values[1]<-S*pnorm(dp)-X*exp(-r*t)*pnorm(dm)
  values[2]<-X*exp(-r*t)*pnorm(-dm)-S*pnorm(-dp)
  values
}

(BS(100,110,0.03,1,0.4))
##################################################
#Praca na plikach

#setwd("C:\\MK")

#W?asne pliki - tworzenie, zapisywanie i odczytywanie
m <- matrix(c(1,2,3,4,5,6), nrow = 2, ncol=3, byrow=TRUE)
write.table(m,file="PierwszyPlik.txt",sep="\t",col.names = FALSE,row.names = FALSE)
m2<-read.table(file="PierwszyPlik.txt",sep="\t")
dim(m2)
m2
?write.table
#Wczytywanie



WIG20 <- read.csv("WIG20.csv", sep=";", dec=",")

View(WIG20)

par(mfrow=c(1,1))
mojedane<-ts(WIG20[,9])
plot(mojedane,type="l",col="red")
curve(dnorm(x,mean=mean(mojedane),sd=sd(mojedane)),xlim=c(-30,30),col="red",main=expression(Porownanie),ylab="")
hist(mojedane,add=F,freq=F)

curve(dnorm(x,mean=mean(mojedane),sd=sd(mojedane)),ylim=c(0,0.01),xlim=c(2200,2600),col="red",main=expression(Porownanie),ylab="")
hist(mojedane,add=T,freq=F,breaks=10)

dane<-read.csv2(file="WIG20.csv",dec=",")
dane<-ts(dane[,9],start=2000,frequency=252)
plot(dane,type="l",col="red")