# Skript na vypocet vzdalenosti pomoci ruznych metrik vzdalenosti. Obsahuje i vizualizace vypoctu vzdalenosti.
# by Eva Koritakova (Janousova), 26/oct/2015.
# -----------------------------------------------------------------------------------------------------------#


# data:
X1=matrix(c(4,3,10,8),2,2)
X1
x0=as.matrix(c(3.5,9))

# vykresleni dat:
plot(X1,xlim=c(2,5),ylim=c(7,11),col="red",pch=16,cex=1.5,asp=1,xlab="p1",ylab="p2") # asp=1 - x and y ranges are same
points(t(x0),pch=16,col="blue",cex=1.5)
# na zaklade tohoto obrazku by se dalo usoudit, ze ma modry bod x0 stejnou vzdalenost od cervenych bodu -> ne ale vzdy! (pri pouziti ruznych metrik to muze byt ruzne, coz si ukazeme)



#### Euklidova metrika - vypocet vzdalenosti subjektu x0 od dvou ostatnich subjektu:
euc.dist <- array(0,nrow(X1))
for (i in 1:nrow(X1)) { 
   euc.dist[i] <- sqrt(sum((X1[i,] - x0) ^ 2)) # vypocet vzdalenosti
}
euc.dist

## Euklidova metrika - vykresleni:
windows(10,5)
par(mfrow=c(1,2),mar=c(5,5,1,1),oma=c(0,0,0,0))
# vzdalenosti subjektu x0 od dvou ostatnich subjektu
	plot(X1,xlim=c(2,5),ylim=c(7,11),col="red",pch=16,cex=1.5,asp=1,xlab="p1",ylab="p2") # asp=1 - x and y ranges are same
	points(t(x0),pch=16,col="blue",cex=1.5)
	lines(c(x0[1],X1[1,1]),c(x0[2],X1[1,2]),col="blue",lwd=2)
	lines(c(x0[1],X1[2,1]),c(x0[2],X1[2,2]),col="blue",lwd=2)
# znazorneni bodu, ktere lezi ve stejne vzdalenosti od bodu x0
	plot(X1,xlim=c(2,5),ylim=c(7,11),col="red",pch=16,cex=1.5,asp=1,xlab="p1",ylab="p2") # asp=1 - x and y ranges are same
	points(t(x0),pch=16,col="blue",cex=1.5)
	#install.packages("plotrix")
	library(plotrix)
	draw.circle(x0[1],x0[2],min(euc.dist),border="blue",lty=1,lwd=2)



#### Hammingova (manhattanska) metrika - vypocet vzdalenosti subjektu x0 od dvou ostatnich subjektu:
h.dist <- array(0,nrow(X1))
for (i in 1:nrow(X1)) { 
   h.dist[i] <- sum(abs(X1[i,]-x0)) # vypocet vzdalenosti 
}
h.dist

## Hammingova (manhattanska) metrika - vykresleni:
windows(10,5)
par(mfrow=c(1,2),mar=c(5,5,1,1),oma=c(0,0,0,0))
# vzdalenosti subjektu x0 od dvou ostatnich subjektu
	plot(X1,xlim=c(2,5),ylim=c(7,11),col="red",pch=16,cex=1.5,asp=1,xlab="p1",ylab="p2") # asp=1 - x and y ranges are same
	points(t(x0),pch=16,col="blue",cex=1.5)
	lines(c(x0[1],X1[1,1]),c(x0[2],x0[2]),col="blue",lwd=2)
	lines(c(X1[1,1],X1[1,1]),c(x0[2],X1[1,2]),col="blue",lwd=2)
	lines(c(x0[1],X1[2,1]),c(x0[2],x0[2]),col="blue",lwd=2)
	lines(c(X1[2,1],X1[2,1]),c(x0[2],X1[2,2]),col="blue",lwd=2)
# znazorneni bodu, ktere lezi ve stejne vzdalenosti od bodu x0
	plot(X1,xlim=c(2,5),ylim=c(7,11),col="red",pch=16,cex=1.5,asp=1,xlab="p1",ylab="p2") # asp=1 - x and y ranges are same
	points(t(x0),pch=16,col="blue",cex=1.5)
	lines(c(x0[1]-min(h.dist),x0[1]),c(x0[2],x0[2]-min(h.dist)),col="blue",lwd=2) 
	lines(c(x0[1]-min(h.dist),x0[1]),c(x0[2],x0[2]+min(h.dist)),col="blue",lwd=2)
	lines(c(x0[1],x0[1]+min(h.dist)),c(x0[2]-min(h.dist),x0[2]),col="blue",lwd=2)
	lines(c(x0[1],x0[1]+min(h.dist)),c(x0[2]+min(h.dist),x0[2]),col="blue",lwd=2)



#### Cebysevova metrika - vypocet vzdalenosti subjektu x0 od dvou ostatnich subjektu:
ceb.dist <- array(0,nrow(X1))
for (i in 1:nrow(X1)) { 
   ceb.dist[i] = max(abs(X1[i,]-x0)) # vypocet vzdalenosti 
}
ceb.dist

## Cebysevova metrika - vykresleni:
windows(10,5)
par(mfrow=c(1,2),mar=c(5,5,1,1),oma=c(0,0,0,0))
# vzdalenosti subjektu x0 od dvou ostatnich subjektu
	plot(X1,xlim=c(2,5),ylim=c(7,11),col="red",pch=16,cex=1.5,asp=1,xlab="p1",ylab="p2") # asp=1 - x and y ranges are same
	points(t(x0),pch=16,col="blue",cex=1.5)
	lines(c(x0[1],X1[1,1]),c(x0[2],x0[2]),col="gray",lwd=2)
	lines(c(X1[1,1],X1[1,1]),c(x0[2],X1[1,2]),col="blue",lwd=2)
	lines(c(x0[1],X1[2,1]),c(x0[2],x0[2]),col="gray",lwd=2)
	lines(c(X1[2,1],X1[2,1]),c(x0[2],X1[2,2]),col="blue",lwd=2)
# znazorneni bodu, ktere lezi ve stejne vzdalenosti od bodu x0
	plot(X1,xlim=c(2,5),ylim=c(7,11),col="red",pch=16,cex=1.5,asp=1,xlab="p1",ylab="p2") # asp=1 - x and y ranges are same
	points(t(x0),pch=16,col="blue",cex=1.5)
	lines(c(x0[1]-min(ceb.dist),x0[1]-min(ceb.dist)),c(x0[2]-min(ceb.dist),x0[2]+min(ceb.dist)),col="blue",lwd=2) 
	lines(c(x0[1]-min(ceb.dist),x0[1]+min(ceb.dist)),c(x0[2]-min(ceb.dist),x0[2]-min(ceb.dist)),col="blue",lwd=2) 
	lines(c(x0[1]-min(ceb.dist),x0[1]+min(ceb.dist)),c(x0[2]+min(ceb.dist),x0[2]+min(ceb.dist)),col="blue",lwd=2) 
	lines(c(x0[1]+min(ceb.dist),x0[1]+min(ceb.dist)),c(x0[2]-min(ceb.dist),x0[2]+min(ceb.dist)),col="blue",lwd=2) 



##### Vykresleni do jednoho grafu:
windows(10,5)
par(mfrow=c(1,2),mar=c(5,5,1,1),oma=c(0,0,0,0))
# vzdalenosti subjektu x0 od dvou ostatnich subjektu
	plot(X1,xlim=c(2,5),ylim=c(7,11),col="red",pch=16,cex=1.5,asp=1,xlab="p1",ylab="p2") # asp=1 - x and y ranges are same
	points(t(x0),pch=16,col="blue",cex=1.5)
	lines(c(x0[1],X1[1,1]),c(x0[2],X1[1,2]),col="green",lwd=2) # Euklidova vzd
	lines(c(x0[1],X1[2,1]),c(x0[2],X1[2,2]),col="green",lwd=2) # Euklidova vzd	
	lines(c(x0[1],X1[1,1]),c(x0[2],x0[2]),col="gray",lwd=2)
	lines(c(X1[1,1],X1[1,1]),c(x0[2],X1[1,2]),col="blue",lwd=2)
	lines(c(x0[1],X1[2,1]),c(x0[2],x0[2]),col="gray",lwd=2)
	lines(c(X1[2,1],X1[2,1]),c(x0[2],X1[2,2]),col="blue",lwd=2)
# znazorneni bodu, ktere lezi ve stejne vzdalenosti od bodu x0
	plot(X1,xlim=c(2,5),ylim=c(7,11),col="red",pch=16,cex=1.5,asp=1,xlab="p1",ylab="p2") # asp=1 - x and y ranges are same
	points(t(x0),pch=16,col="blue",cex=1.5)
	draw.circle(x0[1],x0[2],min(euc.dist),border="green",lty=1,lwd=2) # Euklidova vzd
	lines(c(x0[1]-min(h.dist),x0[1]),c(x0[2],x0[2]-min(h.dist)),col="magenta",lwd=2) # Hammingova (manhattanska) vzd
	lines(c(x0[1]-min(h.dist),x0[1]),c(x0[2],x0[2]+min(h.dist)),col="magenta",lwd=2) # Hammingova (manhattanska) vzd
	lines(c(x0[1],x0[1]+min(h.dist)),c(x0[2]-min(h.dist),x0[2]),col="magenta",lwd=2) # Hammingova (manhattanska) vzd
	lines(c(x0[1],x0[1]+min(h.dist)),c(x0[2]+min(h.dist),x0[2]),col="magenta",lwd=2)	# Hammingova (manhattanska) vzd
	lines(c(x0[1]-min(ceb.dist),x0[1]-min(ceb.dist)),c(x0[2]-min(ceb.dist),x0[2]+min(ceb.dist)),col="blue",lwd=2) # Cebysevova vzd
	lines(c(x0[1]-min(ceb.dist),x0[1]+min(ceb.dist)),c(x0[2]-min(ceb.dist),x0[2]-min(ceb.dist)),col="blue",lwd=2) # Cebysevova vzd
	lines(c(x0[1]-min(ceb.dist),x0[1]+min(ceb.dist)),c(x0[2]+min(ceb.dist),x0[2]+min(ceb.dist)),col="blue",lwd=2) # Cebysevova vzd
	lines(c(x0[1]+min(ceb.dist),x0[1]+min(ceb.dist)),c(x0[2]-min(ceb.dist),x0[2]+min(ceb.dist)),col="blue",lwd=2) # Cebysevova vzd




#### Canberrska metrika - vypocet vzdalenosti subjektu x0 od dvou ostatnich subjektu:
can.dist <- array(0,nrow(X1))
for (i in 1:nrow(X1)) { 
  can.dist[i] <- sum(abs(X1[i,]-x0)/(abs(X1[i,])+abs(x0))) # vypocet vzdalenosti 
}
can.dist

## Canberrska metrika - vykresleni:
x_grid=seq(x0[1,1]-3,x0[1,1]+3,by=0.01)
y_grid=seq(x0[2,1]-3,x0[2,1]+3,by=0.01)
dist_grid=matrix(0,length(x_grid),length(y_grid))
windows(10,10)
plot(x0[1,1],x0[2,1],pch=16,col="blue",cex=1.5,xlim=c(x0[1,1]-3,x0[1,1]+3),asp=1) # asp=1 - x and y ranges are same
d=0.12 
for (i in 1:length(x_grid)) {
  for (j in 1:length(y_grid)) {
    dist_grid[i,j]=(abs(x_grid[i]-x0[1,1])/(abs(x_grid[i])+abs(x0[1,1]))) + (abs(y_grid[j]-x0[2,1])/(abs(y_grid[j])+abs(x0[2,1])))
    if (dist_grid[i,j]<d & dist_grid[i,j]>d-0.001) points(x_grid[i],y_grid[j],pch=16)
  }
}
points(t(x0),pch=16,col="blue",cex=1.5)
points(X1[1,1],X1[1,2],pch=16,col="red",cex=1.5)
points(X1[2,1],X1[2,2],pch=16,col="red",cex=1.5)
d2=1.5 # prikresleni Hammingovy (manhattanske) vzdalenosti
lines(c(x0[1]-d2,x0[1]),c(x0[2],x0[2]-d2),col="blue",lwd=3) 
lines(c(x0[1]-d2,x0[1]),c(x0[2],x0[2]+d2),col="blue",lwd=3)
lines(c(x0[1],x0[1]+d2),c(x0[2]-d2,x0[2]),col="blue",lwd=3)
lines(c(x0[1],x0[1]+d2),c(x0[2]+d2,x0[2]),col="blue",lwd=3)