# 24.11.2010
x<-c(0,0,1,1,2)
y<-c(1,2,0,1,0)
f<-function(x,y) (x+2*y)/12
z<-f(x,y)
xyz<-cbind(x,y,z)

cloud(z~x*y,data=xyz,xlim=c(-1,3),ylim=c(-1,3),type=c("p","h"),
scales=list(arrows=F,distance=1.65,y=list(at=0:2), x=list(at=0:2)),
screen=list(x=-35,y=-35,z=-45))

f.cloud<-cloud(z~x*y,data=xyz,xlim=c(-1,3),ylim=c(-1,3),type=c("p","h"),
scales=list(arrows=F,distance=1.65,y=list(at=0:2), x=list(at=0:2)),
screen=list(x=-35,y=-35,z=-45))

print(f.cloud)

# Tällä tnf, reunajakaumat, plot
m <- matrix(1:4,2)
prop.table(m)
prop.table(m,1)
prop.table(m,2)

============
# Piirtofunktio

function.draw<-function(f,low=-1,hi=1,n=30)
{
r<-seq(low,hi,length=n)
z<-outer(r,r,f)
persp(r,r,z,xlab="x",ylab="y",zlab="z",theta = -90, phi = 30,ticktype="detailed")
}

# f(x,y)=8*x*y
f3<-function(x,y){ifelse(x>=y,8*x*y,0)}
function.draw(f3,0,1,25)

######################
# Tasajakauma Tas(0,1)
######################
# Kf
Ftas <- function(x,y) {ifelse(x>=0 & x<=1 & y>=0 & y<=1,x*y,0) }
function.draw(Ftas,0,1,25)

#tf f(x,y)=1
fTas<-function(x,y) x*y/(x*y)
function.draw(fTas,0,1,25)
######################
# Tasajakauma Tas(0,1)
######################
x <- seq(0, 2, length= 30)
y <- x
f <- function(x,y) {ifelse(x>=0 & x<=1 & y>=0 & y<=1,1,0) }
z <- outer(x, y, f)
#z[is.na(z)] <- 1
#op <- par(bg = "white")
#persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue",ticktype="detailed")
##########
function.draw<-function(f,low=-1,hi=1,n=30)
{
r<-seq(low,hi,length=n)
z<-outer(r,r,f)
persp(r,r,z,xlab="x",ylab="y",zlab="z",theta = -45, phi = 15,ticktype="detailed")
}