# ===============================================
# Newton Raphson
# ===============================================
# x[n+1] = x[n] - f( x[n] )/ f'( x[n] ) 
# x^3-6=0 => x^3=6 => x=6^(1/3)
6^(1/3)

x<--2
x <- x - (x^3-6)/(3*x^2)
x
x <- x - (x^3-6)/(3*x^2)
x
x <- x - (x^3-6)/(3*x^2)
x
x <- x - (x^3-6)/(3*x^2)
x
x <- x - (x^3-6)/(3*x^2)
x
x <- x - (x^3-6)/(3*x^2)
x
x <- x - (x^3-6)/(3*x^2)
x


# ===============================================
#Newton Raphson - command for 
# ===============================================
x<-1
for (i in 1:5)  {
  x <- x - (x^3-6)/(3*x^2)
  print(x)
}


x<-20
for (i in 1:15)  {
  x <- x - (x^3-6)/(3*x^2)
  print(x)
}


# Another Example
x<-1
tolerance<-0.000001
f<-x^3+2*x^2-7
f
f.prime<-3*x^2+4*x
f.prime
while(abs(f)>tolerance)
{
  x<-x-f/f.prime
  f<-x^3+2*x^2-7
  f.prime<-3*x^2+4*x
}
x
f
f.prime


x<-1
tolerance<-0.000001
f<-x^3+2*x^2-7
f.prime<-3*x^2+4*x
repeat
{
  x<-x-f/f.prime
  f<-x^3+2*x^2-7
  f.prime<-3*x^2+4*x
  if(abs(f) <= tolerance) break
}
x
f
f.prime


# same example
x<- -1000000 
tolerance<-0.000001
f<-x^3+2*x^2-7
f.prime<-3*x^2+4*x
step <- 0
for (step in 1:200000){ 
  x<-x-f/f.prime
  f<-x^3+2*x^2-7
  f.prime<-3*x^2+4*x 
  print( round(c(step, x, f),4) ) 
  if ( abs(f) < tolerance ) break
}
# ===============================================