# Library of useful functions
# to load the library: R> source("library.R")

write.data.file <- function(file="data.csv", n=100, min=0, max=1) {
# function to generate a set of data and save them to a file

		x <- runif(n, min, max)
		write(x, file, 10, FALSE, ", ")
}

read.data.file <- function(file1="data.csv", sep1=",") {
# function to read a set of data from a file

  x <- scan(file=file1, sep=sep1)
  return(x)
}


convergence <- function(n=1e3, opt="mean") {

	    if (opt=="mean") y =  mean ( runif(n, 0, 1) )
            if (opt=="sd") y =  sd ( runif(n, 0, 1) )

	    return(y)
}


conv.plot <- function(nmax=1e3, step=1, opt="mean") {
	  n <- seq(1,nmax,step)
	  y <- n
	  for (i in n) {
	     y[i] = convergence(i, opt)
	  }
          quartz(height=4)
	  plot(n,y, type="l", xlab="tries", ylab="frequency", log="x")
}


gauss <-function(n=1e3, sigma=1) {
    quartz(height=4)
    x<-rnorm(n,sd=sigma)
    length(x[x>=0])
    length(x[x>=-1 & x<=1])
    length(x[abs(x)<=1])

    mean(x)
    sd(x)

    hist(x, nc=50, prob=TRUE)
    d <- function(z) dnorm(z, 0, sigma)
    plot(d, -4*sigma, 4*sigma, ty='l', add=TRUE, col='red')
    fx <- function(z) dnorm(z, mean(x), sd(x))
    plot(fx, -4*sigma, 4*sigma, ty='l', add=TRUE, col='brown')
}