# 7-03-2020  in R, type   source("Rlang.q")   to execute Appendix C examples of R

Rdesc = function() {
    cat("\n\n ***** R Tutorial (Appendix C) *****\n\n")
    cat("\t 1. R is a functional language, with arguments inside parentheses ()\n")
    cat("\t 2. Download R from https://cran.r-project.org/ \n")
    cat("\t 3. Type  help.start()  to bring up an interactive search window\n")
    cat("\t 4. We will use R in place of probability tables and for plotting\n")
    cat("\t 5. We will focus on basic R, not RStudio and other advanced options/libraries\n")
    cat("\t 6. Most R functions have optional arguments with default values\n")
    cat("\t 7. We end with a description of how to write your own R function\n\n\n")
  cat("\t type the letter 'c' to continue\n")
  cat("\t type the letter 'Q' to quit\n")
  cat("\t invoke the function 'q()' to exit R\n\n");  browser()
  cat("\n\n\n")
}
Rdesc()


Rbasics = function() {
    cat("Basic Arithmetic, built-in Functions, and Graphics (the R prompt is >)\n\n")
    cat("> x=1+3; y=sin(x); z=exp(x)\t\t separate multiple inline commands with ;\n\n")
        x=1+3; print(paste("x=",x))
        y=sin(x); print(paste("y=",y))
        z=exp(x); print(paste("z=",z))
    cat("\n\t make a vector by concatenation   > xyz = c(x,y,z)\n\n")
        xyz = c(x,y,z); print(paste("xyz=c(",paste(xyz,collapse=","),")"))
    cat("\n\n\t The  browser()  R function takes you  into interactive mode:\n\n")
    cat("\t\t Enter any R command\n")
    cat("\t\t or the letter 'n' to execute the next command\n")
    cat("\t\t or the letter 'c' to continue\n\n")
        browser()

           # basic plotting 
    cat("\n\n Some basic plotting examples\n\n")
    cat("\t 100 random points on unit square\n")
        cat("\t\t > xr=runif(100); yr=runif(100)\n")
	xr=runif(100); yr=runif(100)
    cat("\t\t > plot(xr,yr)\t\t basic plot of scatter diagram\n\n")
        plot(xr,yr);  lim=c(0,1)
	browser()
    cat("\n\t lim=c(0,1)\tmore optional plotting arguments...better?\n\n")
        cat("\t> plot(xr,yr,pch=16,col=2,xlim=lim,ylim=lim,main='Example')\n\n")
        plot(xr,yr,pch=16,col=2,xlim=lim,ylim=lim,main="Example"); browser()

           # line plots
    cat("\n\n line vs scatter plot examples\n\n")
        cat("\t x = seq(0,1,0.01)\t vector of 101 equally spaced points (0:100)/100\n\n")
            x = seq(0,1,0.01)
        cat("\t compute values of sin function at x   y = sin(x)\n") 
            y = sin(x)
	    cat("\n\t y is also a vector with same length as x\n\n")
        cat("\t plot(x,y,type='l')\t  gives a line plot rather than points (default)\n\n")
            plot(x,y,type='l',ylim=c(-1,1)); browser()
        cat("\t\t add another sine curve to plot\n\n")
	    lines(x,sin(8*pi*x),col=2,lty=2)
	        abline(h=0,col=4,lwd=.5); browser()
        cat("\n\n various unix-like command listing objects in file .RData\n\n")
            cat("\t > ls()\t you should type this is yourself\n\n"); browser(); ls()
  browser()
}
Rbasics()



Rprobs = function() {

    cat("Probability Related Functions\n\n")
    cat("\t For any built-in prob mass or density function,\n")
    cat("\t\t there are 4 functions:\n\n")
    cat("\t\t\t The Uniform is  unif\n")
    cat("\t\t\t The standard Normal is  norm\n")
    cat("\t\t\t The Binomial is  binom, etc.\n\n\n");  browser()
    cat("\n\t Examples:\n\n")

    cat("\t\t > fx = dnorm(x)\t\t the pdf at x (x can be a vector)\n")
    cat("\t\t > Fx = pnorm(x)\t\t the cdf at x; Prob( X le x )\n")
    cat("\t\t >  q = qnorm(p)\t\t quantile: P( X le q ) = p\n")
    cat("\t\t >  x = rnorm(100)\t\t generate 100 N(0,1) samples\n\n")
    cat("\t\t > set.seed(123)\t\t set random number seed,\n")
    cat("\t\t\t\t\t\t  so can repeat the same sequence\n\n")
    cat("\n\t Pick some values of   x p q   and try it out.\n\n\n")
  browser()
}
Rprobs()


Rloops = function() {
    cat("\n  **** Looping and Control ****\n\n\n")

    cat("\t > n=100; nrep=1000; ans=rep(0,nrep)\t create a new vector\n\n")
        n=100; nrep=1000; ans=rep(0,nrep);  browser()

    cat("\n\n\t > for(k in 1:nrep) {ans[k]=mean(rnorm(n)}\n")
    cat("\t\t saves (a new) xbar in kth place\n\n")
        for(k in 1:nrep) {ans[k]=mean(rnorm(n))};  browser()

    cat("\n\n\t > hist(ans,40,col=2,main='dist of xbar')\n")
    cat("\t\t plots a histogram of the 1000 sample means\n\n")
        hist(ans,40,col=2,main='dist of xbar');  browser()

    cat("\n\n\t useful logical construct:\n\n")
    cat("\t\t > if(runif(1)>0.5) {side='Heads'} else {side='Tails'}\n\n")
  browser()
}
Rloops()

Rfunc = function(){

    cat("\n\n **** Writing Your Own R Function to Visualize mean and std dev ****\n\n")
    cat("\t Note:  Variables created in functions are not saved on exit (good!)\n")

  hw1 = function(n=100,nrep=1000,seed=123) { set.seed(seed)
   ans=matrix(0,nrow=nrep,ncol=2)     # save simulation results
              # simulation loop
   for( k in 1:nrep ) {
       z=rnorm(n); ans[k,1]=mean(z); ans[k,2]=sd(z)
    }              # save mean and standard deviation in kth row of ans
    hist( ans[,1], 40, col=2 ); abline(v=0)	# 1st column of ans
      browser()     # examine graph; type  c  to continue;  Q  to quit
    hist( ans[,2], 40, col=2 ); abline(v=1)	# 2nd column of ans
   return(list(ans=ans,n=n))
  }       # the function hw1 is now complete

   cat("\n\n ****  print(hw1)  types out the function  hw1  entered ****\n\n")
   print(hw1);  cat("\n");  browser()

   cat("\n\n run function hw1 and save output to list 'results'\n\n")
       cat("\t note that  hw1  plots and returns a list as well\n\n")
   results = hw1()

   cat("\n\t Did it run the first time???  If not, debug in browser\n\n")
  browser()
}
Rfunc()


Rpdf = function() {

    cat("\n\n Making It Easy to Do Your Homework:\n\n")
    cat("\t Type the function  hw1 Into the File  hw1.txt\n\n");  browser()

    cat("\n\n\t\t If you include the command  results=hw1()\n")
    cat("\t\t\t at the end of the file, it will execute below\n\n"); browser()
        cat("\t COPY AND RUN THESE:\n\n")

    cat("\t\t  > source('hw1.txt') \t # read the commands into R and debug if necessary\n\n")
    cat("\t\t  > dev.copy2pdf('fig1.pdf') \t # copy figure to a pdf file to submit\n\n")
    cat("\t\t  > print(results$ans); print(results$n)	\t # access items in the list\n\n")
    cat("\t\t  > q()\t\t # quit R (save to .RData option given)")
  browser()
}
Rpdf()