Example R programs and commands
		      1. Data lists; functions; graphs

#
# Everything between "#" and the end of a line is a comment.
#

###### PLOT TABULATED DATA
x <- c(1.1, 1.7, 2.0, 2.1, 1.9, 1.5)   # assign "x" a column of data 
# NOTE: "<-" means assignment; read it as "gets". "=" can be used as well.
x           # display the value of "x"
x[1]        # first element of "x"
x[4]        # fourth element of "x"
length(x)   # number of elements in "x"
plot(x)     # by default, plot points (i,x[i]) for i=1,...,length(x)

plot(x,type="line")         # piecewise linear interpolation
plot(x,type="l")            # "help(plot)" shows the other abbreviations
plot(x,type="l",asp=10)     # y/x aspect ratio >> 1: tall
plot(x,type="l",asp=0.1)    # y/x aspect ratio << 1: wide
plot(x,type="l",col="red")  # "colors()" lists the choices

###### PLOT A SAMPLED FUNCTION
0:100       # list the integers 0,1,2,...,100
t <- 2*pi*(0:100)*0.01   # R knows about pi
y <- sin(t)              # evaluate sine at all "t" values
plot(t,y)
plot(t,sin(t))
plot(t,sin(t), type="l", col="dark green")


###### PLOT SEVERAL FUNCTIONS ON THE SAME AXES
t <- 2*pi*(0:100)*0.01            # same sampling of [0,2*pi] as before
data2 <- cbind( sin(t), cos(t) )  # bind two columns into a matrix   
matplot( data2, type="l" )        # plot column 1 in black, column 2 in red (default)
matplot( data2, type="l", col=c("lime green","purple"))  # if you prefer other colors
data3 <- cbind( sin(t), cos(t), exp(-t) )
matplot( data3, type="l" )        # col.1 black, col.2 red, col.3 green (default)
matplot( t, data3, type="l" )     # put actual "t" values on the abscissa


###### DEFINE A FUNCTION OF ONE VARIABLE
# Haar's function:
#   haar(t) =  1, if 0<t=<1/2
#   haar(t) = -1, if 1/2<t=<1
#   haar(t) =  0, otherwise
haar <- function(t) {   # code to define the function "haar" follows:
 out <- 0
 if(t>0) {
   if(t<=1/2) {
     out <- 1
   } else {
     if(t<=1) {
       out <- -1
     }
   }
 }
 return(out)
}

###### GENERALIZE TO ALLOW VECTORS AS INPUT:
vhaar <- function(vt) { # code to define the function "vhaar" follows:
 out <- vt      # makes a vector of the same length as input "vt"
 for(n in 1:length(vt)) {
   out[n] <- haar(vt[n])
 }
 return(out)
}

# Plot the generalized function so defined:
t <- (-10:110)*0.01;          # abscissa values -0.10, -0.09,..., 1.09, 1.10.
plot(t,vhaar(t), type="l")

# Plot the function and its dilate by 2 on the same axes:
matplot(t,cbind(vhaar(t), sqrt(2)*vhaar(2*t)), type="l")
# NOTE: "sqrt" is the square-root function
# NOTE: "2*t" multiplies each element of "t" by 2.
# NOTE: "sqrt(2)*vhaar" multiplies by 2 each element of the vector returned by "vhaar".

# Plot the function and its dilates and translates on the same axes:
matplot(t,cbind(vhaar(t), sqrt(2)*vhaar(2*t), sqrt(4)*vhaar(4*t-3) ), type="l")
# NOTE: "4*t-3" subtracts 1 from each element of "4*t".


###### READ PREVIOUSLY DEFINED FUNCTIONS FROM A FILE
# If "haar" and "vhaar" are defined in file "haar.txt" in the current folder,
# then their definitions may be recalled via:
source("haar.txt")