# R script for to make a plot of a function and demonstrate
# calling procedures from separate files.

# The code in this file calls the procedure that evaluates the function ...
#    ... then makes the plot.

#  http://www.math.nyu.edu/faculty/goodman/teaching/MathFin/index.html
# Author: Jonathan Goodman


#        Parameters describing the function

k = 30                       #  the frequency parameter in the function to be plotted

source("PlotFunction.R")     #  Read in the function definition



#        Parameters describing the plot

xMin = 1           #  plot over the intervao [xMin,xMax]
xMax = 4
nPts = 300         #  the number of points to plot, uniformly spaced, including endpoints

dx   = (xMax - xMin)/(nPts-1)    #   The x-distance between plot points


#         Evaluate and record the function at the plot points


xVals = numeric(nPts)
fVals = numeric(nPts)

for ( i in 1:nPts){

    x = xMin + dx*(i-1)
    f = mod_wave( x, k)
    xVals[i] = x
    fVals[i] = f
  }


#           Make the plot, with all the extras that make it professional

xLabel = sprintf("X, from %7.2f to %7.2f", xMin, xMax)       # Create strings ...
title  = sprintf("A modulated wave")                         # ... to put parameters into ...
subtitle = sprintf("k = %7.2f, with %6d points", k, nPts)    # ... plot titles.

#   Make a popup plot on the screen

plot( xVals, fVals,          #   the numbers xVals are the x values and fVals are the y values
      type = "n",            #   the curve is a "not" actually plotted, or plotted as invisible
      tck  = 1,              #   the "tick length" is 1*the plot size, so the "ticks" turn into grid lines
      xlab = xLabel,         #   the string xLabel becomes xlab, which is writton below the x axis
      main = title,          #   written in bigger letters on top of the plot
      sub  = subtitle)       #   the subtitle is below the x label

lines( xVals, fVals,         #   This also plots xVals against fVals, but this time ...
      type = "l",            #   ... type "l" means a solid line
      lwd  = 4)              #   line width = 4 means a wide line.

lineX = numeric(2)           #   Draw a straight line over the tops of the waves
lineX[1] = xMin              #   x coordinates of the endpoints of the line
lineX[2] = xMax
lineY = numeric(2)
lineY[1] = xMin              #   y coordinates of the endpoints of the line
lineY[2] = xMax
lines( lineX, lineY,         #   Draw the line, with width 2, not so wide
      type = "l",
      lwd  = 2)
lineY[1] = -xMin             #   The same thing, a line under the bottoms of the waves
lineY[2] = -xMax
lines( lineX, lineY,
      type = "l",
      lwd  = 2)


#    Put the same plot in a file mod_wave.pdf
#    The code is cut and pasted from above

pdf("mod_wave.pdf")          #   Write the plot to a file called mod_wave.pdf
plot( xVals, fVals,          #   the numbers xVals are the x values and fVals are the y values
      type = "n",            #   the curve is a "not" actually plotted, or plotted as invisible
      tck  = 1,              #   the "tick length" is 1*the plot size, so the "ticks" turn into grid lines
      xlab = xLabel,         #   the string xLabel becomes xlab, which is writton below the x axis
      main = title,          #   written in bigger letters on top of the plot
      sub  = subtitle)       #   the subtitle is below the x label

lines( xVals, fVals,         #   This also plots xVals against fVals, but this time ...
      type = "l",            #   ... type "l" means a solid line
      lwd  = 4)              #   line width = 4 means a wide line.

lineX = numeric(2)           #   Draw a straight line over the tops of the waves
lineX[1] = xMin              #   x coordinates of the endpoints of the line
lineX[2] = xMax
lineY = numeric(2)
lineY[1] = xMin              #   y coordinates of the endpoints of the line
lineY[2] = xMax
lines( lineX, lineY,         #   Draw the line, with width 2, not so wide
      type = "l",
      lwd  = 2)
lineY[1] = -xMin             #   The same thing, a line under the bottoms of the waves
lineY[2] = -xMax
lines( lineX, lineY,
      type = "l",
      lwd  = 2)

dev.off()                    #  close the file and go home