#    Make and save plots of the Gaussian density with two standard deviation
#    File: plotting.R for the class 
#  https://www.math.nyu.edu/faculty/goodman/teaching/MathFin2019/MathFinance.html
#    see the handout Plotting.pdf posted there.

n    = 150   # number of data point in the plot
a    = -1.  # left endpoint of plotting interval
b    = 5.   # plot interval is [a,b]
mu   = 1.5  # mean of gaussian to be plotted
sig1 = .5    # two standard deviations
sig2 = .6    # standard deviation

p = function(x, mu, sig){      # normal density
    p = ( 1/sqrt(2*pi*sig^2 ) ) * exp( -(x-mu)^2/(2*sig^2))
    return(p)
  }
  
dx = (b-a)/(n-1)  # distance between plot points
x  = 1:n          # will be x coordinates
y1 = 1:n          # will be y coordinates for first curve
y2 = 1:n          # will be y coordinates, second curve

for ( i in 1:n){
    x[i]  = a + (i-1)*dx
    y1[i] = p( x[i], mu, sig1)     # the same p() function with different sigma
    y2[i] = p( x[i], mu, sig2)
  }

title    = sprintf("Gaussians with mean %6.2f", mu)
subtitle = sprintf("Using %4d points", n)

color1  = "black"        # colors of the lines
color2  = "darkgreen"    # there are lots of colors

type1   = 1              # line types, the first is solid (type = 1), 
type2   = 4              # the second line is a pattern

legand1 = sprintf("standard deviation =%6.2f", sig1)
legand2 = sprintf("standard deviation =%6.2f", sig2)

legends = c( legand1, legand2)     # put the values into arrays ... 
colors  = c( color1, color2)       # ... for the legend() function
types   = c( type1, type2)

#                  Plot commands 

#------------ copy from here ------------------------------------------------

plot( x, y1,
      main = title,                  #  title at the top of the plot
      sub  = subtitle,               #  subtitle at the bottom
      xlab = "X axis",               #  label of the horizontal axis
      ylab = "probability density",  #  label of the vertical axis
      type = "l",                    #  get rid of the little circles
      lty  = type1,                  #  line style 
      col  = color1,                 #  line color
      panel.first = grid())          #  make a grid on the plot
      
lines( x, y2,                        #  plot the second curve, 
      lty = type2, col = color2)     #  line type and color 
      
legend( "topright",                  #  where the legend box goes.
        legends,                     #  the text of the legends
        col = colors,                #  corresponding line color and type
        lty = types)
        
#------------- copy to here ----------------------------------------------------
        

#               make a file with an image of the plot

pdf("fancyPlot.pdf")    # tell R to create a .pdf file for the plot

#     Plot commands, copy and paste from above 

#------------ copy from here ------------------------------------------------

plot( x, y1,
      main = title,                  #  title at the top of the plot
      sub  = subtitle,               #  subtitle at the bottom
      xlab = "X axis",               #  label of the horizontal axis
      ylab = "probability density",  #  label of the vertical axis
      type = "l",                    #  get rid of the little circles
      lty  = type1,                  #  line style 
      col  = color1,                 #  line color
      panel.first = grid())          #  make a grid on the plot
      
lines( x, y2,                        #  plot the second curve, 
      lty = type2, col = color2)     #  line type and color 
      
legend( "topright",                  #  where the legend box goes.
        legends,                     #  the text of the legends
        col = colors,                #  corresponding line color and type
        lty = types)
        
#------------- copy to here ----------------------------------------------------
        
dev.off()                   # tell R you're done.