# 
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

sigma0 = 1
sigma1 = 2 # we assume that sigma1 > sigma0 

sf = ( ( sigma1^2 - sigma0^2 ) / ( sigma0^2 * sigma1^2 ) )/2

x = seq( -4, +4, length.out=100 )
y = x

z = outer( exp(sf*x^2), exp(sf*y^2), FUN="+" )

gamma = 4
a_intercept = sqrt( log( gamma - 1 )/sf )

#postscript("../../WriteUp/Graphics/Chapter2/prob_2.2.17.eps", onefile=FALSE, horizontal=FALSE)

contour(x,y,z, levels=c(4), xlab="X", ylab="Y", col="black")

z_circle = outer( sf*x^2, sf*y^2, FUN="+" )
contour(x,y,z_circle, levels=c(4), add=T, col="green")

segments( a_intercept, 0, 0, a_intercept, col="red" )
segments( 0, a_intercept, -a_intercept, 0, col="red" )
segments( -a_intercept, 0, 0, -a_intercept, col="red" )
segments( 0, -a_intercept, a_intercept, 0, col="red" )

#dev.off()