#
# 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.
# 
#-----

savePlots = F

at = c(-0.3,0.6,0.9,0.2,0.1,-0.6,1.7,-0.9,-1.3,-0.6,-0.4,0.9,0.0,-1.4,-0.6) # a_0, a_1, to a_{14} 
Na = length(at)
Nam1 = Na-1

zt0 = c(19,20) # z_{-1}, z_0

# Part (a):
#
zt_a = zt0
for( ii in 1:Nam1 ){ # the index of z_t 
  newZ = zt_a[length(zt_a)] + at[ii+1] - 0.5 * at[ii] 
  zt_a = c( zt_a, newZ )
}
plot( -1:(length(zt_a)-2), zt_a, col="green", type="l", xlab="index", ylab="z_t", main="Part (a-b)" )
   
# Part (b):
#
zt_b = zt0
for( ii in 1:Nam1 ){ # the index of z_t 
  newZ = zt_b[length(zt_b)] + at[ii+1] - 0.2 * at[ii] 
  zt_b = c( zt_b, newZ )
}
lines( -1:(length(zt_b)-2), zt_b, col="red", type="l", xlab="index", ylab="z_t", main="Part (a-b)" )

if( savePlots ){
  postscript("../../WriteUp/Graphics/Chapter4/prob_3_a_n_b.eps", onefile=FALSE, horizontal=FALSE)
  plot( -1:(length(zt_a)-2), zt_a, col="green", type="l", xlab="index", ylab="z_t", main="Part (a-b)" )
  lines( -1:(length(zt_b)-2), zt_b, col="red", type="l", xlab="index", ylab="z_t", main="Part (a-b)" )
  dev.off()
}

# Part (c):
#
zt_c = zt0
for( ii in 1:Nam1 ){ # the index of z_t 
  newZ = 1.5*zt_c[length(zt_c)] -0.5*zt_c[length(zt_c)-1] + at[ii+1] 
  zt_c = c( zt_c, newZ )
}
plot( -1:(length(zt_c)-2), zt_c, col="green", type="l", xlab="index", ylab="z_t", main="Part (c-d)" )

# Part (d):
#
zt_d = zt0
for( ii in 1:Nam1 ){ # the index of z_t 
  newZ = 1.2*zt_d[length(zt_d)] -0.2*zt_d[length(zt_d)-1] + at[ii+1] 
  zt_d = c( zt_d, newZ )
}
lines( -1:(length(zt_d)-2), zt_d, col="red", type="l", xlab="index", ylab="z_t", main="Part (c-d)" )

if( savePlots ){
  postscript("../../WriteUp/Graphics/Chapter4/prob_3_c_n_d.eps", onefile=FALSE, horizontal=FALSE)
  plot( -1:(length(zt_c)-2), zt_c, col="green", type="l", xlab="index", ylab="z_t", main="Part (c-d)" )
  lines( -1:(length(zt_d)-2), zt_d, col="red", type="l", xlab="index", ylab="z_t", main="Part (c-d)" )
  dev.off()
}


# Part (e):
#

zt_e = zt0
for( ii in 1:Nam1 ){ # the index of z_t 
  newZ = 1.2*zt_e[length(zt_e)] -0.2*zt_e[length(zt_e)-1] + at[ii+1] - 0.5 * at[ii] 
  zt_e = c( zt_e, newZ )
}
plot( -1:(length(zt_e)-2), zt_e, xlab="index", ylab="z_t", main="Part (e)" )
lines( -1:(length(zt_e)-2), zt_e )

if( savePlots ){
  postscript("../../WriteUp/Graphics/Chapter4/prob_3_e.eps", onefile=FALSE, horizontal=FALSE)
  plot( -1:(length(zt_e)-2), zt_e, type="l", xlab="index", ylab="z_t", main="Part (e)" )
  lines( -1:(length(zt_e)-2), zt_e, type="l", xlab="index", ylab="z_t", main="Part (e)" )
  dev.off() 
}