#
# Problem EPage 159
# 
# 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.
# 
#-----

save_plots = F

library(caret) 
library(kernlab)

# Generate data to predict: 
set.seed(100)
x = runif(100,min=2,max=100)
y = sin(x) + rnorm(length(x)) * 0.25
sinData = data.frame(x=x,y=y)
if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/chap_7_prob_1_vary_sigma.eps", onefile=FALSE, horizontal=FALSE) }
#if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/chap_7_prob_1_vary_cost.eps", onefile=FALSE, horizontal=FALSE) }
#if( save_plots ){ postscript("../../WriteUp/Graphics/Chapter7/chap_7_prob_1_vary_epsilon.eps", onefile=FALSE, horizontal=FALSE) }
plot(x,y)

## Create a grid of x values to use for prediction
dataGrid = data.frame(x=seq(2,100,length=100))

# Train some SVM models on this data and plot them:
#

# Reasonable looking predictions:
# 
rbfSVM = ksvm( x=x, y=y, data=sinData, kernel="rbfdot", kpar="automatic", C=1, epsilon=0.1 )
modelPrediction = predict( rbfSVM, newdata=dataGrid )
points( x=dataGrid$x, y=modelPrediction[,1], type="l", col="blue" )

if( TRUE ){
    # A large value for sigma: 
    # 
    rbfSVM = ksvm( x=x, y=y, data=sinData, kernel="rbfdot", kpar=list(sigma=100.0), C=1, epsilon=0.1 )
    modelPrediction = predict( rbfSVM, newdata=dataGrid )
    points( x=dataGrid$x, y=modelPrediction[,1], type="l", col="red" )

    # A small value for sigma:
    #
    rbfSVM = ksvm( x=x, y=y, data=sinData, kernel="rbfdot", kpar=list(sigma=1e-2), C=1, epsilon=0.1 )
    modelPrediction = predict( rbfSVM, newdata=dataGrid )
    points( x=dataGrid$x, y=modelPrediction[,1], type="l", col="green" )
    
    if( save_plots ){ dev.off() }
}

if( FALSE ){ 
    # A very large value of the cost C (should overfit):
    # 
    rbfSVM = ksvm( x=x, y=y, data=sinData, kernel="rbfdot", kpar="automatic", C=10^7, epsilon=0.1 )
    modelPrediction = predict( rbfSVM, newdata=dataGrid )
    points( x=dataGrid$x, y=modelPrediction[,1], type="l", col="red" )

    # A very small value of the cost C (should underfit):
    #
    rbfSVM = ksvm( x=x, y=y, data=sinData, kernel="rbfdot", kpar="automatic", C=10^(-2), epsilon=0.1 )
    modelPrediction = predict( rbfSVM, newdata=dataGrid )
    points( x=dataGrid$x, y=modelPrediction[,1], type="l", col="green", main='changes in cost' )

    if( save_plots ){ dev.off() }
}

if( FALSE ){
    # A large value for epsilon: 
    # 
    rbfSVM = ksvm( x=x, y=y, data=sinData, kernel="rbfdot", kpar="automatic", C=1, epsilon=0.5 )
    modelPrediction = predict( rbfSVM, newdata=dataGrid )
    points( x=dataGrid$x, y=modelPrediction[,1], type="l", col="red" )

    # A small value for epsilon:
    #
    rbfSVM = ksvm( x=x, y=y, data=sinData, kernel="rbfdot", kpar="automatic", C=1, epsilon=0.001 )
    modelPrediction = predict( rbfSVM, newdata=dataGrid )
    points( x=dataGrid$x, y=modelPrediction[,1], type="l", col="green" )
    
    if( save_plots ){ dev.off() }
}