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dataf.sim.1.CFF07 <- function(numTrain = 100, numTest = 50, numDiscrets = 51, plot = FALSE){
# Processes:
# X(t) = m_0(t) + e(t), m_0(t) = 30*(1-t)*t^1.2
# Y(t) = m_1(t) + e(t), m_1(t) = 30*(1-t)^1.2*t
# e(t): Gaussian with mean = 0, cov(X(s), X(t)) = 0.2*exp(-abs(s - t)/0.3)
t <- 0:(numDiscrets - 1)/(numDiscrets - 1)
mean0 <- 30*(1-t)*t^1.2
mean1 <- 30*(1-t)^1.2*t
cov <- matrix(nrow=numDiscrets, ncol=numDiscrets)
for (i in 1:numDiscrets){
for (j in 1:numDiscrets){
cov[i,j] <- 0.2*exp(-abs(t[i] - t[j])/0.3)
}
}
X <- mvrnorm(n=numTrain+numTest, mu=mean0, Sigma=cov)
Y <- mvrnorm(n=numTrain+numTest, mu=mean1, Sigma=cov)
datafX <- list()
datafY <- list()
labelsX <- as.list(rep(0,numTrain+numTest))
labelsY <- as.list(rep(1,numTrain+numTest))
for (i in 1:(numTrain + numTest)){
datafX[[i]] <- list(args = t, vals = X[i,])
datafY[[i]] <- list(args = t, vals = Y[i,])
}
learn <- list(dataf = c(head(datafX, numTrain), head(datafY, numTrain)),
labels = c(head(labelsX, numTrain), head(labelsY, numTrain)))
class(learn) = "functional"
test <- list(dataf = c(tail(datafX, numTest), tail(datafY, numTest)),
labels = c(tail(labelsX, numTest), tail(labelsY, numTest)))
class(test) = "functional"
if (plot){
plot(0, type="n", xlim=c(0,1), ylim=c(0, 9),
main=paste("Model 1 from CuevasFF07: ",
"0 red (", sum(unlist(learn$labels) == 0), "), ",
"1 blue (", sum(unlist(learn$labels) == 1), "), ", sep=""))
grid()
for (i in 1:length(learn$dataf)){
if (learn$labels[[i]] == 0){
lineColor <- "red"
lineType <- 1
}
if (learn$labels[[i]] == 1){
lineColor <- "blue"
lineType <- 2
}
lines(learn$dataf[[i]]$args, learn$dataf[[i]]$vals, col=lineColor, lty=lineType)
}
}
return (list(learn = learn, test = test))
}
dataf.sim.2.CFF07 <- function(numTrain = 100, numTest = 50, numDiscrets = 51, plot = FALSE){
# Processes
# X(t) = m_0(t) + e(t), m_0(t) = 30*(1-t)*t^2 + 0.5*abs(sin(20*pi*t))
# Y(t) = smooth.spline with 8 knots
# e(t): Gaussian with mean = 0, cov(X(s), X(t)) = 0.2*exp(-abs(s - t)/0.3)
t <- 0:(numDiscrets - 1)/(numDiscrets - 1)
mean0 <- 30*(1 - t)*t^2 + 0.5*abs(sin(20*pi*t))
cov <- matrix(nrow=numDiscrets, ncol=numDiscrets)
for (i in 1:numDiscrets){
for (j in 1:numDiscrets){
cov[i,j] <- 0.2*exp(-abs(t[i] - t[j])/0.3)
}
}
X <- mvrnorm(n=numTrain+numTest, mu=mean0, Sigma=cov)
Y <- NULL
for (i in 1:nrow(X)){
Y <- rbind(Y, smooth.spline(t, X[i,], nknots = 8)$y)
}
datafX <- list()
datafY <- list()
labelsX <- as.list(rep(0,numTrain+numTest))
labelsY <- as.list(rep(1,numTrain+numTest))
for (i in 1:(numTrain + numTest)){
datafX[[i]] <- list(args = t, vals = X[i,])
datafY[[i]] <- list(args = t, vals = Y[i,])
}
learn <- list(dataf = c(head(datafX, numTrain), head(datafY, numTrain)),
labels = c(head(labelsX, numTrain), head(labelsY, numTrain)))
class(learn) = "functional"
test <- list(dataf = c(tail(datafX, numTest), tail(datafY, numTest)),
labels = c(tail(labelsX, numTest), tail(labelsY, numTest)))
class(test) = "functional"
if (plot){
plot(0, type="n", xlim=c(0,1), ylim=c(0, 7),
main=paste("Model 2 from CuevasFF07: ",
"0 red (", sum(unlist(learn$labels) == 0), "), ",
"1 blue (", sum(unlist(learn$labels) == 1), "), ", sep=""))
grid()
for (i in 1:length(learn$dataf)){
if (learn$labels[[i]] == 0){
lineColor <- "red"
lineType <- 1
}
if (learn$labels[[i]] == 1){
lineColor <- "blue"
lineType <- 2
}
lines(learn$dataf[[i]]$args, learn$dataf[[i]]$vals, col=lineColor, lty=lineType)
}
}
return (list(learn = learn, test = test))
}
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