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# Demonstration of the sFPCA package
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# install the package 
# install these three required packages first.  If you cannot install them, please upgrade your R to the latest version
install.packages("devtools")
install.packages("dplyr")
install.packages("fda")

# load these three packages
library(fda)
library(dplyr)
library(devtools)

# download the sFPCA from github and install it automatically 
devtools::install_github("YunlongNie/sFPCA")

# load the sFPCA package 
library(sFPCA)

# a demo for the first simulation study in the paper (section 5.1)

# load the dataset; this data set contains 1000 replicates in total
data(binary_dat);
# xmat is a 365*1000 matrix with each column representing to the trajectory for one replicate at 365 time points
xmat = binary_dat$x;
# y is the vector of length 1000, each element represents the binary response for one replicate
y=binary_dat$y
# input the xmat matrix, the y response vector, the weight parameter theta, the number of sFPCs one is trying to estimate and a new matrix to make predictions on (here I just use the same xmat to do the predictions)

# we first set the theta to be 0.1, for the supervised FPC method 
supervised_res = sFPCA::sfpcs_binary(xmat,y,npc_select=2,theta=0.1,xmat_new = xmat)
# the fitted value for 1000 replicates 
supervised_res$fitted
# the proportion that the fitted values match the observed responses 
mean(y==supervised_res$fitted)

# the estimated sFPCAs are stored in the supervised_res$sfpcs
supervised_res$sfpcs # a list with each element corresponding to one sFPC

# we can visualize them by 
plot(supervised_res$sfpcs[[1]], main="first supervised FPC")
plot(supervised_res$sfpcs[[2]], main="second supervised FPC")


# we then set the theta to be 1, for the unsupervised FPC method 
unsupervised_res = sFPCA::sfpcs_binary(xmat,y,npc_select=2,theta=1,xmat_new = xmat)
# the fitted value for 1000 replicates 
unsupervised_res$fitted
# the proportion that the fitted values match the observed responses 
mean(y==unsupervised_res$fitted)

# the estimated FPCAs are stored in the unsupervised_res$sfpcs
unsupervised_res$sfpcs # a list with each element corresponding to one FPC

# we can visualize them by 
plot(unsupervised_res$sfpcs[[1]], main="unsupervised FPC")
plot(unsupervised_res$sfpcs[[2]], main="unsupervised FPC")