# KS statistic (2-sided)
# Author:  Isabel Darcy 
# Date:  Feb 5, 2017

a <- sort(runif(30, 0,3))  # take 30 random points betwn 0 and 3
                           ## sort in increasing order
sa <-sin(a)                # take sine of these 30 points
b <- sort(runif(25, 0,3))  # 25 random points betwn 0 and 3
sb <-sin(b)                # take sine of these 25 points
c <- sort(runif(30, 0,3))  # 30 random points betwn 0 and 3
sc <- c^2                  # square these 30 points

# plot the data set sa, title = main
# pch = 17:  choose triangle for shape of data points
## see http://www.sthda.com/english/wiki/r-plot-pch-symbols-the-different-point-shapes-available-in-r
# cex.main increases font size of title by 50%
# cex.main increases font size of title by 50%
# cex.main increases font size of title by 50%
plot(sa, main = "data", col="blue", pch = 17, 
     cex.main = 1.5, cex.lab = 1.7, cex.axis = 2)
points(sb, col="red", pch = 19) # add sb dataset to previous plot
points(sc,  pch = 10, cex=2)    # add sc dataset to previous plot

plot(sc, main = "data",  pch = 10,  cex=2, cex.main = 1.5, cex.lab = 1.7, cex.axis = 2)
points(sb, col="red", pch = 19)
points(sa, col="blue", pch = 17)

# Plot empirical cumulative distribution function
## for these 3 data sets
plot(ecdf(sa))
plot(ecdf(sb), add=TRUE, col="red")
plot(ecdf(sc), add=TRUE, col="blue")

plot(ecdf(sc), , col="blue")
plot(ecdf(sb), add=TRUE, col="red")
plot(ecdf(sa), add=TRUE)

# Calculate KS statistics for each pair of data sets
ks.test(sa, sb)
ks.test(sc, sb)
ks.test(sa, sc)

# generate larger datasets 
a1 <- sort(runif(30000, 0,3))
saLarge <-sin(a1)
b1 <- sort(runif(2500, 0,3))
sbLarge <-sin(b1)
c1 <- sort(runif(3000, 0,3))
sc <- c1^2
ks.test(saL, sbL)

a <- sort(runif(30, 0,3))  # take 30 random points betwn 0 and 3
## sort in increasing order
saSmall <-sin(a)                # take sine of these 30 points
b <- sort(runif(25, 0,3))  # 25 random points betwn 0 and 3
sbSmall <-sin(b)    # take sine of these 25 points

ks.test(saSmall, sbSmall)
ks.test(saLarge, sbLarge)
###############################################################
##### Create dendograms for a variety of data sets        #####
###############################################################

## Create dendograms for a variety of data sets including some of the data
## sets that you worked with earlier this week.  Also create dendograms for 
## data sets containing circles, noise, circles plus noise. See below for 
## how to create these data sets.

## Recall that you can determine how to use a command using ? or help
mydata <- Noise
mydata <- c(0,7,2, 10, 6)
d <- dist(as.matrix(mydata))   # find distance matrix for dataset
hc <- hclust(d, method = "single")                 # apply hierarchical clustering 
plot(hc)                        # plot the dendrogram
d
?hclust
plot(as.dendrogram(hclust(dist(data))))
k <-3
#x <- identify(hclust(dist(data)))

?identify
hc

dd <- read.csv("test2.txt", sep = " ", header = FALSE)
plot(dd)
d <- dist(as.matrix(dd))   # find distance matrix for dataset
hc <- hclust(d, method = "single") # apply hierarchical clustering
clusterCut <- cutree(hc, 3)

for (i in 4:15)
clusterCut <- cutree(hc, 2)
clusterCut <- rbind(clusterCut, cutree(hc,3))
a<-2
for (i in 3:15)
  {clusterCut <- rbind(clusterCut, cutree(hc,i))}
for (i in 0:12)
  {plot(dd, col = clusterCut[i,])}