library("TDA")

# create data set containing 100 randomly choosen 
# points from a circle of radius r = 1
circle1 = circleUnif(100, r = 1)

# save circle1 data to current working directory
# as a text file
write.table(circle1, "circleOUT.txt", sep=" ", 
            row.names = FALSE,
            col.names = FALSE)

# plot circle1 data with aspect ratio = 1
plot(circle1, asp=1) 

# save plot to current working directory
# see http://stackoverflow.com/questions/7144118/how-to-save-a-plot-as-image-on-the-disk
dev.copy(png,filename="plotcircle1.png");
dev.off ();

## Apply a linear transformation to circl1 data

# create 2x2 matrix
A <- matrix(c(1, 2, 2, 0), nrow=2, ncol=2) 
C <- t(circle1)  # take the transpose of circle1 data
M <- A %*% C     # multiply A and C
E <- eigen(A)    # calculate eigenvalues and eigenvectors of A
E                # display E (note its data structure)

plot(t(M), asp=1)  # note M is the image of circle C under map A
# Add an eigenvector to this plot (red asterisk)

#points(c(0,E$values[1]*E$vectors[1,1]),c(0,E$values[1]*E$vectors[2,1]))
arrows(0,0,E$values[1]*E$vectors[1,1],E$values[1]*E$vectors[2,1], col="red", lwd = 3)

#points(c(0,E$values[2]*E$vectors[1,2]),c(0,E$values[2]*E$vectors[2,2]))
arrows(0,0,E$values[2]*E$vectors[1,2],E$values[2]*E$vectors[2,2], col="blue", lwd = 3)

plot(t(M), asp=1)  # note M is the image of circle C under map A
# Add an eigenvector to this plot (red asterisk)
points(t(E$values[1]*E$vectors[,1]), pch=8, cex = 2, col=rgb(1, 0, 0))
# Add another eigenvector to this plot (blue asterisk)
points(t(E$values[2]*E$vectors[,2]), pch=8, cex = 2, col=rgb(0, 0, 1))
# Add origin (0, 0) to plot (green +).
points(t(c(0, 0)), pch=3, cex = 2, col=rgb(0, 1, 0))

# Create data for our next homework
sphere <- sphereUnif(100, 2, r = 1)
disk1 <- subset(sphere, select = -c(3) )
disk2 <- cbind(disk1[,1] + 4, disk1[,2])
disk3 <- cbind(disk1[,1], disk1[,2] + 4)
disk4 <- disk1 + 4
noise1 <- cbind(runif(100, -1,5), runif(100, -1,5))

noisy_disk <- rbind(disk1, disk2, disk3, disk4, noise1)
plot(noisy_disk, asp = 1)

line <- cbind(runif(40, -.1,.1), runif(40, 1,3))
new <- rbind(noisy_disk, line)
plot(new, asp = 1)





###########################
##  Create more datasets ##
###########################

# note the following is incorrect
knotdata <- read.csv("trefoilknot.txt", header = FALSE)

# note the following is the correct way to read in knot data
knotdata <- read.csv("trefoilknot.txt", sep = " ", header = FALSE)

# Grab first 2 columns for fun
twodim_data <- cbind(knotdata[1], knotdata[2])
plot(twodim_data)

# Create distance matrix
d <- dist(knotdata)

##########################################################################
###########################################################################
## examples below modified from https://cran.r-project.org/web/packages/TDAmapper/README.html

######################################################
## Example 1: Using mapper1D to identify a figure 8 ##
######################################################

#plot 100 points from a figure 8
plot(x=2*cos(0.5*(1:100)), y=sin(1:100))

########################################################################
## Example 3: using mapper1D to identify two independent spirals as two line segments
###############################################################

# sample 200 points from two intertwined spirals
t <- runif(100, min=1, max=6.3) # theta
X <- data.frame( x = c( t*cos(t), -t*cos(t) ), y = c( t*sin(t), -t*sin(t) ) )
plot(X[,1], X[,2])