# Author:  Isabel Darcy 
# Create a variety of artificial data sets
# Date:  Jan 15, 2018


# create data set with 7 flares.

Noise1 <- cbind(runif(200, -30,30), runif(200, 5,6))
Noise2 <- cbind(runif(200, -6,30), runif(200, -6,-5))
Noise3 <- cbind(runif(200, -6,-5), runif(200, -20,20))
Noise4<- cbind(runif(200, 5,6), runif(200, -20,20))
Noise5<- cbind(runif(200, -6,6), runif(200, -6,6))

flares <- rbind(Noise1, Noise2, Noise3, Noise4, Noise5)
plot(flares, asp=1)


## Apply a linear transformation to flares data

# create 2x2 matrix
A <- matrix(c(1, 2, 2, 0), nrow=2, ncol=2) 
C <- t(flares)  # 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

if (!require(package = "TDA")) {
  install.packages(pkgs = "TDA")
}
library("TDA")

##  The TDA package has several commands for generating data sets 
##  with known topology:

# choose 300 points randomly (with uniform distribution)from a circle of radius 1.

Circle = circleUnif(300, r = 1)  

# choose 300 points randomly (with uniform distribution)from a 2-dimensional 
# sphere of radius 1.  Note the 2nd parameter determines the dimension of the 
# sphere.  
# 2nd parameter = 1: 1-d sphere in R^2 = circle in R^2 
# 2nd parameter = 2: 2-d sphere in R^3 
# 2nd parameter = 3: 3-d sphere in R^4 

Sphere = sphereUnif(300, 2, r = 1)

# choose 300 points randomly (with uniform distribution)from a torus with tube  
# radius 1 where the center of the tube is a circle of radius 2 centered at the 
# origin.  Note the center of the tube is not part of the torus.

Torus = torusUnif(300,  1, 2)

############################################################################

## To plot your points in a new window of size 4x5

windows(4,5);plot(torus)

## To save your data points to the csv file, circle.csv
## Note ncolumns = dimension of your data set (unless you also have a column 
## containing the names of your rows).

write(Circle, file = "circle.csv", ncolumns = 2, sep = ",")

# To determine the directory where your file was saved

getwd()

# Recall you can specify where you would like to save your file, by giving the 
# path to the directory.  For example,

write(torus, file = "C:/users/YourUserName/Downloads/torus.csv", ncolumns = 3, sep = 
        ",")


################################################

## You can write for loops in R
## To get help for some special characters and words, one must use quotes

help("for")

# Create Noise data set containing 20 pts randomly chosen such that -2 < x,y < 2

Noise =cbind(runif(20, -2,2),runif(20, -2,2))

# Create a list where first element on the list is the Noise data set with 20pts.

NoiseList <- list(Noise)

# For each i = 2, 3, 4, 5, we create a new data set of noisy points by adding
# 20 more points to the previously created noisy data set.

for (i in 1:5)
{ 
  MoreNoise <- cbind(runif(20, -2,2),runif(20, -2,2)) 
  NoiseList[i] <- list(rbind(Noise, MoreNoise))    
  Noise <- NoiseList[[i]]
  windows(5,5); plot(Noise, sub = "20i points from noise.", asp = 1)
  filename <- "Noise.csv" 
  write(Noise, file = filename, ncolumns = 2, sep = ",")
}


# Load trefoil knot data

knotdata <- read.csv("../Data/trefoilknot.txt", sep = " ", header = FALSE)

install.packages("scatterplot3d")
library("scatterplot3d")

scatterplot3d(knotdata, highlight.3d=TRUE, col.axis="blue",
              scttr3col.grid="lightblue", main="scatterplot3d - 1", pch=20)

install.packages("rgl")
library("rgl")
plot3d(knotdata, col = rainbow(1000))