##########################################################################
# Installing packages.
# The following checks if a package is installed.  
#    The package is installed if it hasn't been installed before
# If you have already installed these packages, you can skip these steps 
##########################################################################

If (!require(package = "TDAmapper")) {
  install.packages(pkgs = "TDAmapper")
}

If (!require(package = "fastcluster")) {
  install.packages(pkgs = "fastcluster")
}

If (!require(package = "igraph")) {
  install.packages(pkgs = "igraph")
}


#############################################################
# Load the libraries
# A library only needs to be loaded once per session
#############################################################

library("TDAmapper")

# The fastcluster package is not necessary.  By loading the
# fastcluster package, the fastcluster::hclust() function 
# automatically replaces the slower stats::hclust() function
# whenever hclust() is called.

require(fastcluster) 

# The igraph package is necessary to view simplicial complexes
# (undirected graph) resulting from mapper1D().

library(igraph)

##################################################
# We are now ready to run TDA mapper on some data
##################################################

# Either create or load a dataset
# You can change the DataSet to any dataset you choose
# In other words, modify the command below to try TDAmapper
#    on different datasets.

DataSet = cbind(runif(50, -1,1),runif(50, -1,1))

# Set the parameters needed for TDAmapper (listed below)

distance_matrix = dist(DataSet)           # Create distance matrix from DataSet

filter <- DataSet[,1] # projection to first coordinate.
                      # You can choose any filter function you like.
                      # Filter function is a vector with same 
                      #   number of entries as your dataset.
        # See below for some examples of filter functions.

num_intervals <- 10    	# Number of intervals.
                        # For mapper1D, number of overlapping bins = num_intervals 
                        # For mapper2D, number of overlapping bins = num_intervals^2
percent_overlap <- 50   # The percent that these intervals overlap.  
num_bins_when_clustering <- 10  # A parameter for determining clusters.
                                # We will discuss this parameter later.

# Call the mapper1D to apply TDAmapper to dataset

m1 <- mapper1D(
  distance_matrix,
  filter,
  num_intervals,
  percent_overlap,
  num_bins_when_clustering)

# create and plot mapper graph

g1 <- graph.adjacency(m1$adjacency, mode="undirected")
plot(g1, layout = layout.auto(g1) )
title("Filter = projection to x-axis", 
      sub =paste("num_intervals = ", num_intervals,
                 "\n percent_overlap = ", percent_overlap,
                 "\n num_bins_when_clustering =", num_bins_when_clustering)
)

###########################################
#
# Some other filter functions
#  f:  Dataset to Real line
#  Thus x is a point in dataset,
#  and f(x) is a real number
#
###########################################	

# f(x) = length of x

filter <- sqrt(rowSums(DataSet^2))

#  Project onto first principle component

filter <- prcomp(DataSet, center = TRUE)