options(warn=-1) # turns off warnings, to turn on: "options(warn=0)"

library(imager)
library(png)

for (f in list.files(path="nt_toolbox/toolbox_general/", pattern="*.R")) {
    source(paste("nt_toolbox/toolbox_general/", f, sep=""))
}

for (f in list.files(path="nt_toolbox/toolbox_signal/", pattern="*.R")) {
    source(paste("nt_toolbox/toolbox_signal/", f, sep=""))
}
options(repr.plot.width=6, repr.plot.height=5)

n <- 1000

x <- array(runif(2*n), c(2,n))

v <- 3*pi/2*(.1 + 2*x[1,])
X  <- array(0, c(3,n))
X[2,] <- 20*x[2,]
X[1,] <- - cos(v)*v
X[3,] <- sin(v)*v

ms <- 200
el <- 20; az <- -110

library(scatterplot3d)

color_vec <- rev(rainbow(100))

color_function <- function(x, y, z){
  idx <- round( x**2 + z**2 ) + 1
  return(color_vec[idx])
}

#swiss roll
scatterplot3d(X[1,], X[2,], X[3,], axis=F, grid=F, box=F, type="p", pch=19, color=color_function(X[1,], X[2,], X[3,]))

D1 <- array( rep(apply(X**2, 2, sum), n), c(n,n) )
D1 <- sqrt(pmax(D1 + t(D1) - 2*t(X)%*%X, 0))

k <- 6

DNN <- t( apply( D1, 1, function(l){return(l[order(l)])} ) )
NN <- t( apply( D1, 1, order) )
NN <- NN[,2:(k+1)]
DNN <- DNN[,2:(k+1)]

B <- t(array(rep(1:n,k), c(n, k)))
I <- as.vector(B) ; J <- as.vector(t(NN))
A <- array(0, c(n,n))
for (idx in 1:(k*n)){ A[I[idx], J[idx]] <- 1}

W <- array(0, c(n,n))
DNN_vector <- as.vector(t(DNN))
for (idx in 1:(k*n)){ W[I[idx], J[idx]] <- DNN_vector[idx]}

color_vec <- rev(rainbow(100))

color_function <- function(x, y, z){
  idx <- round( x**2 + z**2 ) + 1
  return(color_vec[idx])
}

#swiss roll
s3d <- scatterplot3d(X[1,], X[2,], X[3,], axis=F, grid=F, box=F, type="p", pch=19, color=color_function(X[1,], X[2,], X[3,]))

#graph
xx <- array(0, c(2, k*n)) ; xx[1,] <- X[1,I] ; xx[2,] <- X[1,J]
yy <- array(0, c(2, k*n)) ; yy[1,] <- X[2,I] ; yy[2,] <- X[2,J]
zz <- array(0, c(2, k*n)) ; zz[1,] <- X[3,I] ; zz[2,] <- X[3,J]
    
for (i in 1:length(I)){
    s3d$points3d(xx[,i], yy[,i], zz[,i], type="l", lw=1.5)
}

D <- W
D <- (D + t(D))/2.

D[D == 0] <- Inf

diag(D) <- Inf
D[is.nan(D)] <- Inf

source("nt_solutions/shapes_7_isomap/exo1.R")

## Insert your code here.

Iremove <- (D[,1] == Inf)

D[D == Inf] <- 0

source("nt_solutions/shapes_7_isomap/exo2.R")

## Insert your code here.

ev <- eigen( (Xstrain %*% t(Xstrain))/n )
L <- ev$values ; U <- ev$vectors
Xstrain1 <- -t(U) %*% Xstrain

Xstrain1[,Iremove] <- Inf

#plot points
plot(Xstrain1[1,], Xstrain1[2,], axes=FALSE, ann=FALSE, pch=19, col=color_function(X[1,], X[2,], X[3,]))

#plot vertices
I <- as.vector(B) ; J <- as.vector(t(NN))
xx <- array(0, c(2, k*n)) ; xx[1,] <- Xstrain1[1,I] ; xx[2,] <- Xstrain1[1,J]
yy <- array(0, c(2, k*n)) ; yy[1,] <- Xstrain1[2,I] ; yy[2,] <- Xstrain1[2,J]

for (i in 1:length(I)){
  lines(xx[,i], yy[,i], col="black", lw=1.5)
}

Y <- array(0, c(2,length(v)))
Y[1,] <- v ; Y[2,] <- X[2,]
Y[1,] <- rescale(Y[1,], min(Xstrain[1,]), max(Xstrain[1,]))
Y[2,] <- rescale(Y[2,], min(Xstrain[2,]), max(Xstrain[2,]))

#plot points
plot(Y[1,], Y[2,], axes=FALSE, ann=FALSE, pch=19, col=color_function(X[1,], X[2,], X[3,]))

#plot vertices
I <- as.vector(B) ; J <- as.vector(t(NN))
xx <- array(0, c(2, k*n)) ; xx[1,] <- Y[1,I] ; xx[2,] <- Y[1,J]
yy <- array(0, c(2, k*n)) ; yy[1,] <- Y[2,I] ; yy[2,] <- Y[2,J]

for (i in 1:length(I)){
  lines(xx[,i], yy[,i], col="black", lw=1.5)
}

options(repr.plot.width=8, repr.plot.height=6.5)
        
source("nt_solutions/shapes_7_isomap/exo3.R")

## Insert your code here.

options(repr.plot.width=6, repr.plot.height=5)

plot(stress, type="o", col="blue", pch=19)

ev <- eigen( (Xstress %*% t(Xstress))/n )
L <- ev$values ; U <- ev$vectors

I <- order(L)
L <- L[I]

U <- U[,I[2:3]]

Xstress1 <- -t(U) %*% Xstress

Xstress1[,Iremove] <- Inf

options(repr.plot.width=6, repr.plot.height=5)

#plot points
plot(Xstress1[2,], Xstress1[1,], axes=FALSE, ann=FALSE, pch=19, col=color_function(X[1,], X[2,], X[3,]))

#plot vertices
I <- as.vector(t(array(rep(1:n,k), c(n, k)))) ; J <- as.vector(t(NN))
xx <- array(0, c(2, k*n)) ; xx[1,] <- Xstress1[2,I] ; xx[2,] <- Xstress1[2,J]
yy <- array(0, c(2, k*n)) ; yy[1,] <- Xstress1[1,I] ; yy[2,] <- Xstress1[1,J]

for (i in 1:length(I)){
  lines(xx[,i], yy[,i], col="black", lw=1.5)
}
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