options(warn=-1) # turns off warnings, to turn on: "options(warn=0)"
library(plot3D)
library(pracma)

# Importing the libraries
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=""))
}

fs = 10

Xm = function(X){as.matrix(X - rep(colMeans(X), rep.int(nrow(X), ncol(X))))}
Cov = function(X){data.matrix(1. / (n - 1) * t(Xm(X)) %*% Xm(X))}

f = function(x,i)
{
    if (i==1)
    {
        return(0.5 * (x - 1)**2)
    }
    else
    {
        return(0.5 * (x + 1)**2)
    }
}

df = function(x,i)
{
    if (i==1)
    {
        return(x - 1)
    }
    else
    {
        return(x + 1)
    }
}

F = function(x){f(x,1) + f(x,2)}

options(repr.plot.width=6, repr.plot.height=6)
t = seq(-3,3, length=201)
plot(t, f(t,1), col="blue", type='l', ylab="", xlab="")
lines(t, f(t,2), col="orange", type='l')
lines(t, F(t), col="green", type='l')
legend("top", legend=c("f1", "f2", "F"), col=c("blue", "orange", "green"), pch="-")

source("nt_solutions/ml_4_sgd/exo0.R")

## Insert your code here.

file_name = 'nt_toolbox/data/quantum.csv'
A = read.table(file_name, sep=",", head=FALSE)
#A = A[sample(dim(A)[1]),]
X = A[,1:(dim(A)[2] - 1)]
y = A[,dim(A)[2]]

y = (2 * y - 1)

X[,1] = as.numeric(X[,1])
I = colMeans(abs(as.matrix(X))) > 1e-1 
X = X[,I]
X = scale(X)

n = dim(X)[1]
p = dim(X)[2]

svd_decomp = svd(Xm(X))
U = svd_decomp$u
s = svd_decomp$d
V = svd_decomp$v
Xr = X %*% t(V)

options(repr.plot.width=4, repr.plot.height=4)
plot(s, type="o", col=4, ylab="", xlab="", pch=16)

options(repr.plot.width=5, repr.plot.height=5)
I = sample(n)
I = I[1:200]
plot_multiclasses(X[I,],y[I], 2)

plot_multiclasses(X[I,],y[I], 3)

L = function(s,y){1/n * sum( log(1 + exp(-s * y)))}
E = function(w,X,y){L(X %*% w, y)}
theta = function(v){1 / (1 + exp(-v))}
nablaL = function(s, r){ - 1/n * y * theta(-s * y)}
nablaE = function(w,X,y){t(X) %*% nablaL(X %*% w,y)}

source("nt_solutions/ml_4_sgd/exo1.R")

## Insert your code here.

nablaEi = function(w,i){as.numeric(-y[i] * t(X[i,]) * c(theta(-y[i] * (X[i,] %*% w))))}

l0 = 100
tau0 = 0.05

source("nt_solutions/ml_4_sgd/exo2.R")

## Insert your code here.

source("nt_solutions/ml_4_sgd/exo3.R")

## Insert your code here.

source("nt_solutions/ml_4_sgd/exo4.R")

## Insert your code here.