library(pracma)

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

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

set.seed(0)

n = 400

p = round(n/4)

A = randn(p,n) / sqrt(p)

s = 17

sel = sample(c(1 : n))
x0 = zeros(n, 1)
x0[sel[1:s]] = 1

y = A %*% x0

proxG = function(x, gamma) {x * pmax(1 - ((gamma) / abs(x)), 0)}

options(repr.plot.width=5, repr.plot.height=3.5)
t = linspace(-1,1)
plot(t, proxG(t, 0.3), type="l", col="blue", ylab="", xlab="")

pA = t(A) %*% solve(A%*% t(A))
proxF = function(x,y){x + pA %*% (y - A %*% x)}

mu = 1
gamma = 1

rproxG = function(x,tau){2 * proxG(x,tau) - x}
rproxF = function(x, tau){2 * proxF(x,tau) - x}

niter = 500

source("nt_solutions/optim_4b_dr/exo1.R")

# Insert your code here

# Insert your code here.

# Insert your code here.

source("nt_solutions/optim_4b_dr/exo2.R")

# Insert your code here.

q = 1000

slist = seq(14, 42, 2)

Slist = slist[mod(c(1 : q), length(slist)) + 1]

# Genetate signals so that |x0(:,j)| has sparsity |Slist(j)|.
U = rand(n,q)
v = c(apply(U,2,sort))
v = v[c(0: (q - 1)) * n + Slist]
x0 = 1 * (U <= t(matrix(rep(v, n), ncol=n)))

y = A %*% x0

source("nt_solutions/optim_4b_dr/exo3.R")

# Insert your code here.