library(pracma)
# library(SynchWave)

# 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=""))
}

N = 1024

s = 5

t = c(-(N/2) : ((N/2) - 1))
h = (1-t**2/s**2)*exp(-(t**2)/(2*s**2))
h = h - mean(h)

fftshift = SynchWave::fftshift
h1 = fftshift(h) # Recenter the filter for fft use.
Phi = function (u) {Re(ifft(fft(h1) * fft(c(u))))}

# Fourier transform (normalized)
hf = Re(pracma::fftshift(fft(h1))) / sqrt(N)

options(repr.plot.width=5, repr.plot.height=3.5)

q = 200

plot(t, h, type="l", main="Filter, Spacial (zoom)", 
     col="blue", xlim=c(-200,200), ylab="")

plot(t, hf, type="l", 
     main="Filter, Fourrier (zoom)", col="blue", 
     xlim=c(-200,200), ylab="")

s = round(N * 0.03)

set.seed(1)

sel = sample(c(1 : N))
sel = sel[0:s]

x0 = zeros(1, N)
x0[sel] = 1.
x0 = x0 * sign(randn(1, N)) * (1 - .3 * rand(1, N))

sigma = 0.06

y = Phi(x0) + sigma * randn(1, N)

stemplot(x0, col="blue", ylab="", xlab="", main="Signal")
plot(c(1:N), y, xlab="", ylab="", col="blue", main="Measurements y", type="l")

Lambda = 1.

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

source("nt_solutions/optim_2_condat_fb/exo1.R")

# Insert your code here.

L = max(abs(fft(h)))**2

gamma = 1.95 / L

source("nt_solutions/optim_2_condat_fb/exo2.R")

# Insert code here.

# Insert code here.

# Insert code here.

gamma = 1 / L

source("nt_solutions/optim_2_condat_fb/exo3.R")

# Insert code here.

source("nt_solutions/optim_2_condat_fb/exo4.R")

# Insert code here.