#using Pkg
#Pkg.add("Images")
#Pkg.add("ImageMagick")

using Images
using LinearAlgebra

img = load("./duck.jpg");
display(img)

display(Gray.(img))
# convert to a matrix
A=float64.(channelview(Gray.(img[:,:])))
println("size of A = ", size(A,1)," x ", size(A,2))
println("storage   = ", size(A,1) * size(A,2))

A

U, S, V = svd(A)
# check the accuracy of SVD
print("||USV'-A||=", norm(U*diagm(S)*V' - A))

rank_list = [1,5,10,20,30,40]

for rank in rank_list
    
    Acompress = U[:,1:rank] * diagm(S[1:rank]) * V[:,1:rank]'

    println("Compression rank = ", rank)
    println("Storage          = ", (size(A,1)+size(A,2))*rank)

    flush(stdout)
    display(Gray.(Acompress))
end

using PyPlot
plot(S, "b-.")
title("singular values, linear-scale")

semilogy(S, "b-.")
title("singular values, log-scale")