# Helpful packages for working with images and factorizations
 using Pkg; Pkg.add("Images")
using Pkg; Pkg.add("ImageMagick") # And this allows us to load JPEG-encoded images
using Images, LinearAlgebra, Interact

strang = download("https://ocw.mit.edu/faculty/gilbert-strang/strang-blue.jpg","strang.jpg")

cb = download("https://i.barkpost.com/wp-content/uploads/2015/01/corgi2.jpg?q=70&fit=crop&crop=entropy&w=808&h=500","cb.jpg")

s = load(strang)

img = load(cb)

channels = Float64.(channelview(s));

[ colorview(RGB, channels.*[1; 0; 0]) colorview(RGB, channels.*[0; 1; 0]) colorview(RGB, channels.*[0; 0; 1])]

function rank_approx(M, k)
    U, s, V = svd(M)    
    M = U[:, 1:k] * Diagonal(s[1:k]) * V[:, 1:k]'    
    M = min.(max.(M, 0.0), 1.) # Clip to between 0 and 1
end

n = 100
@manipulate for k ∈ slider(1:n,value=1)
    colorview(  RGB, 
                rank_approx(channels[1,:,:], k),
                rank_approx(channels[2,:,:], k),
                rank_approx(channels[3,:,:], k)
    )
end

n = 100
@manipulate for r ∈ slider(1:n,value=1,label="r"), 
                g ∈ slider(1:n,value=1,label="g"), 
                b ∈ slider(1:n,value=1,label="b")
    colorview(  RGB, 
                rank_approx(channels[1,:,:], r),
                rank_approx(channels[2,:,:], g),
                rank_approx(channels[3,:,:], b)
    )
end