using PyPlot
using Convex
using SCS

# passing in verbose=0 to hide output from SCS
solver = SCSSolver(verbose = 0)
set_default_solver(solver);

# logistic function
lgc(x) = 1 ./ (1 + exp(-x));

# Construct a random m-by-n binary matrix matrix
m, n, k = 40, 40, 2
M = randn(m, k) * randn(k, n)       # Underlying low-rank matrix
fM = lgc(M)                     # Probability matrix, maps M onto interval [0,1]
Y = map(x -> x > rand() ? 1 : -1, fM) # True data, binary matrix

# Suppose that we only observe a fraction of entries in Y
n_obs = 800
Yobs = fill(NaN, (m, n))
obs = randperm(m * n)[1: n_obs]
Yobs[obs] = Y[obs]

# Plot the ground-truth, full dataset and our partial observations
figure(figsize = (7, 14))
subplot(1, 2, 1)
imshow(Y, cmap = ColorMap("bwr"), interpolation = "None")
xticks([]), yticks([]), title("True Data", fontweight = "bold")

subplot(1, 2, 2)
imshow(Yobs, cmap = ColorMap("bwr"), interpolation = "None")
xticks([]), yticks([]), title("Observed Data", fontweight = "bold")
show()