import numpy as np
import matplotlib.pyplot as plt
from PIL import Image

billede = Image.open("Advent.bmp")
graybillede = billede.convert("LA")

billedearray = np.array(list(graybillede.getdata(band=0)),float)
billedearray.shape = (graybillede.size[1], graybillede.size[0])
print ("billedearray = \n", billedearray,"\n")
billedematrix = np.matrix(billedearray)
print ("billedematrix = \n", billedematrix,"\n")

U, sigma, V = np.linalg.svd(billedematrix)
print ("V =\n", np.round(V,decimals=2))

kompri = np.matrix(U[:, :1]*np.diag(sigma[:1])*np.matrix(V[:1, :]))
plt.imshow(kompri, cmap="gray")
plt.title("efter svd v = 1")

fig = plt.figure()

for i in range (10, 50+1, 10):
    komprirange = np.matrix(U[:, :i]*np.diag(sigma[:i])*np.matrix(V[:i, :]))
    plt.imshow(komprirange, cmap="gray")
    plt.title("billede v =" + str(i))
    plt.figure()

for i in range (1,100+1,1):
    plt.plot(250000/(1001*i),i, color="green",marker=".")

plt.show()