import numpy as np
from imageio import imread
import matplotlib.pyplot as plt

def sinusBilde(u, v, N, M):
    bilde = np.zeros((N, M))
    for i in range(N):
        for j in range(M):
            bilde[i, j] = np.sin( -2*np.pi* ((u*i/np.float(N)) + (v*j/np.float(M))) )
    return bilde

def cosinusBilde(u, v, N, M):
    bilde = np.zeros((N, M))
    for i in range(N):
        for j in range(M):
            bilde[i, j] = np.cos( -2*np.pi* ((u*i/np.float(N)) + (v*j/np.float(M))) )
    return bilde

M = 256
N = 512

u, v = 10, 10

# Oppgave a

sinimage = sinusBilde(u, v, N, M)

plt.figure()
plt.imshow(sinimage, cmap="gray")
plt.colorbar()
plt.title('u = {}, v = {}'.format(u, v))
plt.show()

# Oppgave b

cosimage = cosinusBilde(u, v, N, M)
indreprodukt = np.sum(cosimage * sinimage)
print(indreprodukt) # Skal bli (tiln?rmet) 0

# Oppgave c

c1 = cosinusBilde(10, 10, N, M)
c2 = cosinusBilde(14, 15, N, M)
s1 = sinusBilde(10, 10, N, M)
s2 = sinusBilde(14, 15, N, M)

print(np.sum(c1*c2))
print(np.sum(c1*s1))
print(np.sum(c1*s2))
print(np.sum(s1*s2))

# Oppgave d

u, v = 3, 5
c1 = cosinusBilde(u, v, N, M)
c2 = cosinusBilde(N-u, M-u, N, M)
s1 = sinusBilde(u, v, N, M)
s2 = sinusBilde(N-u, M-u, N, M)

fig = plt.figure()
fig.add_subplot(2, 2, 1)
plt.imshow(c1, cmap="gray")
plt.title('cos | u = {}, v = {}'.format(u, v))
fig.add_subplot(2, 2, 2)
plt.imshow(c2, cmap="gray")
plt.title('cos | u = {}, v = {}'.format(u, v))
fig.add_subplot(2, 2, 3)
plt.imshow(s1, cmap="gray")
plt.title('sin | u = {}, v = {}'.format(u, v))
fig.add_subplot(2, 2, 4)
plt.imshow(s2, cmap="gray")
plt.title('sin | u = {}, v = {}'.format(u, v))
plt.show()

# Oppgave e

print(N*M/2)
print(np.sum(c1*c1))
print(np.sum(c2*c2))
print(np.sum(s1*s1))
print(np.sum(s2*s2))