import numpy as np
from scipy.misc import imread
import matplotlib.pyplot as plt

# Oppgave a

f = imread('car.png', flatten=True)

(N,M) = f.shape
F = np.fft.fft2(f)
F_r = np.real(F)  # Real-delen (cosinusbilde-bidragene)
F_i = np.imag(F)  # Imagin?r-delen (sinusbilde-bidragene)

amp_shifted = np.fft.fftshift(np.log10(abs(F)))
phase_shifted = np.fft.fftshift(np.angle(F))

fig = plt.figure()
fig.add_subplot(1,2,1)
plt.imshow(amp_shifted, vmin=0)
plt.colorbar()
plt.title('Amplitude spectrum [log10]')
fig.add_subplot(1,2,2)
plt.imshow(phase_shifted/np.pi*180)
plt.colorbar()
plt.title('Phase [deg]')
plt.show()

## Oppgave b

print(F[0,0], sum(sum(f))) # Indreprodukt mellom basis [[1 1 ... 1 1], ..., [1 1 ... 1 1]]

## Oppgave c

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

u = 2
v = 7
sinimage = sinusBilde(u, v, N, N)
plt.figure()
plt.imshow(sinimage, cmap="gray")
plt.colorbar()
plt.title('u = {}, v = {}'.format(u, v))
plt.show()

## Oppgave d

indreprodukt = np.sum(sinimage * f)

print(indreprodukt, F_i[u, v])

# Oppgave e

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

cosimage = cosinusBilde(u, v, N, N)
indreprodukt = np.sum(cosimage * f)
print(indreprodukt, F_r[u, v])