import numpy as np

from scipy import signal

##########################################

# Convolution étendue

def convolution(A, M):

return signal.convolve2d(A, M, mode='full')

##########################################

# Matrices aléatoires de taille n x p

n, p = 6, 4

A = np.random.randint(0, 10, size = (n,p))

# Motifs aléatoires de taille 3 x 3

M = np.random.randint(-5,5, size = (3,3))

N = np.random.randint(-5,5, size = (3,3))

##########################################

# Exemple d'associativité

# Calcul de (A*M)*N

AM = convolution(A, M)

AMN1 = convolution(AM, N)

# Calcul de A*(M*N)

MN = convolution(M, N)

AMN2 = convolution(A, MN)

print('A =', A)

print('M =', M)

print('N =', N)

print('(A*M)*N =', AMN1)

print('A*(M*N) =', AMN2)

print("Associativité pour la convolution ?\n", AMN1==AMN2)

##########################################

# Retournement

def retourner(M):

M1 = M.flatten()

M2 = M1[::-1]

M3 = np.reshape(M2,np.shape(M))

return M3

##########################################

# Retournement

def correlation(A, M):

B = convolution(A,retourner(M))

return B

##########################################

# Exemple de non associativité pour la correlation

n, p = 4, 4

A = np.random.randint(0, 10, size = (n,p))

M = np.random.randint(-5,5, size = (3,3))

N = np.random.randint(-5,5, size = (3,3))

##########################################

# Exemple d'associativité

# Calcul de (A*M)*N

AM = correlation(A, M)

AMN1 = correlation(AM, N)

# Calcul de A*(M*N)

MN = correlation(M, N)

AMN2 = correlation(A, MN)

print('A =', A)

print('M =', M)

print('N =', N)

print('(A*M)*N =', AMN1)

print('A*(M*N) =', AMN2)

print("Associativité pour la corrélation ?\n", AMN1==AMN2)