numerics-2022/Task 1/convolutions.ipynb

In [1]:

import numpy as np
import itertools

In [2]:

c = 3

In [3]:

# Generate some data
np.random.seed(42)
lambda1 = np.random.normal(size=(c, c))
lambda2 = np.random.normal(size=(c, c))
lambda3 = np.random.normal(size=(c, c))
G1 = np.random.normal(size=(c, c, c))
G2 = np.random.normal(size=(c, c, c))
U = np.random.normal(size=(c, c, c, c))

In [4]:

def Z_naive(lambda1, lambda2, lambda3, G1, G2, U):
    c = lambda1.shape[0]
    Z = np.zeros(shape=(c, c, c, c))
    for a, b, c, d, e, f, g, h, i, j in itertools.product(*([range(c)]*10)):
        Z[a, h, i, j] += lambda1[a, b]*lambda2[d, e]*lambda3[g, h]*G1[c, b, d]*G2[f, e, g]*U[i, j, c, f]
    return Z

In [5]:

%%timeit
Z = Z_naive(lambda1, lambda2, lambda3, G1, G2, U)

198 ms ± 30.6 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)

In [6]:

Z = Z_naive(lambda1, lambda2, lambda3, G1, G2, U)
Z.shape

Out[6]:

(3, 3, 3, 3)