5 ######################################################################
8 def naive_rec(A, X, Y0):
10 for t in range(X.size(1)):
12 Y.append(A[:, t] * Y0 + X[:, t])
14 Y.append(A[:, t] * Y[-1] + X[:, t])
16 return torch.cat([y[:, None, :] for y in Y], dim=1)
19 ######################################################################
25 # Returns Y defined with
27 # Y[:, 0] = A[:, 0] * Y0 + X[:,0]
28 # for t > 0 Y[:, t] = A[:, t] * Y[:, t - 1] + X[:, t]
31 def pscan_rec(A, X, Y0):
32 if X.size(1) % 2 == 1:
34 return A[:, :1] * Y0[:, None] + X[:, :1]
36 Y = pscan_rec(A[:, :-1], X[:, :-1], Y0)
37 return torch.cat([Y, A[:, -1:] * Y[:, -1:] + X[:, -1:]], dim=1)
39 A2 = A.reshape(A.size(0), A.size(1) // 2, 2, A.size(2))
40 X2 = X.reshape(X.size(0), X.size(1) // 2, 2, X.size(2))
42 X_star = X2[:, :, 0].clone()
43 X_star[:, 1:] += A2[:, 1:, 0] * X2[:, :-1, 1]
45 A_star = A2[:, :, 0].clone()
46 A_star[:, 1:] *= A2[:, :-1, 1]
48 Y_star = pscan_rec(A_star, X_star, Y0)[:, :, None]
50 Y = torch.cat([Y_star, A2[:, :, 1, None] * Y_star + X2[:, :, 1, None]], dim=2)
52 Y = Y.reshape(Y.size(0), -1, Y.size(-1))
57 ######################################################################
61 A = torch.rand(N, T, 1, dtype=torch.float64)
62 X = torch.randint(10, (N, T, D), dtype=torch.float64)
63 Y0 = torch.randint(10, (N, D), dtype=torch.float64)
65 naive_Y = naive_rec(A, X, Y0)
67 pscan_Y = pscan_rec(A, X, Y0)
69 print((naive_Y - pscan_Y).pow(2).mean())
71 pscan_Y1 = pscan_rec(A[:, :15], X[:, :15], Y0)
72 pscan_Y2 = pscan_rec(A[:, 15:], X[:, 15:], pscan_Y1[:, -1])
74 print((naive_Y - torch.cat([pscan_Y1, pscan_Y2], dim=1)).pow(2).mean())