def test_rff_feature_map_derivatives_equals_feature_map_derivatives_loop():
N = 10
D = 20
m = 3
X = np.random.randn(N, D)
omega = np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
derivatives = rff_feature_map_grad(X, omega, u)
derivatives_loop = rff_feature_map_grad_loop(X, omega, u)
assert_allclose(derivatives_loop, derivatives)
def test_rff_feature_map_derivatives_equals_feature_map_derivatives_loop():
N = 10
D = 20
m = 3
X = np.random.randn(N, D)
omega = np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
derivatives = rff_feature_map_grad(X, omega, u)
derivatives_loop = rff_feature_map_grad_loop(X, omega, u)
assert_allclose(derivatives_loop, derivatives)
def test_rff_feature_map_grad_theano_result_equals_manual():
if not theano_available:
raise SkipTest("Theano not available.")
D = 2
x = np.random.randn(D)
X = x[np.newaxis, :]
m = 10
sigma = 1.
omega, u = rff_sample_basis(D, m, sigma)
grad_manual = rff_feature_map_grad(X, omega, u)[:, 0, :]
for i in range(m):
# phi_manual is a monte carlo average, so have to normalise by np.sqrt(m) here
grad = rff_feature_map_comp_grad_theano(x, omega[:, i], u[i]) / np.sqrt(m)
assert_close(grad, grad_manual[:, i])
def test_rff_feature_map_grad_theano_result_equals_manual():
if not theano_available:
raise SkipTest("Theano not available.")
D = 2
x = np.random.randn(D)
X = x[np.newaxis, :]
m = 10
sigma = 1.
omega, u = rff_sample_basis(D, m, sigma)
grad_manual = rff_feature_map_grad(X, omega, u)[:, 0, :]
for i in range(m):
# phi_manual is a monte carlo average, so have to normalise by np.sqrt(m) here
grad = rff_feature_map_comp_grad_theano(x, omega[:, i],
u[i]) / np.sqrt(m)
assert_close(grad, grad_manual[:, i])
def compute_C_memory(X, omega, u):
assert len(X.shape) == 2
Phi2 = rff_feature_map_grad(X, omega, u)
d = X.shape[1]
N = X.shape[0]
m = Phi2.shape[2]
# # bottleneck! loop version is very slow
# C = np.zeros((m, m))
# t = time.time()
# for i in range(N):
# for ell in range(d):
# phi2 = Phi2[ell, i]
# C += np.outer(phi2, phi2)
# print("loop", time.time()-t)
#
# # roughly 5x faster than the above loop
# t = time.time()
# Phi2_reshaped = Phi2.reshape(N*d, m)
# C2=np.einsum('ij,ik->jk', Phi2_reshaped, Phi2_reshaped)
# print("einsum", time.time()-t)
#
# # cython implementation, is slowest
# t = time.time()
# Phi2_reshaped = Phi2.reshape(N*d, m)
# C3 = outer_sum_cython(Phi2_reshaped)
# print("cython", time.time()-t)
# t = time.time()
# fastest version using multicore: tensordot method
Phi2_reshaped = Phi2.reshape(N * d, m)
C4 = np.tensordot(Phi2_reshaped, Phi2_reshaped, [0, 0])
# print("tensordot", time.time()-t)
return C4 / N
def compute_C_memory(X, omega, u):
assert len(X.shape) == 2
Phi2 = rff_feature_map_grad(X, omega, u)
d = X.shape[1]
N = X.shape[0]
m = Phi2.shape[2]
# # bottleneck! loop version is very slow
# C = np.zeros((m, m))
# t = time.time()
# for i in range(N):
# for ell in range(d):
# phi2 = Phi2[ell, i]
# C += np.outer(phi2, phi2)
# print("loop", time.time()-t)
#
# # roughly 5x faster than the above loop
# t = time.time()
# Phi2_reshaped = Phi2.reshape(N*d, m)
# C2=np.einsum('ij,ik->jk', Phi2_reshaped, Phi2_reshaped)
# print("einsum", time.time()-t)
#
# # cython implementation, is slowest
# t = time.time()
# Phi2_reshaped = Phi2.reshape(N*d, m)
# C3 = outer_sum_cython(Phi2_reshaped)
# print("cython", time.time()-t)
# t = time.time()
# fastest version using multicore: tensordot method
Phi2_reshaped = Phi2.reshape(N * d, m)
C4 = np.tensordot(Phi2_reshaped, Phi2_reshaped, [0, 0])
# print("tensordot", time.time()-t)
return C4 / N