def test_compute_C_matches_sym():
sigma = 1.
Z = np.random.randn(10, 2)
K = gaussian_kernel(Z, sigma=sigma)
C_sym = develop_gaussian.compute_C_sym(Z, K, sigma=sigma)
C = gaussian.compute_C(Z, Z, K, sigma=sigma)
assert_allclose(C, C_sym)
def test_compute_C_matches_sym():
sigma = 1.
Z = np.random.randn(10, 2)
K = gaussian_kernel(Z, sigma=sigma)
C_sym = develop_gaussian.compute_C_sym(Z, K, sigma=sigma)
C = gaussian.compute_C(Z, Z, K, sigma=sigma)
assert_allclose(C, C_sym)
def test_compute_C_sym_against_paper():
sigma = 1.
D = 1
Z = np.random.randn(1, D)
K = gaussian_kernel(Z, sigma=sigma)
C = develop_gaussian.compute_C_sym(Z, K, sigma)
# compute by hand, well, it's just zero (look at it)
x = Z[0]
k = K[0, 0]
C_paper = (x * k - k * x) * (k * x - x * k)
assert_equal(C, C_paper)
def test_objective_sym_same_as_from_estimation():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a = develop_gaussian.fit_sym(Z, sigma, lmbda, K)
C = develop_gaussian.compute_C_sym(Z, K, sigma)
b = develop_gaussian.compute_b_sym(Z, K, sigma)
J = develop_gaussian.objective_sym(Z, sigma, lmbda, a, K, b, C)
J2 = develop_gaussian.objective_sym(Z, sigma, lmbda, a, K)
assert_almost_equal(J, J2)
def test_apply_C_left_sym_matches_full():
sigma = 1.
N = 10
Z = np.random.randn(N, 2)
K = gaussian_kernel(Z, sigma=sigma)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
v = np.random.randn(Z.shape[0])
lmbda = 1.
x = (develop_gaussian.compute_C_sym(Z, K, sigma) + lmbda * (K + np.eye(len(K)))).dot(v)
y = develop_gaussian_low_rank.apply_left_C_sym(v, Z, R.T, lmbda)
assert_allclose(x, y, atol=2e-1, rtol=2e-1)
def test_compute_C_sym_against_paper():
sigma = 1.
D = 1
Z = np.random.randn(1, D)
K = gaussian_kernel(Z, sigma=sigma)
C = develop_gaussian.compute_C_sym(Z, K, sigma)
# compute by hand, well, it's just zero (look at it)
x = Z[0]
k = K[0, 0]
C_paper = (x * k - k * x) * (k * x - x * k)
assert_equal(C, C_paper)
def test_objective_sym_same_as_from_estimation():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a = develop_gaussian.fit_sym(Z, sigma, lmbda, K)
C = develop_gaussian.compute_C_sym(Z, K, sigma)
b = develop_gaussian.compute_b_sym(Z, K, sigma)
J = develop_gaussian.objective_sym(Z, sigma, lmbda, a, K, b, C)
J2 = develop_gaussian.objective_sym(Z, sigma, lmbda, a, K)
assert_almost_equal(J, J2)
def test_apply_C_left_sym_matches_full():
sigma = 1.
N = 10
Z = np.random.randn(N, 2)
K = gaussian_kernel(Z, sigma=sigma)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
v = np.random.randn(Z.shape[0])
lmbda = 1.
x = (develop_gaussian.compute_C_sym(Z, K, sigma) + lmbda *
(K + np.eye(len(K)))).dot(v)
y = develop_gaussian_low_rank.apply_left_C_sym(v, Z, R.T, lmbda)
assert_allclose(x, y, atol=2e-1, rtol=2e-1)
def test_objective_matches_sym_precomputed_KbC():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
alpha = np.random.randn(len(Z))
C = develop_gaussian.compute_C_sym(Z, K, sigma)
b = develop_gaussian.compute_b_sym(Z, K, sigma)
K = gaussian_kernel(Z, sigma=sigma)
J_sym = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha, K, b, C)
J = gaussian.objective(Z, Z, sigma, lmbda, alpha, K_XY=K, b=b, C=C)
assert_equal(J, J_sym)
def test_objective_matches_sym_precomputed_KbC():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
alpha = np.random.randn(len(Z))
C = develop_gaussian.compute_C_sym(Z, K, sigma)
b = develop_gaussian.compute_b_sym(Z, K, sigma)
K = gaussian_kernel(Z, sigma=sigma)
J_sym = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha, K, b, C)
J = gaussian.objective(Z, Z, sigma, lmbda, alpha, K_XY=K, b=b, C=C)
assert_equal(J, J_sym)
def test_compute_C_against_initial_notebook():
D = 2
sigma = 1.
Z = np.random.randn(100, D)
K = gaussian_kernel(Z, sigma=sigma)
# build matrix expressions from notes
m = Z.shape[0]
D = Z.shape[1]
C = np.zeros((m, m))
for l in np.arange(D):
x_l = Z[:, l]
C += (np.diag(x_l).dot(K) - K.dot(np.diag(x_l))).dot(K.dot(np.diag(x_l)) - np.diag(x_l).dot(K))
C_test = develop_gaussian.compute_C_sym(Z, K, sigma)
assert_allclose(C, C_test)
def test_compute_C_against_initial_notebook():
D = 2
sigma = 1.
Z = np.random.randn(100, D)
K = gaussian_kernel(Z, sigma=sigma)
# build matrix expressions from notes
m = Z.shape[0]
D = Z.shape[1]
C = np.zeros((m, m))
for l in np.arange(D):
x_l = Z[:, l]
C += (np.diag(x_l).dot(K) - K.dot(
np.diag(x_l))).dot(K.dot(np.diag(x_l)) - np.diag(x_l).dot(K))
C_test = develop_gaussian.compute_C_sym(Z, K, sigma)
assert_allclose(C, C_test)
