def test_divergence_positivity(div, entropy, reach, p, m, n):
entropy.reach = reach
cost = euclidean_cost(p)
a, x = generate_measure(1, 5, 2)
b, y = generate_measure(1, 6, 2)
func = div(m * a, x, n * b, y, cost, entropy, solver=solver)
assert torch.ge(func, 0.0).all()
def test_sinkhorn_consistency_exp_log_asym(entropy, rtol, p, m, reach):
"""Test if the exp sinkhorn is consistent with its log form"""
entropy.reach = reach
cost = euclidean_cost(p)
a, x = generate_measure(2, 5, 3)
b, y = generate_measure(2, 6, 3)
solver1 = BatchVanillaSinkhorn(nits=10000,
nits_grad=10,
tol=1e-12,
assume_convergence=True)
solver2 = BatchExpSinkhorn(nits=10000,
nits_grad=10,
tol=1e-12,
assume_convergence=True)
f_a, g_a = solver1.sinkhorn_asym(m * a,
x,
m * b,
y,
cost=cost,
entropy=entropy)
u_a, v_a = solver2.sinkhorn_asym(m * a,
x,
m * b,
y,
cost=cost,
entropy=entropy)
assert torch.allclose(f_a, u_a, rtol=rtol)
assert torch.allclose(g_a, v_a, rtol=rtol)
def test_consistency_infinite_blur_sinkhorn_div(entropy, reach, p):
entropy.reach = reach
cost = euclidean_cost(p)
a, x = generate_measure(1, 5, 2)
b, y = generate_measure(1, 6, 2)
control = energyDistance(a, x, b, y, p)
func = sinkhorn_divergence(a, x, b, y, cost, entropy, solver)
assert torch.allclose(func, control, rtol=1e-0)
def test_consistency_infinite_blur_regularized_ot_balanced(entropy, p):
"""Control consistency in OT_eps when eps goes to infinity,
especially for balanced OT"""
cost = euclidean_cost(p)
a, x = generate_measure(1, 5, 2)
b, y = generate_measure(1, 6, 2)
f, g = convolution(a, x, b, y, cost)
control = scal(a, f)
func = regularized_ot(a, x, b, y, cost, entropy, solver)
assert torch.allclose(func, control, rtol=1e-0)
def test_consistency_infinite_blur_regularized_ot_unbalanced(
entropy, reach, p, m, n):
entropy.reach = reach
cost = euclidean_cost(p)
torch.set_default_dtype(torch.float64)
a, x = generate_measure(1, 5, 2)
b, y = generate_measure(1, 6, 2)
phi = entropy.entropy
f, g = convolution(a, x, b, y, cost)
control = (scal(a, f) + m * phi(torch.Tensor([n])) +
n * phi(torch.Tensor([m])))
func = regularized_ot(m * a, x, n * b, y, cost, entropy, solver=solver)
assert torch.allclose(func, control, rtol=1e-0)
def test_sinkhorn_asym_infinite_blur_unbalanced(solv, entropy, atol, p, m, n,
reach):
entropy.reach = reach
cost = euclidean_cost(p)
a, x = generate_measure(2, 5, 3)
b, y = generate_measure(2, 6, 3)
f_c, g_c = entropy.init_potential(m * a, x, n * b, y, p)
f, g = solv.sinkhorn_asym(m * a, x, n * b, y, cost=cost, entropy=entropy)
assert torch.allclose(torch.tensor([0.0]),
entropy.error_sink(f, f_c),
atol=atol)
assert torch.allclose(torch.tensor([0.0]),
entropy.error_sink(g, g_c),
atol=atol)
def test_gradient_unbalanced_weight_and_position_sym(solv, div, entropy, reach,
p, m):
entropy.reach = reach
cost = euclidean_cost(p)
a, x = generate_measure(1, 5, 2)
a = m * a
a.requires_grad = True
x.requires_grad = True
_, f = solv.sinkhorn_asym(a, x, a, x, cost, entropy)
func = entropy.output_regularized(a, x, a, x, cost, f, f)
[grad_num_x, grad_num_a] = torch.autograd.grad(func, [x, a])
grad_th_a = (
-2 * entropy.legendre_entropy(-f) + 2 * entropy.blur * m -
2 * entropy.blur *
((f[:, :, None] + f[:, None, :] - dist_matrix(x, x, p)).exp() *
a[:, None, :]).sum(dim=2))
pi = (a[:, :, None] * a[:, None, :] *
((f[:, :, None] + f[:, None, :] - dist_matrix(x, x, p)) /
entropy.blur).exp())
grad_th_x = 4 * x * pi.sum(dim=2)[:, :, None] - 4 * torch.einsum(
"ijk, ikl->ijl", pi, x)
print(f"Symmetric potential = {f}")
print(f"gradient ratio = {grad_num_a / grad_th_a}")
print(f"gradient ratio = {grad_num_x / grad_th_x}")
assert torch.allclose(grad_th_a, grad_num_a, rtol=1e-5)
assert torch.allclose(grad_th_x, grad_num_x, rtol=1e-5)
def test_sanity_control_exp_sinkhorn_small(entropy):
a, x = generate_measure(2, 5, 3)
b, y = generate_measure(2, 6, 3)
solver = BatchExpSinkhorn(nits=10000,
nits_grad=10,
tol=1e-12,
assume_convergence=True)
f, g = solver.sinkhorn_asym(a,
x,
b,
y,
cost=euclidean_cost(1),
entropy=entropy)
_, h = solver.sinkhorn_sym(a, x, cost=euclidean_cost(1), entropy=entropy)
assert f is None
assert g is None
assert h is None
def test_gradient_balanced_weight_and_position_asym(solv, div, entropy, p, m):
cost = euclidean_cost(p)
a, x = generate_measure(1, 5, 2)
b, y = generate_measure(1, 6, 2)
a, b = m * a, m * b
a.requires_grad = True
x.requires_grad = True
f, g = solv.sinkhorn_asym(a, x, b, y, cost, entropy)
func = entropy.output_regularized(a, x, b, y, cost, f, g)
[grad_num_x, grad_num_a] = torch.autograd.grad(func, [x, a])
grad_th_a = f
pi = (a[:, :, None] * b[:, None, :] *
((f[:, :, None] + g[:, None, :] - dist_matrix(x, y, p)) /
entropy.blur).exp())
grad_th_x = 2 * x * pi.sum(dim=2)[:, :, None] - 2 * torch.einsum(
"ijk, ikl->ijl", pi, y)
assert torch.allclose(grad_th_a, grad_num_a, rtol=1e-5)
assert torch.allclose(grad_th_x, grad_num_x, rtol=1e-5)
def test_consistency_regularized_sym_asym(entropy, reach, p, m):
entropy.reach = reach
cost = euclidean_cost(p)
a, x = generate_measure(1, 5, 2)
f_xy, g_xy = solver.sinkhorn_asym(a, x, a, x, cost, entropy)
_, f_xx = solver.sinkhorn_sym(a, x, cost, entropy)
func_asym = entropy.output_regularized(a, x, a, x, cost, f_xy, g_xy)
func_sym = entropy.output_regularized(a, x, a, x, cost, f_xx, f_xx)
assert torch.allclose(func_asym, func_sym, rtol=1e-6)
def test_sinkhorn_sym_infinite_blur(solv, entropy, atol, p, m, reach):
entropy.reach = reach
cost = euclidean_cost(p)
a, x = generate_measure(2, 5, 3)
f_c, _ = entropy.init_potential(m * a, x, m * a, x, cost=cost)
_, f = solv.sinkhorn_sym(m * a, x, cost=cost, entropy=entropy)
assert torch.allclose(entropy.error_sink(f, f_c),
torch.tensor([0.0]),
atol=atol)
def test_gradient_balanced_zero_grad_sinkhorn(solv, div, entropy, p, m):
cost = euclidean_cost(p)
a, x = generate_measure(1, 5, 2)
a = m * a
b, y = torch.zeros_like(a), torch.zeros_like(x)
b.copy_(a)
y.copy_(x)
a.requires_grad = True
x.requires_grad = True
func = sinkhorn_divergence(a, x, b, y, cost, entropy, solver=solv)
[grad_num_x, grad_num_a] = torch.autograd.grad(func, [x, a])
assert torch.allclose(torch.zeros_like(grad_num_a), grad_num_a, atol=1e-5)
assert torch.allclose(torch.zeros_like(grad_num_x), grad_num_x, atol=1e-5)
def test_gradient_unbalanced_weight_and_position_asym(solv, div, entropy,
reach, p, m, n):
entropy.reach = reach
cost = euclidean_cost(p)
a, x = generate_measure(1, 5, 2)
a = m * a
a.requires_grad = True
x.requires_grad = True
b, y = generate_measure(1, 6, 2)
f, g = solv.sinkhorn_asym(a, x, n * b, y, cost, entropy)
func = entropy.output_regularized(a, x, n * b, y, cost, f, g)
[grad_num_x, grad_num_a] = torch.autograd.grad(func, [x, a])
grad_th_a = (
-entropy.legendre_entropy(-f) + entropy.blur * n - entropy.blur *
((f[:, :, None] + g[:, None, :] - dist_matrix(x, y, p)).exp() * n *
b[:, None, :]).sum(dim=2))
pi = (n * a[:, :, None] * b[:, None, :] *
((f[:, :, None] + g[:, None, :] - dist_matrix(x, y, p)) /
entropy.blur).exp())
grad_th_x = 2 * x * pi.sum(dim=2)[:, :, None] - 2 * torch.einsum(
"ijk, ikl->ijl", pi, y)
assert torch.allclose(grad_th_a, grad_num_a, rtol=1e-5)
assert torch.allclose(grad_th_x, grad_num_x, rtol=1e-5)
def test_sinkhorn_consistency_sym_asym(solv, entropy, atol, p, m, reach):
"""Test if the symmetric and assymetric Sinkhorn
output the same results when (a,x)=(b,y)"""
entropy.reach = reach
cost = euclidean_cost(p)
a, x = generate_measure(2, 5, 3)
f_a, g_a = solv.sinkhorn_asym(m * a,
x,
m * a,
x,
cost=cost,
entropy=entropy)
_, f_s = solv.sinkhorn_sym(m * a, x, cost=cost, entropy=entropy)
assert torch.allclose(entropy.error_sink(f_a, f_s),
torch.tensor([0.0]),
atol=atol)
assert torch.allclose(entropy.error_sink(g_a, f_s),
torch.tensor([0.0]),
atol=atol)
def test_divergence_zero(div, entropy, reach, p, m):
entropy.reach = reach
cost = euclidean_cost(p)
a, x = generate_measure(1, 5, 2)
func = div(m * a, x, m * a, x, cost, entropy, solver=solver)
assert torch.allclose(func, torch.Tensor([0.0]), rtol=1e-6)
def test_sinkhorn_no_bug(entropy, solv):
a, x = generate_measure(2, 5, 3)
b, y = generate_measure(2, 6, 3)
solv.sinkhorn_asym(a, x, b, y, cost=euclidean_cost(1), entropy=entropy)
solv.sinkhorn_sym(a, x, cost=euclidean_cost(1), entropy=entropy, y_j=y)
