def pending_test_inv_matmul():
left_interp_indices = Variable(torch.LongTensor([[2, 3], [3, 4], [4, 5]]))
left_interp_values = Variable(torch.Tensor([[1, 2], [0.5, 1], [1, 3]]))
right_interp_indices = Variable(torch.LongTensor([[2, 3], [3, 4], [4, 5]]))
right_interp_values = Variable(torch.Tensor([[1, 2], [0.5, 1], [1, 3]]))
base_lazy_variable_mat = torch.randn(6, 6)
base_lazy_variable_mat = base_lazy_variable_mat.t().matmul(base_lazy_variable_mat)
base_lazy_variable = NonLazyVariable(Variable(base_lazy_variable_mat))
test_matrix = torch.randn(3, 4)
interp_lazy_var = InterpolatedLazyVariable(base_lazy_variable, left_interp_indices, left_interp_values,
right_interp_indices, right_interp_values)
res = interp_lazy_var.inv_matmul(Variable(test_matrix)).data
left_matrix = torch.Tensor([
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
])
right_matrix = torch.Tensor([
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
])
actual_mat = Variable(left_matrix.matmul(base_lazy_variable_mat).matmul(right_matrix.t()))
actual = gpytorch.inv_matmul(actual_mat, Variable(test_matrix)).data
assert approx_equal(res, actual)
def test_exact_posterior():
train_mean = Variable(torch.randn(4))
train_y = Variable(torch.randn(4))
test_mean = Variable(torch.randn(4))
# Test case
c1_var = Variable(torch.Tensor([5, 1, 2, 0]), requires_grad=True)
c2_var = Variable(torch.Tensor([6, 0, 1, -1]), requires_grad=True)
indices = Variable(torch.arange(0, 4).long().view(4, 1))
values = Variable(torch.ones(4).view(4, 1))
toeplitz_1 = InterpolatedLazyVariable(ToeplitzLazyVariable(c1_var),
indices, values, indices, values)
toeplitz_2 = InterpolatedLazyVariable(ToeplitzLazyVariable(c2_var),
indices, values, indices, values)
sum_lv = toeplitz_1 + toeplitz_2
# Actual case
actual = sum_lv.evaluate()
# Test forward
actual_alpha = gpytorch.posterior_strategy(actual).exact_posterior_alpha(
train_mean, train_y)
actual_mean = gpytorch.posterior_strategy(actual).exact_posterior_mean(
test_mean, actual_alpha)
sum_lv_alpha = sum_lv.posterior_strategy().exact_posterior_alpha(
train_mean, train_y)
sum_lv_mean = sum_lv.posterior_strategy().exact_posterior_mean(
test_mean, sum_lv_alpha)
assert (torch.norm(actual_mean.data - sum_lv_mean.data) < 1e-4)
def test_batch_diag(self):
left_interp_indices = Variable(
torch.LongTensor([[2, 3], [3, 4], [4, 5]]).repeat(5, 1, 1))
left_interp_values = Variable(
torch.Tensor([[1, 1], [1, 1], [1, 1]]).repeat(5, 1, 1))
right_interp_indices = Variable(
torch.LongTensor([[0, 1], [1, 2], [2, 3]]).repeat(5, 1, 1))
right_interp_values = Variable(
torch.Tensor([[1, 1], [1, 1], [1, 1]]).repeat(5, 1, 1))
base_lazy_variable_mat = torch.randn(5, 6, 6)
base_lazy_variable_mat = base_lazy_variable_mat.transpose(
1, 2).matmul(base_lazy_variable_mat)
base_lazy_variable = NonLazyVariable(
Variable(base_lazy_variable_mat, requires_grad=True))
interp_lazy_var = InterpolatedLazyVariable(base_lazy_variable,
left_interp_indices,
left_interp_values,
right_interp_indices,
right_interp_values)
actual = interp_lazy_var.evaluate()
actual_diag = torch.stack([
actual[0].diag(), actual[1].diag(), actual[2].diag(),
actual[3].diag(), actual[4].diag()
])
self.assertTrue(
approx_equal(actual_diag.data,
interp_lazy_var.diag().data))
def test_derivatives():
left_interp_indices = Variable(torch.LongTensor([[2, 3], [3, 4], [4, 5]])).repeat(5, 3, 1)
left_interp_values = Variable(torch.Tensor([[1, 2], [0.5, 1], [1, 3]])).repeat(5, 3, 1)
right_interp_indices = Variable(torch.LongTensor([[2, 3], [3, 4], [4, 5]])).repeat(5, 3, 1)
right_interp_values = Variable(torch.Tensor([[1, 2], [0.5, 1], [1, 3]])).repeat(5, 3, 1)
base_lazy_variable_mat = torch.randn(5, 6, 6)
base_lazy_variable_mat = base_lazy_variable_mat.transpose(1, 2).matmul(base_lazy_variable_mat)
test_matrix = Variable(torch.randn(1, 9, 4))
base_lazy_variable = NonLazyVariable(Variable(base_lazy_variable_mat, requires_grad=True))
interp_lazy_var = InterpolatedLazyVariable(base_lazy_variable, left_interp_indices, left_interp_values,
right_interp_indices, right_interp_values)
res = interp_lazy_var.matmul(test_matrix)
res.sum().backward()
base_lazy_variable2 = Variable(base_lazy_variable_mat, requires_grad=True)
left_matrix = torch.Tensor([
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
]).repeat(5, 1, 1)
actual = Variable(left_matrix).matmul(base_lazy_variable2).matmul(Variable(left_matrix).transpose(-1, -2))
actual = actual.matmul(test_matrix)
actual.sum().backward()
assert approx_equal(base_lazy_variable.var.grad.data, base_lazy_variable2.grad.data)
def test_diag(self):
left_interp_indices = Variable(torch.LongTensor([[2, 3], [3, 4], [4, 5]]))
left_interp_values = Variable(torch.Tensor([[1, 1], [1, 1], [1, 1]]))
right_interp_indices = Variable(torch.LongTensor([[0, 1], [1, 2], [2, 3]]))
right_interp_values = Variable(torch.Tensor([[1, 1], [1, 1], [1, 1]]))
base_lazy_variable_mat = torch.randn(6, 6)
base_lazy_variable_mat = (
base_lazy_variable_mat.t().
matmul(base_lazy_variable_mat)
)
base_lazy_variable = NonLazyVariable(
Variable(base_lazy_variable_mat, requires_grad=True)
)
interp_lazy_var = InterpolatedLazyVariable(
base_lazy_variable,
left_interp_indices,
left_interp_values,
right_interp_indices,
right_interp_values,
)
actual = interp_lazy_var.evaluate()
self.assertTrue(approx_equal(actual.diag().data, interp_lazy_var.diag().data))
def test_inv_matmul(self):
base_lazy_variable_mat = torch.randn(6, 6)
base_lazy_variable_mat = base_lazy_variable_mat.t().matmul(
base_lazy_variable_mat)
test_matrix = torch.randn(3, 4)
left_interp_indices = Variable(torch.LongTensor([[2, 3], [3, 4],
[4, 5]]),
requires_grad=True)
left_interp_values = Variable(torch.Tensor([[1, 2], [0.5, 1], [1, 3]]),
requires_grad=True)
right_interp_indices = Variable(torch.LongTensor([[2, 3], [3, 4],
[4, 5]]),
requires_grad=True)
right_interp_values = Variable(torch.Tensor([[1, 2], [0.5, 1], [1,
3]]),
requires_grad=True)
left_interp_values_copy = Variable(left_interp_values.data,
requires_grad=True)
right_interp_values_copy = Variable(right_interp_values.data,
requires_grad=True)
base_lazy_variable = Variable(base_lazy_variable_mat,
requires_grad=True)
base_lazy_variable_copy = Variable(base_lazy_variable_mat,
requires_grad=True)
test_matrix_var = Variable(test_matrix, requires_grad=True)
test_matrix_var_copy = Variable(test_matrix, requires_grad=True)
interp_lazy_var = InterpolatedLazyVariable(
NonLazyVariable(base_lazy_variable),
left_interp_indices,
left_interp_values,
right_interp_indices,
right_interp_values,
)
res = interp_lazy_var.inv_matmul(test_matrix_var)
left_matrix = Variable(torch.zeros(3, 6))
right_matrix = Variable(torch.zeros(3, 6))
left_matrix.scatter_(1, left_interp_indices, left_interp_values_copy)
right_matrix.scatter_(1, right_interp_indices,
right_interp_values_copy)
actual_mat = left_matrix.matmul(base_lazy_variable_copy).matmul(
right_matrix.transpose(-1, -2))
actual = gpytorch.inv_matmul(actual_mat, test_matrix_var_copy)
self.assertTrue(approx_equal(res.data, actual.data))
# Backward pass
res.sum().backward()
actual.sum().backward()
self.assertTrue(
approx_equal(base_lazy_variable.grad.data,
base_lazy_variable_copy.grad.data))
self.assertTrue(
approx_equal(left_interp_values.grad.data,
left_interp_values_copy.grad.data))
def test_batch_matmul():
left_interp_indices = Variable(
torch.LongTensor([[2, 3], [3, 4], [4, 5]]).repeat(5, 3, 1))
left_interp_values = Variable(torch.Tensor([[1, 2], [0.5, 1],
[1, 3]]).repeat(5, 3, 1),
requires_grad=True)
left_interp_values_copy = Variable(left_interp_values.data,
requires_grad=True)
right_interp_indices = Variable(
torch.LongTensor([[0, 1], [1, 2], [2, 3]]).repeat(5, 3, 1))
right_interp_values = Variable(torch.Tensor([[1, 2], [2, 0.5],
[1, 3]]).repeat(5, 3, 1),
requires_grad=True)
right_interp_values_copy = Variable(right_interp_values.data,
requires_grad=True)
base_lazy_variable_mat = torch.randn(5, 6, 6)
base_lazy_variable_mat = base_lazy_variable_mat.transpose(
-1, -2).matmul(base_lazy_variable_mat)
base_variable = Variable(base_lazy_variable_mat, requires_grad=True)
base_variable_copy = Variable(base_lazy_variable_mat, requires_grad=True)
base_lazy_variable = NonLazyVariable(base_variable)
test_matrix = torch.randn(5, 9, 4)
interp_lazy_var = InterpolatedLazyVariable(base_lazy_variable,
left_interp_indices,
left_interp_values,
right_interp_indices,
right_interp_values)
res = interp_lazy_var.matmul(Variable(test_matrix))
left_matrix_comps = []
right_matrix_comps = []
for i in range(5):
left_matrix_comp = Variable(torch.zeros(9, 6))
right_matrix_comp = Variable(torch.zeros(9, 6))
left_matrix_comp.scatter_(1, left_interp_indices[i],
left_interp_values_copy[i])
right_matrix_comp.scatter_(1, right_interp_indices[i],
right_interp_values_copy[i])
left_matrix_comps.append(left_matrix_comp.unsqueeze(0))
right_matrix_comps.append(right_matrix_comp.unsqueeze(0))
left_matrix = torch.cat(left_matrix_comps)
right_matrix = torch.cat(right_matrix_comps)
actual = left_matrix.matmul(base_variable_copy).matmul(
right_matrix.transpose(-1, -2))
actual = actual.matmul(Variable(test_matrix))
assert approx_equal(res.data, actual.data)
res.sum().backward()
actual.sum().backward()
assert approx_equal(base_variable.grad.data, base_variable_copy.grad.data)
assert approx_equal(left_interp_values.grad.data,
left_interp_values_copy.grad.data)
def test_matmul(self):
left_interp_indices = Variable(
torch.LongTensor([[2, 3], [3, 4], [4, 5]]).repeat(3, 1))
left_interp_values = Variable(torch.Tensor([[1, 2], [0.5, 1],
[1, 3]]).repeat(3, 1),
requires_grad=True)
left_interp_values_copy = Variable(left_interp_values.data,
requires_grad=True)
right_interp_indices = Variable(
torch.LongTensor([[0, 1], [1, 2], [2, 3]]).repeat(3, 1))
right_interp_values = Variable(torch.Tensor([[1, 2], [2, 0.5],
[1, 3]]).repeat(3, 1),
requires_grad=True)
right_interp_values_copy = Variable(right_interp_values.data,
requires_grad=True)
base_lazy_variable_mat = torch.randn(6, 6)
base_lazy_variable_mat = (
base_lazy_variable_mat.t().matmul(base_lazy_variable_mat))
base_variable = Variable(base_lazy_variable_mat, requires_grad=True)
base_variable_copy = Variable(base_lazy_variable_mat,
requires_grad=True)
base_lazy_variable = NonLazyVariable(base_variable)
test_matrix = torch.randn(9, 4)
interp_lazy_var = InterpolatedLazyVariable(
base_lazy_variable,
left_interp_indices,
left_interp_values,
right_interp_indices,
right_interp_values,
)
res = interp_lazy_var.matmul(Variable(test_matrix))
left_matrix = Variable(torch.zeros(9, 6))
right_matrix = Variable(torch.zeros(9, 6))
left_matrix.scatter_(1, left_interp_indices, left_interp_values_copy)
right_matrix.scatter_(1, right_interp_indices,
right_interp_values_copy)
actual = (left_matrix.matmul(base_variable_copy).matmul(
right_matrix.t()).matmul(Variable(test_matrix)))
self.assertTrue(approx_equal(res.data, actual.data))
res.sum().backward()
actual.sum().backward()
self.assertTrue(
approx_equal(base_variable.grad.data,
base_variable_copy.grad.data))
self.assertTrue(
approx_equal(left_interp_values.grad.data,
left_interp_values_copy.grad.data))
def test_matmul_batch(self):
left_interp_indices = Variable(
torch.LongTensor([[2, 3], [3, 4], [4, 5]])).repeat(5, 3, 1)
left_interp_values = Variable(torch.Tensor([[1, 2], [0.5, 1],
[1, 3]])).repeat(5, 3, 1)
right_interp_indices = Variable(
torch.LongTensor([[0, 1], [1, 2], [2, 3]])).repeat(5, 3, 1)
right_interp_values = Variable(torch.Tensor([[1, 2], [2, 0.5],
[1, 3]])).repeat(5, 3, 1)
base_lazy_variable_mat = torch.randn(5, 6, 6)
base_lazy_variable_mat = (base_lazy_variable_mat.transpose(
1, 2).matmul(base_lazy_variable_mat))
test_matrix = Variable(torch.randn(1, 9, 4))
base_lazy_variable = NonLazyVariable(
Variable(base_lazy_variable_mat, requires_grad=True))
interp_lazy_var = InterpolatedLazyVariable(
base_lazy_variable,
left_interp_indices,
left_interp_values,
right_interp_indices,
right_interp_values,
)
res = interp_lazy_var.matmul(test_matrix)
left_matrix = torch.Tensor([
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
]).repeat(5, 1, 1)
right_matrix = torch.Tensor([
[1, 2, 0, 0, 0, 0],
[0, 2, 0.5, 0, 0, 0],
[0, 0, 1, 3, 0, 0],
[1, 2, 0, 0, 0, 0],
[0, 2, 0.5, 0, 0, 0],
[0, 0, 1, 3, 0, 0],
[1, 2, 0, 0, 0, 0],
[0, 2, 0.5, 0, 0, 0],
[0, 0, 1, 3, 0, 0],
]).repeat(5, 1, 1)
actual = (left_matrix.matmul(base_lazy_variable_mat).matmul(
right_matrix.transpose(-1, -2)).matmul(test_matrix.data))
self.assertTrue(approx_equal(res.data, actual))
def test_exact_posterior():
train_mean = Variable(torch.randn(4))
train_y = Variable(torch.randn(4))
test_mean = Variable(torch.randn(4))
# Test case
c1_var = Variable(torch.Tensor([5, 1, 2, 0]), requires_grad=True)
c2_var = Variable(torch.Tensor([[6, 0], [1, -1]]), requires_grad=True)
c3_var = Variable(torch.Tensor([7, 2, 1, 0]), requires_grad=True)
indices_1 = torch.arange(0, 4).long().view(4, 1)
values_1 = torch.ones(4).view(4, 1)
indices_2 = torch.arange(0, 2).expand(4, 2).long().view(2, 4, 1)
values_2 = torch.ones(8).view(2, 4, 1)
indices_3 = torch.arange(0, 4).long().view(4, 1)
values_3 = torch.ones(4).view(4, 1)
toeplitz_1 = InterpolatedLazyVariable(ToeplitzLazyVariable(c1_var),
Variable(indices_1),
Variable(values_1),
Variable(indices_1),
Variable(values_1))
kronecker_product = KroneckerProductLazyVariable(c2_var, indices_2,
values_2, indices_2,
values_2)
toeplitz_2 = InterpolatedLazyVariable(ToeplitzLazyVariable(c3_var),
Variable(indices_3),
Variable(values_3),
Variable(indices_3),
Variable(values_3))
mul_lv = toeplitz_1 * kronecker_product * toeplitz_2
# Actual case
actual = mul_lv.evaluate()
# Test forward
actual_alpha = gpytorch.posterior_strategy(actual).exact_posterior_alpha(
train_mean, train_y)
actual_mean = gpytorch.posterior_strategy(actual).exact_posterior_mean(
test_mean, actual_alpha)
mul_lv_alpha = mul_lv.posterior_strategy().exact_posterior_alpha(
train_mean, train_y)
mul_lv_mean = mul_lv.posterior_strategy().exact_posterior_mean(
test_mean, mul_lv_alpha)
assert (torch.norm(actual_mean.data - mul_lv_mean.data) < 1e-3)
def test_matmul():
left_interp_indices = Variable(torch.LongTensor([[2, 3], [3, 4], [4, 5]])).repeat(3, 1)
left_interp_values = Variable(torch.Tensor([[1, 2], [0.5, 1], [1, 3]])).repeat(3, 1)
right_interp_indices = Variable(torch.LongTensor([[0, 1], [1, 2], [2, 3]])).repeat(3, 1)
right_interp_values = Variable(torch.Tensor([[1, 2], [2, 0.5], [1, 3]])).repeat(3, 1)
base_lazy_variable_mat = torch.randn(6, 6)
base_lazy_variable_mat = base_lazy_variable_mat.t().matmul(base_lazy_variable_mat)
base_lazy_variable = NonLazyVariable(Variable(base_lazy_variable_mat))
test_matrix = torch.randn(9, 4)
test_matrix = torch.ones(9)
interp_lazy_var = InterpolatedLazyVariable(base_lazy_variable, left_interp_indices, left_interp_values,
right_interp_indices, right_interp_values)
res = interp_lazy_var.matmul(Variable(test_matrix)).data
left_matrix = torch.Tensor([
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
[0, 0, 1, 2, 0, 0],
[0, 0, 0, 0.5, 1, 0],
[0, 0, 0, 0, 1, 3],
])
right_matrix = torch.Tensor([
[1, 2, 0, 0, 0, 0],
[0, 2, 0.5, 0, 0, 0],
[0, 0, 1, 3, 0, 0],
[1, 2, 0, 0, 0, 0],
[0, 2, 0.5, 0, 0, 0],
[0, 0, 1, 3, 0, 0],
[1, 2, 0, 0, 0, 0],
[0, 2, 0.5, 0, 0, 0],
[0, 0, 1, 3, 0, 0],
])
actual = left_matrix.matmul(base_lazy_variable_mat).matmul(right_matrix.t()).matmul(test_matrix)
assert approx_equal(res, actual)
def test_getitem_batch(self):
left_interp_indices = Variable(
torch.LongTensor([[2, 3], [3, 4], [4, 5]]).repeat(5, 1, 1))
left_interp_values = Variable(
torch.Tensor([[1, 1], [1, 1], [1, 1]]).repeat(5, 1, 1))
right_interp_indices = Variable(
torch.LongTensor([[0, 1], [1, 2], [2, 3]]).repeat(5, 1, 1))
right_interp_values = Variable(
torch.Tensor([[1, 1], [1, 1], [1, 1]]).repeat(5, 1, 1))
base_lazy_variable_mat = torch.randn(5, 6, 6)
base_lazy_variable_mat = (base_lazy_variable_mat.transpose(
1, 2).matmul(base_lazy_variable_mat))
base_lazy_variable = NonLazyVariable(
Variable(base_lazy_variable_mat, requires_grad=True))
interp_lazy_var = InterpolatedLazyVariable(
base_lazy_variable,
left_interp_indices,
left_interp_values,
right_interp_indices,
right_interp_values,
)
actual = (base_lazy_variable[:, 2:5, 0:3] +
base_lazy_variable[:, 2:5, 1:4] +
base_lazy_variable[:, 3:6, 0:3] +
base_lazy_variable[:, 3:6, 1:4]).evaluate()
self.assertTrue(
approx_equal(interp_lazy_var[2].evaluate().data, actual[2].data))
self.assertTrue(
approx_equal(interp_lazy_var[0:2].evaluate().data,
actual[0:2].data))
self.assertTrue(
approx_equal(interp_lazy_var[:, 2:3].evaluate().data,
actual[:, 2:3].data))
self.assertTrue(
approx_equal(interp_lazy_var[:, 0:2].evaluate().data,
actual[:, 0:2].data))
self.assertTrue(
approx_equal(interp_lazy_var[1, :1, :2].evaluate().data,
actual[1, :1, :2].data))
self.assertTrue(
approx_equal(interp_lazy_var[1, 1, :2].data, actual[1,
1, :2].data))
self.assertTrue(
approx_equal(interp_lazy_var[1, :1, 2].data, actual[1, :1,
2].data))
def test_inv_matmul_batch(self):
base_lazy_variable_mat = torch.randn(6, 6)
base_lazy_variable_mat = ((base_lazy_variable_mat.t().matmul(
base_lazy_variable_mat)).unsqueeze(0).repeat(5, 1, 1))
test_matrix = torch.randn(5, 3, 4)
left_interp_indices = Variable(torch.LongTensor(
[[2, 3], [3, 4], [4, 5]]).unsqueeze(0).repeat(5, 1, 1),
requires_grad=True)
left_interp_values = Variable(torch.Tensor(
[[1, 2], [0.5, 1], [1, 3]]).unsqueeze(0).repeat(5, 1, 1),
requires_grad=True)
right_interp_indices = Variable(torch.LongTensor(
[[2, 3], [3, 4], [4, 5]]).unsqueeze(0).repeat(5, 1, 1),
requires_grad=True)
right_interp_values = Variable(torch.Tensor(
[[1, 2], [0.5, 1], [1, 3]]).unsqueeze(0).repeat(5, 1, 1),
requires_grad=True)
left_interp_values_copy = Variable(left_interp_values.data,
requires_grad=True)
right_interp_values_copy = Variable(right_interp_values.data,
requires_grad=True)
base_lazy_variable = Variable(base_lazy_variable_mat,
requires_grad=True)
base_lazy_variable_copy = Variable(base_lazy_variable_mat,
requires_grad=True)
test_matrix_var = Variable(test_matrix, requires_grad=True)
test_matrix_var_copy = Variable(test_matrix, requires_grad=True)
interp_lazy_var = InterpolatedLazyVariable(
NonLazyVariable(base_lazy_variable),
left_interp_indices,
left_interp_values,
right_interp_indices,
right_interp_values,
)
res = interp_lazy_var.inv_matmul(test_matrix_var)
left_matrix_comps = []
right_matrix_comps = []
for i in range(5):
left_matrix_comp = Variable(torch.zeros(3, 6))
right_matrix_comp = Variable(torch.zeros(3, 6))
left_matrix_comp.scatter_(1, left_interp_indices[i],
left_interp_values_copy[i])
right_matrix_comp.scatter_(1, right_interp_indices[i],
right_interp_values_copy[i])
left_matrix_comps.append(left_matrix_comp.unsqueeze(0))
right_matrix_comps.append(right_matrix_comp.unsqueeze(0))
left_matrix = torch.cat(left_matrix_comps)
right_matrix = torch.cat(right_matrix_comps)
actual_mat = left_matrix.matmul(base_lazy_variable_copy).matmul(
right_matrix.transpose(-1, -2))
actual = gpytorch.inv_matmul(actual_mat, test_matrix_var_copy)
self.assertTrue(approx_equal(res.data, actual.data))
# Backward pass
res.sum().backward()
actual.sum().backward()
self.assertTrue(
approx_equal(base_lazy_variable.grad.data,
base_lazy_variable_copy.grad.data))
self.assertTrue(
approx_equal(left_interp_values.grad.data,
left_interp_values_copy.grad.data))