def test_root_decomposition_inv_forward(self):
a = torch.randn(5, 5)
a = torch.matmul(a, a.t())
a_lv = NonLazyVariable(Variable(a, requires_grad=True))
a_root = a_lv.root_inv_decomposition()
actual = a.inverse()
diff = (a_root.matmul(a_root.transpose(-1, -2)).data - actual).abs()
self.assertLess(torch.max(diff / actual), 1e-2)
def test_root_decomposition_inv_backward(self):
a = torch.Tensor([
[5.0212, 0.5504, -0.1810, 1.5414, 2.9611],
[0.5504, 2.8000, 1.9944, 0.6208, -0.8902],
[-0.1810, 1.9944, 3.0505, 1.0790, -1.1774],
[1.5414, 0.6208, 1.0790, 2.9430, 0.4170],
[2.9611, -0.8902, -1.1774, 0.4170, 3.3208],
])
a_var = Variable(a, requires_grad=True)
a_lv = NonLazyVariable(a_var)
a_root = a_lv.root_inv_decomposition()
res = a_root.matmul(a_root.transpose(-1, -2))
res.trace().backward()
a_var_copy = Variable(a, requires_grad=True)
a_var_copy.inverse().trace().backward()
self.assertTrue(approx_equal(a_var.grad.data, a_var_copy.grad.data))
