Improve differential operators (#528)
* Improve grad logic and fix issues * Add operators' fast versions * Fix bug in laplacian + new tests + restructuring Co-authored-by: Dario Coscia <dariocos99@gmail.com> * fix advection bug --------- Co-authored-by: Dario Coscia <dariocos99@gmail.com>
This commit is contained in:
Giovanni Canali
committed by
Dario Coscia
Dario Coscia
parent
ce0c033de1
commit
485c8dd789
@@ -1,205 +1,317 @@
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import torch
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import pytest
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from pina import LabelTensor
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from pina.operator import grad, div, laplacian
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from pina.operator import grad, div, laplacian, advection
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def func_vector(x):
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return x**2
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class Function(object):
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def __iter__(self):
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functions = [
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(
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getattr(self, f"{name}_input"),
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getattr(self, f"{name}"),
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getattr(self, f"{name}_grad"),
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getattr(self, f"{name}_div"),
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getattr(self, f"{name}_lap"),
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)
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for name in [
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"scalar_scalar",
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"scalar_vector",
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"vector_scalar",
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"vector_vector",
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]
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]
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return iter(functions)
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# Scalar to scalar function
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@staticmethod
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def scalar_scalar(x):
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return x**2
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@staticmethod
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def scalar_scalar_grad(x):
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return 2 * x
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@staticmethod
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def scalar_scalar_div(x):
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return 2 * x
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@staticmethod
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def scalar_scalar_lap(x):
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return 2 * torch.ones_like(x)
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@staticmethod
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def scalar_scalar_input():
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input_ = torch.rand((20, 1), requires_grad=True)
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return LabelTensor(input_, ["x"])
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# Scalar to vector function
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@staticmethod
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def scalar_vector(x):
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u = x**2
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v = x**3 + x
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return torch.cat((u, v), dim=-1)
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@staticmethod
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def scalar_vector_grad(x):
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u = 2 * x
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v = 3 * x**2 + 1
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return torch.cat((u, v), dim=-1)
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@staticmethod
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def scalar_vector_div(x):
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return ValueError
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@staticmethod
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def scalar_vector_lap(x):
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u = 2 * torch.ones_like(x)
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v = 6 * x
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return torch.cat((u, v), dim=-1)
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@staticmethod
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def scalar_vector_input():
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input_ = torch.rand((20, 1), requires_grad=True)
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return LabelTensor(input_, ["x"])
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# Vector to scalar function
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@staticmethod
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def vector_scalar(x):
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return torch.prod(x**2, dim=-1, keepdim=True)
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@staticmethod
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def vector_scalar_grad(x):
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return 2 * torch.prod(x**2, dim=-1, keepdim=True) / x
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@staticmethod
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def vector_scalar_div(x):
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return ValueError
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@staticmethod
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def vector_scalar_lap(x):
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return 2 * torch.sum(
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torch.prod(x**2, dim=-1, keepdim=True) / x**2,
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dim=-1,
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keepdim=True,
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)
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@staticmethod
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def vector_scalar_input():
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input_ = torch.rand((20, 2), requires_grad=True)
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return LabelTensor(input_, ["x", "yy"])
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# Vector to vector function
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@staticmethod
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def vector_vector(x):
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u = torch.prod(x**2, dim=-1, keepdim=True)
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v = torch.sum(x**2, dim=-1, keepdim=True)
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return torch.cat((u, v), dim=-1)
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@staticmethod
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def vector_vector_grad(x):
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u = 2 * torch.prod(x**2, dim=-1, keepdim=True) / x
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v = 2 * x
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return torch.cat((u, v), dim=-1)
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@staticmethod
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def vector_vector_div(x):
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u = 2 * torch.prod(x**2, dim=-1, keepdim=True) / x[..., 0]
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v = 2 * x[..., 1]
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return u + v
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@staticmethod
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def vector_vector_lap(x):
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u = torch.sum(
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2 * torch.prod(x**2, dim=-1, keepdim=True) / x**2,
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dim=-1,
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keepdim=True,
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)
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v = 2 * x.shape[-1] * torch.ones_like(u)
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return torch.cat((u, v), dim=-1)
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@staticmethod
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def vector_vector_input():
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input_ = torch.rand((20, 2), requires_grad=True)
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return LabelTensor(input_, ["x", "yy"])
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def func_scalar(x):
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x_ = x.extract(["x"])
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y_ = x.extract(["y"])
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z_ = x.extract(["z"])
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return x_**2 + y_**2 + z_**2
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@pytest.mark.parametrize(
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"f",
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Function(),
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ids=["scalar_scalar", "scalar_vector", "vector_scalar", "vector_vector"],
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)
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def test_gradient(f):
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# Unpack the function
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func_input, func, func_grad, _, _ = f
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data = torch.rand((20, 3))
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inp = LabelTensor(data, ["x", "y", "z"]).requires_grad_(True)
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labels = ["a", "b", "c"]
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tensor_v = LabelTensor(func_vector(inp), labels)
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tensor_s = LabelTensor(func_scalar(inp).reshape(-1, 1), labels[0])
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# Define input and output
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input_ = func_input()
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output_ = func(input_)
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labels = [f"u{i}" for i in range(output_.shape[-1])]
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output_ = LabelTensor(output_, labels)
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# Compute the true gradient and the pina gradient
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pina_grad = grad(output_=output_, input_=input_)
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true_grad = func_grad(input_)
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def test_grad_scalar_output():
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grad_tensor_s = grad(tensor_s, inp)
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true_val = 2 * inp
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true_val.labels = inp.labels
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assert grad_tensor_s.shape == inp.shape
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assert grad_tensor_s.labels == [
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f"d{tensor_s.labels[0]}d{i}" for i in inp.labels
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# Check the shape and labels of the gradient
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n_components = len(output_.labels) * len(input_.labels)
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assert pina_grad.shape == (*output_.shape[:-1], n_components)
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assert pina_grad.labels == [
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f"d{c}d{i}" for c in output_.labels for i in input_.labels
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]
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assert torch.allclose(grad_tensor_s, true_val)
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grad_tensor_s = grad(tensor_s, inp, d=["x", "y"])
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assert grad_tensor_s.shape == (20, 2)
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assert grad_tensor_s.labels == [
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f"d{tensor_s.labels[0]}d{i}" for i in ["x", "y"]
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]
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assert torch.allclose(grad_tensor_s, true_val.extract(["x", "y"]))
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# Compare the values
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assert torch.allclose(pina_grad, true_grad)
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# Test if labels are handled correctly
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grad(output_=output_, input_=input_, components=output_.labels[0])
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grad(output_=output_, input_=input_, d=input_.labels[0])
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# Should fail if input not a LabelTensor
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with pytest.raises(TypeError):
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grad(output_=output_, input_=input_.tensor)
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# Should fail if output not a LabelTensor
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with pytest.raises(TypeError):
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grad(output_=output_.tensor, input_=input_)
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# Should fail for non-existent input labels
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with pytest.raises(RuntimeError):
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grad(output_=output_, input_=input_, d=["x", "y"])
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# Should fail for non-existent output labels
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with pytest.raises(RuntimeError):
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grad(output_=output_, input_=input_, components=["a", "b", "c"])
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def test_grad_vector_output():
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grad_tensor_v = grad(tensor_v, inp)
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true_val = torch.cat(
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(
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2 * inp.extract(["x"]),
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torch.zeros_like(inp.extract(["y"])),
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torch.zeros_like(inp.extract(["z"])),
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torch.zeros_like(inp.extract(["x"])),
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2 * inp.extract(["y"]),
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torch.zeros_like(inp.extract(["z"])),
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torch.zeros_like(inp.extract(["x"])),
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torch.zeros_like(inp.extract(["y"])),
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2 * inp.extract(["z"]),
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),
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dim=1,
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@pytest.mark.parametrize(
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"f",
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Function(),
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ids=["scalar_scalar", "scalar_vector", "vector_scalar", "vector_vector"],
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)
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def test_divergence(f):
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# Unpack the function
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func_input, func, _, func_div, _ = f
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# Define input and output
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input_ = func_input()
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output_ = func(input_)
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labels = [f"u{i}" for i in range(output_.shape[-1])]
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output_ = LabelTensor(output_, labels)
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# Scalar to vector or vector to scalar functions
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if func_div(input_) == ValueError:
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with pytest.raises(ValueError):
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div(output_=output_, input_=input_)
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# Scalar to scalar or vector to vector functions
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else:
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# Compute the true divergence and the pina divergence
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pina_div = div(output_=output_, input_=input_)
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true_div = func_div(input_)
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# Check the shape and labels of the divergence
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assert pina_div.shape == (*output_.shape[:-1], 1)
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tmp_labels = [
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f"d{c}d{d_}" for c, d_ in zip(output_.labels, input_.labels)
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]
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assert pina_div.labels == ["+".join(tmp_labels)]
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# Compare the values
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assert torch.allclose(pina_div, true_div)
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# Test if labels are handled correctly. Performed in a single call to
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# avoid components and d having different lengths.
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div(
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output_=output_,
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input_=input_,
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components=output_.labels[0],
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d=input_.labels[0],
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)
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# Should fail if input not a LabelTensor
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with pytest.raises(TypeError):
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div(output_=output_, input_=input_.tensor)
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# Should fail if output not a LabelTensor
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with pytest.raises(TypeError):
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div(output_=output_.tensor, input_=input_)
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# Should fail for non-existent labels
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with pytest.raises(RuntimeError):
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div(output_=output_, input_=input_, d=["x", "y"])
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with pytest.raises(RuntimeError):
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div(output_=output_, input_=input_, components=["a", "b", "c"])
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@pytest.mark.parametrize(
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"f",
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Function(),
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ids=["scalar_scalar", "scalar_vector", "vector_scalar", "vector_vector"],
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)
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def test_laplacian(f):
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# Unpack the function
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func_input, func, _, _, func_lap = f
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# Define input and output
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input_ = func_input()
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output_ = func(input_)
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labels = [f"u{i}" for i in range(output_.shape[-1])]
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output_ = LabelTensor(output_, labels)
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# Compute the true laplacian and the pina laplacian
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pina_lap = laplacian(output_=output_, input_=input_)
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true_lap = func_lap(input_)
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# Check the shape and labels of the laplacian
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assert pina_lap.shape == output_.shape
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assert pina_lap.labels == [f"dd{l}" for l in output_.labels]
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# Compare the values
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assert torch.allclose(pina_lap, true_lap)
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# Test if labels are handled correctly
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laplacian(output_=output_, input_=input_, components=output_.labels[0])
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laplacian(output_=output_, input_=input_, d=input_.labels[0])
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# Should fail if input not a LabelTensor
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with pytest.raises(TypeError):
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laplacian(output_=output_, input_=input_.tensor)
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# Should fail if output not a LabelTensor
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with pytest.raises(TypeError):
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laplacian(output_=output_.tensor, input_=input_)
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# Should fail for non-existent input labels
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with pytest.raises(RuntimeError):
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laplacian(output_=output_, input_=input_, d=["x", "y"])
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# Should fail for non-existent output labels
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with pytest.raises(RuntimeError):
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laplacian(output_=output_, input_=input_, components=["a", "b", "c"])
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def test_advection():
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# Define input and output
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input_ = torch.rand((20, 3), requires_grad=True)
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input_ = LabelTensor(input_, ["x", "y", "z"])
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output_ = LabelTensor(input_**2, ["u", "v", "c"])
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# Define the velocity field
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velocity = output_.extract(["c"])
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# Compute the true advection and the pina advection
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pina_advection = advection(
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output_=output_, input_=input_, velocity_field="c"
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)
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assert grad_tensor_v.shape == (20, 9)
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assert grad_tensor_v.labels == [
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f"d{j}d{i}" for j in tensor_v.labels for i in inp.labels
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]
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assert torch.allclose(grad_tensor_v, true_val)
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true_advection = velocity * 2 * input_.extract(["x", "y"])
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grad_tensor_v = grad(tensor_v, inp, d=["x", "y"])
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true_val = torch.cat(
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(
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2 * inp.extract(["x"]),
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torch.zeros_like(inp.extract(["y"])),
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torch.zeros_like(inp.extract(["x"])),
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2 * inp.extract(["y"]),
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torch.zeros_like(inp.extract(["x"])),
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torch.zeros_like(inp.extract(["y"])),
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),
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dim=1,
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)
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assert grad_tensor_v.shape == (inp.shape[0], 6)
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assert grad_tensor_v.labels == [
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f"d{j}d{i}" for j in tensor_v.labels for i in ["x", "y"]
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]
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assert torch.allclose(grad_tensor_v, true_val)
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def test_div_vector_output():
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div_tensor_v = div(tensor_v, inp)
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true_val = 2 * torch.sum(inp, dim=1).reshape(-1, 1)
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assert div_tensor_v.shape == (20, 1)
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assert div_tensor_v.labels == [f"dadx+dbdy+dcdz"]
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assert torch.allclose(div_tensor_v, true_val)
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div_tensor_v = div(tensor_v, inp, components=["a", "b"], d=["x", "y"])
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true_val = 2 * torch.sum(inp.extract(["x", "y"]), dim=1).reshape(-1, 1)
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assert div_tensor_v.shape == (inp.shape[0], 1)
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assert div_tensor_v.labels == [f"dadx+dbdy"]
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assert torch.allclose(div_tensor_v, true_val)
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def test_laplacian_scalar_output():
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laplace_tensor_s = laplacian(tensor_s, inp)
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true_val = 6 * torch.ones_like(laplace_tensor_s)
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assert laplace_tensor_s.shape == tensor_s.shape
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assert laplace_tensor_s.labels == [f"dd{tensor_s.labels[0]}"]
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assert torch.allclose(laplace_tensor_s, true_val)
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laplace_tensor_s = laplacian(tensor_s, inp, components=["a"], d=["x", "y"])
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true_val = 4 * torch.ones_like(laplace_tensor_s)
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assert laplace_tensor_s.shape == tensor_s.shape
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assert laplace_tensor_s.labels == [f"dd{tensor_s.labels[0]}"]
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assert torch.allclose(laplace_tensor_s, true_val)
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def test_laplacian_vector_output():
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laplace_tensor_v = laplacian(tensor_v, inp)
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print(laplace_tensor_v.labels)
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print(tensor_v.labels)
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true_val = 2 * torch.ones_like(tensor_v)
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assert laplace_tensor_v.shape == tensor_v.shape
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assert laplace_tensor_v.labels == [f"dd{i}" for i in tensor_v.labels]
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assert torch.allclose(laplace_tensor_v, true_val)
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laplace_tensor_v = laplacian(
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tensor_v, inp, components=["a", "b"], d=["x", "y"]
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)
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true_val = 2 * torch.ones_like(tensor_v.extract(["a", "b"]))
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assert laplace_tensor_v.shape == tensor_v.extract(["a", "b"]).shape
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assert laplace_tensor_v.labels == [f"dd{i}" for i in ["a", "b"]]
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assert torch.allclose(laplace_tensor_v, true_val)
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def test_laplacian_vector_output2():
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x = LabelTensor(
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torch.linspace(0, 1, 10, requires_grad=True).reshape(-1, 1),
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labels=["x"],
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)
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y = LabelTensor(
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torch.linspace(3, 4, 10, requires_grad=True).reshape(-1, 1),
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labels=["y"],
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)
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input_ = LabelTensor(torch.cat((x, y), dim=1), labels=["x", "y"])
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# Construct two scalar functions:
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# u = x**2 + y**2
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# v = x**2 - y**2
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u = LabelTensor(
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input_.extract("x") ** 2 + input_.extract("y") ** 2, labels="u"
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)
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v = LabelTensor(
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input_.extract("x") ** 2 - input_.extract("y") ** 2, labels="v"
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)
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# Define a vector-valued function, whose components are u and v.
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f = LabelTensor(torch.cat((u, v), dim=1), labels=["u", "v"])
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# Compute the scalar laplacian of both u and v:
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# Lap(u) = [4, 4, 4, ..., 4]
|
||||
# Lap(v) = [0, 0, 0, ..., 0]
|
||||
lap_u = laplacian(u, input_, components=["u"])
|
||||
lap_v = laplacian(v, input_, components=["v"])
|
||||
|
||||
# Compute the laplacian of f: the two columns should correspond
|
||||
# to the laplacians of u and v, respectively...
|
||||
lap_f = laplacian(f, input_, components=["u", "v"])
|
||||
|
||||
assert torch.allclose(lap_f.extract("ddu"), lap_u)
|
||||
assert torch.allclose(lap_f.extract("ddv"), lap_v)
|
||||
|
||||
|
||||
def test_label_format():
|
||||
# Testing the format of `components` or `d` in case of single str of length
|
||||
# greater than 1; e.g.: "aaa".
|
||||
# This test is conducted only for gradient and laplacian, since div is not
|
||||
# implemented for single components.
|
||||
inp.labels = ["xx", "yy", "zz"]
|
||||
tensor_v = LabelTensor(func_vector(inp), ["aa", "bbb", "c"])
|
||||
comp = tensor_v.labels[0]
|
||||
single_d = inp.labels[0]
|
||||
|
||||
# Single component as string + list of d
|
||||
grad_tensor_v = grad(tensor_v, inp, components=comp, d=None)
|
||||
assert grad_tensor_v.labels == [f"d{comp}d{i}" for i in inp.labels]
|
||||
|
||||
lap_tensor_v = laplacian(tensor_v, inp, components=comp, d=None)
|
||||
assert lap_tensor_v.labels == [f"dd{comp}"]
|
||||
|
||||
# Single component as list + list of d
|
||||
grad_tensor_v = grad(tensor_v, inp, components=[comp], d=None)
|
||||
assert grad_tensor_v.labels == [f"d{comp}d{i}" for i in inp.labels]
|
||||
|
||||
lap_tensor_v = laplacian(tensor_v, inp, components=[comp], d=None)
|
||||
assert lap_tensor_v.labels == [f"dd{comp}"]
|
||||
|
||||
# List of components + single d as string
|
||||
grad_tensor_v = grad(tensor_v, inp, components=None, d=single_d)
|
||||
assert grad_tensor_v.labels == [f"d{i}d{single_d}" for i in tensor_v.labels]
|
||||
|
||||
lap_tensor_v = laplacian(tensor_v, inp, components=None, d=single_d)
|
||||
assert lap_tensor_v.labels == [f"dd{i}" for i in tensor_v.labels]
|
||||
|
||||
# List of components + single d as list
|
||||
grad_tensor_v = grad(tensor_v, inp, components=None, d=[single_d])
|
||||
assert grad_tensor_v.labels == [f"d{i}d{single_d}" for i in tensor_v.labels]
|
||||
|
||||
lap_tensor_v = laplacian(tensor_v, inp, components=None, d=[single_d])
|
||||
assert lap_tensor_v.labels == [f"dd{i}" for i in tensor_v.labels]
|
||||
# Check the shape of the advection
|
||||
assert pina_advection.shape == (*output_.shape[:-1], output_.shape[-1] - 1)
|
||||
assert torch.allclose(pina_advection, true_advection)
|
||||
|
||||
Reference in New Issue
Block a user