156 lines
5.4 KiB
Python
156 lines
5.4 KiB
Python
import torch
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import pytest
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from pina import LabelTensor
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from pina.operators import grad, div, laplacian
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def func_vector(x):
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return x**2
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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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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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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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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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]
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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)
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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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(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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), dim=1
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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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grad_tensor_v = grad(tensor_v, inp, d=['x', 'y'])
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true_val = torch.cat(
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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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), 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 == [
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f'dd{i}' for i in tensor_v.labels
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]
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assert torch.allclose(laplace_tensor_v, true_val)
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laplace_tensor_v = laplacian(tensor_v,
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inp,
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components=['a', 'b'],
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d=['x', 'y'])
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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 == [
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f'dd{i}' for i in ['a', 'b']
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]
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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(torch.linspace(0,1,10, requires_grad=True).reshape(-1,1), labels = ['x'])
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y = LabelTensor(torch.linspace(3,4,10, requires_grad=True).reshape(-1,1), labels = ['y'])
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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(input_.extract('x')**2 + input_.extract('y')**2, labels='u')
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v = LabelTensor(input_.extract('x')**2 - input_.extract('y')**2, labels='v')
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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]
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# Lap(v) = [0, 0, 0, ..., 0]
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lap_u = laplacian(u, input_, components=['u'])
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lap_v = laplacian(v, input_, components=['v'])
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# Compute the laplacian of f: the two columns should correspond
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# to the laplacians of u and v, respectively...
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lap_f = laplacian(f, input_, components=['u', 'v'])
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assert torch.allclose(lap_f.extract('ddu'), lap_u)
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assert torch.allclose(lap_f.extract('ddv'), lap_v)
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