add spline model (#321)

* add spline model
* add tests for splines
* rst files for splines

---------

Co-authored-by: AleDinve <giuseppealessio.d@student.unisi.it>
Co-authored-by: dario-coscia <dariocos99@gmail.com>

tests/test_model/test_spline.py

@@ -0,0 +1,74 @@
+import torch
+import pytest
+
+from pina.model import Spline
+
+data = torch.rand((20, 3))
+input_vars = 3
+output_vars = 4
+
+valid_args = [
+    {
+        'knots': torch.tensor([0., 0., 0., 1., 2., 3., 3., 3.]),
+        'control_points': torch.tensor([0., 0., 1., 0., 0.]),
+        'order': 3
+    },
+    {
+        'knots': torch.tensor([-2., -2., -2., -2., -1., 0., 1., 2., 2., 2., 2.]),
+        'control_points': torch.tensor([0., 0., 0., 6., 0., 0., 0.]),
+        'order': 4
+    },
+    # {'control_points': {'n': 5, 'dim': 1}, 'order': 2},
+    # {'control_points': {'n': 7, 'dim': 1}, 'order': 3}
+]
+ 
+def scipy_check(model, x, y):
+    from scipy.interpolate._bsplines import BSpline
+    import numpy as np
+    spline = BSpline(
+        t=model.knots.detach().numpy(),
+        c=model.control_points.detach().numpy(),
+        k=model.order-1
+    )
+    y_scipy = spline(x).flatten()
+    y = y.detach().numpy()
+    np.testing.assert_allclose(y, y_scipy, atol=1e-5)
+
+@pytest.mark.parametrize("args", valid_args)
+def test_constructor(args):
+    Spline(**args)
+
+def test_constructor_wrong():
+    with pytest.raises(ValueError):
+        Spline()
+
+@pytest.mark.parametrize("args", valid_args)
+def test_forward(args):
+    min_x = args['knots'][0]
+    max_x = args['knots'][-1]
+    xi = torch.linspace(min_x, max_x, 1000)
+    model = Spline(**args)
+    yi = model(xi).squeeze()
+    scipy_check(model, xi, yi)
+    return 
+    
+
+@pytest.mark.parametrize("args", valid_args)
+def test_backward(args):
+    min_x = args['knots'][0]
+    max_x = args['knots'][-1]
+    xi = torch.linspace(min_x, max_x, 100)
+    model = Spline(**args)
+    yi = model(xi)
+    fake_loss = torch.sum(yi)
+    assert model.control_points.grad is None
+    fake_loss.backward()
+    assert model.control_points.grad is not None
+
+    # dim_in, dim_out = 3, 2
+    # fnn = FeedForward(dim_in, dim_out)
+    # data.requires_grad = True
+    # output_ = fnn(data)
+    # l=torch.mean(output_)
+    # l.backward()
+    # assert data._grad.shape == torch.Size([20,3])