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>

docs/source/_rst/_code.rst

@@ -59,6 +59,7 @@ Models
     FeedForward <models/fnn.rst>
     MultiFeedForward <models/multifeedforward.rst>
     ResidualFeedForward <models/fnn_residual.rst>
+    Spline <models/spline.rst>
     DeepONet <models/deeponet.rst>
     MIONet <models/mionet.rst>
     FourierIntegralKernel <models/fourier_kernel.rst>

docs/source/_rst/models/spline.rst

@@ -0,0 +1,7 @@
+Spline
+========
+.. currentmodule:: pina.model.spline
+
+.. autoclass:: Spline
+    :members:
+    :show-inheritance:

pina/model/__init__.py

@@ -9,6 +9,7 @@ __all__ = [
     "KernelNeuralOperator",
     "AveragingNeuralOperator",
     "LowRankNeuralOperator",
+    "Spline",
 ]
 
 from .feed_forward import FeedForward, ResidualFeedForward
@@ -18,3 +19,4 @@ from .fno import FNO, FourierIntegralKernel
 from .base_no import KernelNeuralOperator
 from .avno import AveragingNeuralOperator
 from .lno import LowRankNeuralOperator
+from .spline import Spline

pina/model/spline.py

@@ -0,0 +1,166 @@
+"""Module for Spline model"""
+
+import torch
+import torch.nn as nn
+from ..utils import check_consistency
+ 
+class Spline(torch.nn.Module):
+
+    def __init__(self, order=4, knots=None, control_points=None) -> None:
+        """
+        Spline model.
+
+        :param int order: the order of the spline.
+        :param torch.Tensor knots: the knot vector.
+        :param torch.Tensor control_points: the control points.
+        """
+        super().__init__()
+
+        check_consistency(order, int)
+
+        if order < 0:
+            raise ValueError("Spline order cannot be negative.")
+        if knots is None and control_points is None:
+            raise ValueError("Knots and control points cannot be both None.")
+
+        self.order = order
+        self.k = order - 1
+
+        if knots is not None and control_points is not None:
+            self.knots = knots
+            self.control_points = control_points
+
+        elif knots is not None:
+            print('Warning: control points will be initialized automatically.')
+            print('         experimental feature')
+
+            self.knots = knots
+            n = len(knots) - order
+            self.control_points = torch.nn.Parameter(
+                torch.zeros(n), requires_grad=True)
+            
+        elif control_points is not None:
+            print('Warning: knots will be initialized automatically.')
+            print('         experimental feature')
+            
+            self.control_points = control_points
+
+            n = len(self.control_points)-1
+            self.knots = {
+                'type': 'auto',
+                'min': 0,
+                'max': 1,
+                'n': n+2+self.order}
+
+        else:
+            raise ValueError(
+                "Knots and control points cannot be both None."
+            )
+
+
+        if self.knots.ndim != 1:
+            raise ValueError("Knot vector must be one-dimensional.")
+
+    def basis(self, x, k, i, t):
+        '''
+        Recursive function to compute the basis functions of the spline.
+
+        :param torch.Tensor x: points to be evaluated.
+        :param int k: spline degree
+        :param int i: the index of the interval
+        :param torch.Tensor t: vector of knots
+        :return: the basis functions evaluated at x
+        :rtype: torch.Tensor
+        '''
+        
+        if k == 0:
+            a = torch.where(torch.logical_and(t[i] <= x, x < t[i+1]), 1.0, 0.0)
+            if i == len(t) - self.order - 1:
+                 a = torch.where(x == t[-1], 1.0, a)
+            a.requires_grad_(True)
+            return a
+
+
+        if t[i+k] == t[i]:
+            c1 = torch.tensor([0.0]*len(x), requires_grad=True)
+        else:
+            c1 = (x - t[i])/(t[i+k] - t[i]) * self.basis(x, k-1, i, t)
+
+        if t[i+k+1] == t[i+1]:
+            c2 = torch.tensor([0.0]*len(x), requires_grad=True)
+        else:
+            c2 = (t[i+k+1] - x)/(t[i+k+1] - t[i+1]) * self.basis(x, k-1, i+1, t)
+
+        return c1 + c2
+    
+
+    @property
+    def control_points(self):
+        return self._control_points
+
+    @control_points.setter
+    def control_points(self, value):
+        if isinstance(value, dict):
+            if 'n' not in value:
+                raise ValueError('Invalid value for control_points')
+            n = value['n']
+            dim = value.get('dim', 1)
+            value = torch.zeros(n, dim)
+
+        if not isinstance(value, torch.Tensor):
+            raise ValueError('Invalid value for control_points')
+        self._control_points = torch.nn.Parameter(value, requires_grad=True)
+
+    @property
+    def knots(self):
+        return self._knots
+    
+    @knots.setter
+    def knots(self, value):
+        if isinstance(value, dict):
+
+            type_ = value.get('type', 'auto')
+            min_ = value.get('min', 0)
+            max_ = value.get('max', 1)
+            n = value.get('n', 10)
+
+            if type_ == 'uniform':
+                value = torch.linspace(min_, max_, n + self.k + 1)
+            elif type_ == 'auto':
+                initial_knots = torch.ones(self.order+1)*min_
+                final_knots = torch.ones(self.order+1)*max_
+
+                if n < self.order + 1:
+                    value = torch.concatenate((initial_knots, final_knots))
+                elif n - 2*self.order + 1 == 1:
+                    value = torch.Tensor([(max_ + min_)/2])
+                else:
+                    value = torch.linspace(min_, max_, n - 2*self.order - 1)
+
+                value = torch.concatenate(
+                    (
+                        initial_knots, value, final_knots
+                    )
+                )
+
+        if not isinstance(value, torch.Tensor):
+            raise ValueError('Invalid value for knots')
+
+        self._knots = value
+
+    def forward(self, x_):
+        """
+        Forward pass of the spline model.
+
+        :param torch.Tensor x_: points to be evaluated.
+        :return: the spline evaluated at x_
+        :rtype: torch.Tensor        
+        """
+        t = self.knots
+        k = self.k
+        c = self.control_points
+
+        basis = map(lambda i: self.basis(x_, k, i, t)[:, None], range(len(c)))
+        y = (torch.cat(list(basis), dim=1) * c).sum(axis=1)
+
+        return y

setup.py

@@ -26,7 +26,11 @@ EXTRAS = {
         'sphinx_design',
         'pydata_sphinx_theme'
         ],
-    'test': ['pytest', 'pytest-cov'],
+    'test': [
+        'pytest',
+        'pytest-cov',
+        'scipy'
+    ],
 }
 
 LDESCRIPTION = (

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])