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>
This commit is contained in:
Nicola Demo
@@ -9,6 +9,7 @@ __all__ = [
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"KernelNeuralOperator",
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"AveragingNeuralOperator",
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"LowRankNeuralOperator",
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"Spline",
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]
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from .feed_forward import FeedForward, ResidualFeedForward
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@@ -18,3 +19,4 @@ from .fno import FNO, FourierIntegralKernel
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from .base_no import KernelNeuralOperator
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from .avno import AveragingNeuralOperator
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from .lno import LowRankNeuralOperator
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from .spline import Spline
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166
pina/model/spline.py
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166
pina/model/spline.py
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@@ -0,0 +1,166 @@
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"""Module for Spline model"""
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import torch
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import torch.nn as nn
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from ..utils import check_consistency
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class Spline(torch.nn.Module):
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def __init__(self, order=4, knots=None, control_points=None) -> None:
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"""
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Spline model.
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:param int order: the order of the spline.
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:param torch.Tensor knots: the knot vector.
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:param torch.Tensor control_points: the control points.
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"""
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super().__init__()
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check_consistency(order, int)
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if order < 0:
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raise ValueError("Spline order cannot be negative.")
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if knots is None and control_points is None:
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raise ValueError("Knots and control points cannot be both None.")
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self.order = order
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self.k = order - 1
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if knots is not None and control_points is not None:
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self.knots = knots
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self.control_points = control_points
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elif knots is not None:
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print('Warning: control points will be initialized automatically.')
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print(' experimental feature')
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self.knots = knots
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n = len(knots) - order
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self.control_points = torch.nn.Parameter(
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torch.zeros(n), requires_grad=True)
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elif control_points is not None:
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print('Warning: knots will be initialized automatically.')
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print(' experimental feature')
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self.control_points = control_points
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n = len(self.control_points)-1
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self.knots = {
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'type': 'auto',
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'min': 0,
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'max': 1,
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'n': n+2+self.order}
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else:
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raise ValueError(
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"Knots and control points cannot be both None."
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)
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if self.knots.ndim != 1:
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raise ValueError("Knot vector must be one-dimensional.")
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def basis(self, x, k, i, t):
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'''
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Recursive function to compute the basis functions of the spline.
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:param torch.Tensor x: points to be evaluated.
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:param int k: spline degree
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:param int i: the index of the interval
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:param torch.Tensor t: vector of knots
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:return: the basis functions evaluated at x
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:rtype: torch.Tensor
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'''
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if k == 0:
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a = torch.where(torch.logical_and(t[i] <= x, x < t[i+1]), 1.0, 0.0)
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if i == len(t) - self.order - 1:
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a = torch.where(x == t[-1], 1.0, a)
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a.requires_grad_(True)
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return a
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if t[i+k] == t[i]:
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c1 = torch.tensor([0.0]*len(x), requires_grad=True)
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else:
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c1 = (x - t[i])/(t[i+k] - t[i]) * self.basis(x, k-1, i, t)
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if t[i+k+1] == t[i+1]:
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c2 = torch.tensor([0.0]*len(x), requires_grad=True)
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else:
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c2 = (t[i+k+1] - x)/(t[i+k+1] - t[i+1]) * self.basis(x, k-1, i+1, t)
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return c1 + c2
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@property
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def control_points(self):
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return self._control_points
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@control_points.setter
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def control_points(self, value):
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if isinstance(value, dict):
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if 'n' not in value:
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raise ValueError('Invalid value for control_points')
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n = value['n']
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dim = value.get('dim', 1)
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value = torch.zeros(n, dim)
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if not isinstance(value, torch.Tensor):
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raise ValueError('Invalid value for control_points')
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self._control_points = torch.nn.Parameter(value, requires_grad=True)
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@property
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def knots(self):
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return self._knots
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@knots.setter
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def knots(self, value):
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if isinstance(value, dict):
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type_ = value.get('type', 'auto')
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min_ = value.get('min', 0)
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max_ = value.get('max', 1)
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n = value.get('n', 10)
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if type_ == 'uniform':
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value = torch.linspace(min_, max_, n + self.k + 1)
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elif type_ == 'auto':
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initial_knots = torch.ones(self.order+1)*min_
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final_knots = torch.ones(self.order+1)*max_
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if n < self.order + 1:
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value = torch.concatenate((initial_knots, final_knots))
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elif n - 2*self.order + 1 == 1:
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value = torch.Tensor([(max_ + min_)/2])
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else:
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value = torch.linspace(min_, max_, n - 2*self.order - 1)
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value = torch.concatenate(
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(
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initial_knots, value, final_knots
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)
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)
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if not isinstance(value, torch.Tensor):
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raise ValueError('Invalid value for knots')
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self._knots = value
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def forward(self, x_):
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"""
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Forward pass of the spline model.
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:param torch.Tensor x_: points to be evaluated.
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:return: the spline evaluated at x_
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:rtype: torch.Tensor
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"""
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t = self.knots
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k = self.k
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c = self.control_points
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basis = map(lambda i: self.basis(x_, k, i, t)[:, None], range(len(c)))
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y = (torch.cat(list(basis), dim=1) * c).sum(axis=1)
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return y
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