"""Module for Spline model"""
import torch
import torch.nn as nn
from ..utils import check_consistency
[docs]
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.")
[docs]
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
[docs]
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
