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Revert "Improve and fix spline (#610)"

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This reverts commit 0844282335.
This commit is contained in:
GiovanniCanali
2025-10-15 17:35:24 +02:00
parent 0844282335
commit 4a3748c735
7 changed files with 176 additions and 838 deletions
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1
docs/source/_rst/_code.rst
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@@ -95,7 +95,6 @@ Models
MultiFeedForward <model/multi_feed_forward.rst>
ResidualFeedForward <model/residual_feed_forward.rst>
Spline <model/spline.rst>
SplineSurface <model/spline_surface.rst>
DeepONet <model/deeponet.rst>
MIONet <model/mionet.rst>
KernelNeuralOperator <model/kernel_neural_operator.rst>

7
docs/source/_rst/model/spline_surface.rst
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@@ -1,7 +0,0 @@
Spline Surface
================
.. currentmodule:: pina.model.spline_surface
.. autoclass:: SplineSurface
:members:
:show-inheritance:

1
pina/model/__init__.py
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@@ -26,7 +26,6 @@ from .kernel_neural_operator import KernelNeuralOperator
from .average_neural_operator import AveragingNeuralOperator
from .low_rank_neural_operator import LowRankNeuralOperator
from .spline import Spline
from .spline_surface import SplineSurface
from .graph_neural_operator import GraphNeuralOperator
from .pirate_network import PirateNet
from .equivariant_graph_neural_operator import EquivariantGraphNeuralOperator

417
pina/model/spline.py
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@@ -1,244 +1,109 @@
"""Module for the B-Spline model class."""
"""Module for the Spline model class."""
import warnings
import torch
from ..utils import check_positive_integer, check_consistency
from ..utils import check_consistency
class Spline(torch.nn.Module):
r"""
The univariate B-Spline curve model class.
A univariate B-spline curve of order :math:`k` is a parametric curve defined
as a linear combination of B-spline basis functions and control points:
.. math::
S(x) = \sum_{i=1}^{n} B_{i,k}(x) C_i, \quad x \in [x_1, x_m]
where:
- :math:`C_i \in \mathbb{R}` are the control points. These fixed points
influence the shape of the curve but are not generally interpolated,
except at the boundaries under certain knot multiplicities.
- :math:`B_{i,k}(x)` are the B-spline basis functions of order :math:`k`,
i.e., piecewise polynomials of degree :math:`k-1` with support on the
interval :math:`[x_i, x_{i+k}]`.
- :math:`X = \{ x_1, x_2, \dots, x_m \}` is the non-decreasing knot vector.
If the first and last knots are repeated :math:`k` times, then the curve
interpolates the first and last control points.
.. note::
The curve is forced to be zero outside the interval defined by the
first and last knots.
:Example:
>>> from pina.model import Spline
>>> import torch
>>> knots1 = torch.tensor([0.0, 0.0, 0.0, 1.0, 2.0, 2.0, 2.0])
>>> spline1 = Spline(order=3, knots=knots1, control_points=None)
>>> knots2 = {"n": 7, "min": 0.0, "max": 2.0, "mode": "auto"}
>>> spline2 = Spline(order=3, knots=knots2, control_points=None)
>>> knots3 = torch.tensor([0.0, 0.0, 0.0, 1.0, 2.0, 2.0, 2.0])
>>> control_points3 = torch.tensor([0.0, 1.0, 3.0, 2.0])
>>> spline3 = Spline(order=3, knots=knots3, control_points=control_points3)
"""
Spline model class.
"""
def __init__(self, order=4, knots=None, control_points=None):
def __init__(self, order=4, knots=None, control_points=None) -> None:
"""
Initialization of the :class:`Spline` class.
:param int order: The order of the spline. The corresponding basis
functions are polynomials of degree ``order - 1``. Default is 4.
:param knots: The knots of the spline. If a tensor is provided, knots
are set directly from the tensor. If a dictionary is provided, it
must contain the keys ``"n"``, ``"min"``, ``"max"``, and ``"mode"``.
Here, ``"n"`` specifies the number of knots, ``"min"`` and ``"max"``
define the interval, and ``"mode"`` selects the sampling strategy.
The supported modes are ``"uniform"``, where the knots are evenly
spaced over :math:`[min, max]`, and ``"auto"``, where knots are
constructed to ensure that the spline interpolates the first and
last control points. In this case, the number of knots is adjusted
if :math:`n < 2 * order`. If None is given, knots are initialized
automatically over :math:`[0, 1]` ensuring interpolation of the
first and last control points. Default is None.
:type knots: torch.Tensor | dict
:param torch.Tensor control_points: The control points of the spline.
If None, they are initialized as learnable parameters with an
initial value of zero. Default is None.
:raises AssertionError: If ``order`` is not a positive integer.
:raises ValueError: If ``knots`` is neither a torch.Tensor nor a
dictionary, when provided.
:raises ValueError: If ``control_points`` is not a torch.Tensor,
when provided.
:raises ValueError: If both ``knots`` and ``control_points`` are None.
:raises ValueError: If ``knots`` is not one-dimensional.
:raises ValueError: If ``control_points`` is not one-dimensional.
:raises ValueError: If the number of ``knots`` is not equal to the sum
of ``order`` and the number of ``control_points.``
:raises UserWarning: If the number of control points is lower than the
order, resulting in a degenerate spline.
:param int order: The order of the spline. Default is ``4``.
:param torch.Tensor knots: The tensor representing knots. If ``None``,
the knots will be initialized automatically. Default is ``None``.
:param torch.Tensor control_points: The control points. Default is
``None``.
:raises ValueError: If the order is negative.
:raises ValueError: If both knots and control points are ``None``.
:raises ValueError: If the knot tensor is not one-dimensional.
"""
super().__init__()
# Check consistency
check_positive_integer(value=order, strict=True)
check_consistency(knots, (type(None), torch.Tensor, dict))
check_consistency(control_points, (type(None), torch.Tensor))
check_consistency(order, int)
# Raise error if neither knots nor control points are provided
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 both be None.")
raise ValueError("Knots and control points cannot be both None.")
# Initialize knots if not provided
if knots is None and control_points is not None:
knots = {
"n": len(control_points) + order,
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,
"mode": "auto",
"n": n + 2 + self.order,
}
# Initialization - knots and control points managed by their setters
self.order = order
self.knots = knots
self.control_points = control_points
else:
raise ValueError("Knots and control points cannot be both None.")
# Check dimensionality of knots
if self.knots.ndim > 1:
raise ValueError("knots must be one-dimensional.")
if self.knots.ndim != 1:
raise ValueError("Knot vector must be one-dimensional.")
# Check dimensionality of control points
if self.control_points.ndim > 1:
raise ValueError("control_points must be one-dimensional.")
# Raise error if #knots != order + #control_points
if len(self.knots) != self.order + len(self.control_points):
raise ValueError(
f" The number of knots must be equal to order + number of"
f" control points. Got {len(self.knots)} knots, {self.order}"
f" order and {len(self.control_points)} control points."
)
# Raise warning if spline is degenerate
if len(self.control_points) < self.order:
warnings.warn(
"The number of control points is smaller than the spline order."
" This creates a degenerate spline with limited flexibility.",
UserWarning,
)
# Precompute boundary interval index
self._boundary_interval_idx = self._compute_boundary_interval()
def _compute_boundary_interval(self):
def basis(self, x, k, i, t):
"""
Precompute the index of the rightmost non-degenerate interval to improve
performance, eliminating the need to perform a search loop in the basis
function on each call.
:return: The index of the rightmost non-degenerate interval.
:rtype: int
"""
# Return 0 if there is a single interval
if len(self.knots) < 2:
return 0
# Find all indices where knots are strictly increasing
diffs = self.knots[1:] - self.knots[:-1]
valid = torch.nonzero(diffs > 0, as_tuple=False)
# If all knots are equal, return 0 for degenerate spline
if valid.numel() == 0:
return 0
# Otherwise, return the last valid index
return int(valid[-1])
def basis(self, x):
"""
Compute the basis functions for the spline using an iterative approach.
This is a vectorized implementation based on the Cox-de Boor recursion.
Recursive method to compute the basis functions of the spline.
:param torch.Tensor x: The points to be evaluated.
:return: The basis functions evaluated at x.
:param int k: The spline degree.
:param int i: The index of the interval.
:param torch.Tensor t: The tensor of knots.
:return: The basis functions evaluated at x
:rtype: torch.Tensor
"""
# Add a final dimension to x
x = x.unsqueeze(-1)
# Add an initial dimension to knots
knots = self.knots.unsqueeze(0)
# Base case of recursion: indicator functions for the intervals
basis = (x >= knots[..., :-1]) & (x < knots[..., 1:])
basis = basis.to(x.dtype)
# One-dimensional knots case: ensure rightmost boundary inclusion
if self._boundary_interval_idx is not None:
# Extract left and right knots of the rightmost interval
knot_left = knots[..., self._boundary_interval_idx]
knot_right = knots[..., self._boundary_interval_idx + 1]
# Identify points at the rightmost boundary
at_rightmost_boundary = (
x.squeeze(-1) >= knot_left
) & torch.isclose(x.squeeze(-1), knot_right, rtol=1e-8, atol=1e-10)
# Ensure the correct value is set at the rightmost boundary
if torch.any(at_rightmost_boundary):
basis[..., self._boundary_interval_idx] = torch.logical_or(
basis[..., self._boundary_interval_idx].bool(),
at_rightmost_boundary,
).to(basis.dtype)
# Iterative case of recursion
for i in range(1, self.order):
# Compute the denominators for both terms
denom1 = knots[..., i:-1] - knots[..., : -(i + 1)]
denom2 = knots[..., i + 1 :] - knots[..., 1:-i]
# Ensure no division by zero
denom1 = torch.where(
torch.abs(denom1) < 1e-8, torch.ones_like(denom1), denom1
if k == 0:
a = torch.where(
torch.logical_and(t[i] <= x, x < t[i + 1]), 1.0, 0.0
)
denom2 = torch.where(
torch.abs(denom2) < 1e-8, torch.ones_like(denom2), denom2
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)
)
# Compute the two terms of the recursion
term1 = ((x - knots[..., : -(i + 1)]) / denom1) * basis[..., :-1]
term2 = ((knots[..., i + 1 :] - x) / denom2) * basis[..., 1:]
# Combine terms to get the new basis
basis = term1 + term2
return basis
def forward(self, x):
"""
Forward pass for the :class:`Spline` model.
:param x: The input tensor.
:type x: torch.Tensor | LabelTensor
:return: The output tensor.
:rtype: torch.Tensor
"""
return torch.einsum(
"...bi, i -> ...b",
self.basis(x.as_subclass(torch.Tensor)).squeeze(-1),
self.control_points,
)
return c1 + c2
@property
def control_points(self):
@@ -251,34 +116,24 @@ class Spline(torch.nn.Module):
return self._control_points
@control_points.setter
def control_points(self, control_points):
def control_points(self, value):
"""
Set the control points of the spline.
:param torch.Tensor control_points: The control points tensor. If None,
control points are initialized to learnable parameters with zero
initial value. Default is None.
:raises ValueError: If there are not enough knots to define the control
points, due to the relation: #knots = order + #control_points.
:param value: The control points.
:type value: torch.Tensor | dict
:raises ValueError: If invalid value is passed.
"""
# If control points are not provided, initialize them
if control_points is None:
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)
# Check that there are enough knots to define control points
if len(self.knots) < self.order + 1:
raise ValueError(
f"Not enough knots to define control points. Got "
f"{len(self.knots)} knots, but need at least "
f"{self.order + 1}."
)
# Initialize control points to zero
control_points = torch.zeros(len(self.knots) - self.order)
# Set control points
self._control_points = torch.nn.Parameter(
control_points, requires_grad=True
)
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):
@@ -295,72 +150,50 @@ class Spline(torch.nn.Module):
"""
Set the knots of the spline.
:param value: The knots of the spline. If a tensor is provided, knots
are set directly from the tensor. If a dictionary is provided, it
must contain the keys ``"n"``, ``"min"``, ``"max"``, and ``"mode"``.
Here, ``"n"`` specifies the number of knots, ``"min"`` and ``"max"``
define the interval, and ``"mode"`` selects the sampling strategy.
The supported modes are ``"uniform"``, where the knots are evenly
spaced over :math:`[min, max]`, and ``"auto"``, where knots are
constructed to ensure that the spline interpolates the first and
last control points. In this case, the number of knots is inferred
and the ``"n"`` key is ignored.
:param value: The knots.
:type value: torch.Tensor | dict
:raises ValueError: If a dictionary is provided but does not contain
the required keys.
:raises ValueError: If the mode specified in the dictionary is invalid.
:raises ValueError: If invalid value is passed.
"""
# If a dictionary is provided, initialize knots accordingly
if isinstance(value, dict):
# Check that required keys are present
required_keys = {"n", "min", "max", "mode"}
if not required_keys.issubset(value.keys()):
raise ValueError(
f"When providing knots as a dictionary, the following "
f"keys must be present: {required_keys}. Got "
f"{value.keys()}."
)
type_ = value.get("type", "auto")
min_ = value.get("min", 0)
max_ = value.get("max", 1)
n = value.get("n", 10)
# Uniform sampling of knots
if value["mode"] == "uniform":
value = torch.linspace(value["min"], value["max"], value["n"])
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_
# Automatic sampling of interpolating knots
elif value["mode"] == "auto":
# Repeat the first and last knots 'order' times
initial_knots = torch.ones(self.order) * value["min"]
final_knots = torch.ones(self.order) * value["max"]
# Number of internal knots
n_internal = value["n"] - 2 * self.order
# If no internal knots are needed, just concatenate boundaries
if n_internal <= 0:
value = torch.cat((initial_knots, final_knots))
# Else, sample internal knots uniformly and exclude boundaries
# Recover the correct number of internal knots when slicing by
# adding 2 to n_internal
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:
internal_knots = torch.linspace(
value["min"], value["max"], n_internal + 2
)[1:-1]
value = torch.cat(
(initial_knots, internal_knots, final_knots)
)
value = torch.linspace(min_, max_, n - 2 * self.order - 1)
# Raise error if mode is invalid
else:
raise ValueError(
f"Invalid mode for knots initialization. Got "
f"{value['mode']}, but expected 'uniform' or 'auto'."
)
value = torch.concatenate((initial_knots, value, final_knots))
# Set knots
self.register_buffer("_knots", value.sort(dim=0).values)
if not isinstance(value, torch.Tensor):
raise ValueError("Invalid value for knots")
# Recompute boundary interval when knots change
if hasattr(self, "_boundary_interval_idx"):
self._boundary_interval_idx = self._compute_boundary_interval()
self._knots = value
def forward(self, x):
"""
Forward pass for the :class:`Spline` model.
:param torch.Tensor x: The input tensor.
:return: The output tensor.
: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

212
pina/model/spline_surface.py
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@@ -1,212 +0,0 @@
"""Module for the bivariate B-Spline surface model class."""
import torch
from .spline import Spline
from ..utils import check_consistency
class SplineSurface(torch.nn.Module):
r"""
The bivariate B-Spline surface model class.
A bivariate B-spline surface is a parametric surface defined as the tensor
product of two univariate B-spline curves:
.. math::
S(x, y) = \sum_{i,j=1}^{n_x, n_y} B_{i,k}(x) B_{j,s}(y) C_{i,j},
\quad x \in [x_1, x_m], y \in [y_1, y_l]
where:
- :math:`C_{i,j} \in \mathbb{R}^2` are the control points. These fixed
points influence the shape of the surface but are not generally
interpolated, except at the boundaries under certain knot multiplicities.
- :math:`B_{i,k}(x)` and :math:`B_{j,s}(y)` are the B-spline basis functions
defined over two orthogonal directions, with orders :math:`k` and
:math:`s`, respectively.
- :math:`X = \{ x_1, x_2, \dots, x_m \}` and
:math:`Y = \{ y_1, y_2, \dots, y_l \}` are the non-decreasing knot
vectors along the two directions.
"""
def __init__(self, orders, knots_u=None, knots_v=None, control_points=None):
"""
Initialization of the :class:`SplineSurface` class.
:param list[int] orders: The orders of the spline along each parametric
direction. Each order defines the degree of the corresponding basis
as ``degree = order - 1``.
:param knots_u: The knots of the spline along the first direction.
For details on valid formats and initialization modes, see the
:class:`Spline` class. Default is None.
:type knots_u: torch.Tensor | dict
:param knots_v: The knots of the spline along the second direction.
For details on valid formats and initialization modes, see the
:class:`Spline` class. Default is None.
:type knots_v: torch.Tensor | dict
:param torch.Tensor control_points: The control points defining the
surface geometry. It must be a two-dimensional tensor of shape
``[len(knots_u) - orders[0], len(knots_v) - orders[1]]``.
If None, they are initialized as learnable parameters with zero
values. Default is None.
:raises ValueError: If ``orders`` is not a list of integers.
:raises ValueError: If ``knots_u`` is neither a torch.Tensor nor a
dictionary, when provided.
:raises ValueError: If ``knots_v`` is neither a torch.Tensor nor a
dictionary, when provided.
:raises ValueError: If ``control_points`` is not a torch.Tensor,
when provided.
:raises ValueError: If ``orders`` is not a list of two elements.
:raises ValueError: If ``knots_u``, ``knots_v``, and ``control_points``
are all None.
"""
super().__init__()
# Check consistency
check_consistency(orders, int)
check_consistency(control_points, (type(None), torch.Tensor))
check_consistency(knots_u, (type(None), torch.Tensor, dict))
check_consistency(knots_v, (type(None), torch.Tensor, dict))
# Check orders is a list of two elements
if len(orders) != 2:
raise ValueError("orders must be a list of two elements.")
# Raise error if neither knots nor control points are provided
if (knots_u is None or knots_v is None) and control_points is None:
raise ValueError(
"control_points cannot be None if knots_u or knots_v is None."
)
# Initialize knots_u if not provided
if knots_u is None and control_points is not None:
knots_u = {
"n": control_points.shape[0] + orders[0],
"min": 0,
"max": 1,
"mode": "auto",
}
# Initialize knots_v if not provided
if knots_v is None and control_points is not None:
knots_v = {
"n": control_points.shape[1] + orders[1],
"min": 0,
"max": 1,
"mode": "auto",
}
# Create two univariate b-splines
self.spline_u = Spline(order=orders[0], knots=knots_u)
self.spline_v = Spline(order=orders[1], knots=knots_v)
self.control_points = control_points
# Delete unneeded parameters
delattr(self.spline_u, "_control_points")
delattr(self.spline_v, "_control_points")
def forward(self, x):
"""
Forward pass for the :class:`SplineSurface` model.
:param x: The input tensor.
:type x: torch.Tensor | LabelTensor
:return: The output tensor.
:rtype: torch.Tensor
"""
return torch.einsum(
"...bi, ...bj, ij -> ...b",
self.spline_u.basis(x.as_subclass(torch.Tensor)[..., 0]),
self.spline_v.basis(x.as_subclass(torch.Tensor)[..., 1]),
self.control_points,
).unsqueeze(-1)
@property
def knots(self):
"""
The knots of the univariate splines defining the spline surface.
:return: The knots.
:rtype: tuple(torch.Tensor, torch.Tensor)
"""
return self.spline_u.knots, self.spline_v.knots
@knots.setter
def knots(self, value):
"""
Set the knots of the spline surface.
:param value: A tuple (knots_u, knots_v) containing the knots for both
parametric directions.
:type value: tuple(torch.Tensor | dict, torch.Tensor | dict)
:raises ValueError: If value is not a tuple of two elements.
"""
# Check value is a tuple of two elements
if not (isinstance(value, tuple) and len(value) == 2):
raise ValueError("Knots must be a tuple of two elements.")
knots_u, knots_v = value
self.spline_u.knots = knots_u
self.spline_v.knots = knots_v
@property
def control_points(self):
"""
The control points of the spline.
:return: The control points.
:rtype: torch.Tensor
"""
return self._control_points
@control_points.setter
def control_points(self, control_points):
"""
Set the control points of the spline surface.
:param torch.Tensor control_points: The bidimensional control points
tensor, where each dimension refers to a direction in the parameter
space. If None, control points are initialized to learnable
parameters with zero initial value. Default is None.
:raises ValueError: If in any direction there are not enough knots to
define the control points, due to the relation:
#knots = order + #control_points.
:raises ValueError: If ``control_points`` is not of the correct shape.
"""
# Save correct shape of control points
__valid_shape = (
len(self.spline_u.knots) - self.spline_u.order,
len(self.spline_v.knots) - self.spline_v.order,
)
# If control points are not provided, initialize them
if control_points is None:
# Check that there are enough knots to define control points
if (
len(self.spline_u.knots) < self.spline_u.order + 1
or len(self.spline_v.knots) < self.spline_v.order + 1
):
raise ValueError(
f"Not enough knots to define control points. Got "
f"{len(self.spline_u.knots)} knots along u and "
f"{len(self.spline_v.knots)} knots along v, but need at "
f"least {self.spline_u.order + 1} and "
f"{self.spline_v.order + 1}, respectively."
)
# Initialize control points to zero
control_points = torch.zeros(__valid_shape)
# Check control points
if control_points.shape != __valid_shape:
raise ValueError(
"control_points must be of the correct shape. ",
f"Expected {__valid_shape}, got {control_points.shape}.",
)
# Register control points as a learnable parameter
self._control_points = torch.nn.Parameter(
control_points, requires_grad=True
)

196
tests/test_model/test_spline.py
View File

@@ -1,175 +1,81 @@
import torch
import pytest
from scipy.interpolate import BSpline
from pina.model import Spline
from pina import LabelTensor
data = torch.rand((20, 3))
input_vars = 3
output_vars = 4
# Utility quantities for testing
order = torch.randint(1, 8, (1,)).item()
n_ctrl_pts = torch.randint(order, order + 5, (1,)).item()
n_knots = order + n_ctrl_pts
# Input tensor
points = [
LabelTensor(torch.rand(100, 1), ["x"]),
LabelTensor(torch.rand(2, 100, 1), ["x"]),
valid_args = [
{
"knots": torch.tensor([0.0, 0.0, 0.0, 1.0, 2.0, 3.0, 3.0, 3.0]),
"control_points": torch.tensor([0.0, 0.0, 1.0, 0.0, 0.0]),
"order": 3,
},
{
"knots": torch.tensor(
[-2.0, -2.0, -2.0, -2.0, -1.0, 0.0, 1.0, 2.0, 2.0, 2.0, 2.0]
),
"control_points": torch.tensor([0.0, 0.0, 0.0, 6.0, 0.0, 0.0, 0.0]),
"order": 4,
},
# {'control_points': {'n': 5, 'dim': 1}, 'order': 2},
# {'control_points': {'n': 7, 'dim': 1}, 'order': 3}
]
# Function to compare with scipy implementation
def check_scipy_spline(model, x, output_):
def scipy_check(model, x, y):
from scipy.interpolate._bsplines import BSpline
import numpy as np
# Define scipy spline
scipy_spline = BSpline(
spline = BSpline(
t=model.knots.detach().numpy(),
c=model.control_points.detach().numpy(),
k=model.order - 1,
)
# Compare outputs
torch.allclose(
output_,
torch.tensor(scipy_spline(x), dtype=output_.dtype),
atol=1e-5,
rtol=1e-5,
)
# Define all possible combinations of valid arguments for Spline class
valid_args = [
{
"order": order,
"control_points": torch.rand(n_ctrl_pts),
"knots": torch.linspace(0, 1, n_knots),
},
{
"order": order,
"control_points": torch.rand(n_ctrl_pts),
"knots": {"n": n_knots, "min": 0, "max": 1, "mode": "auto"},
},
{
"order": order,
"control_points": torch.rand(n_ctrl_pts),
"knots": {"n": n_knots, "min": 0, "max": 1, "mode": "uniform"},
},
{
"order": order,
"control_points": None,
"knots": torch.linspace(0, 1, n_knots),
},
{
"order": order,
"control_points": None,
"knots": {"n": n_knots, "min": 0, "max": 1, "mode": "auto"},
},
{
"order": order,
"control_points": None,
"knots": {"n": n_knots, "min": 0, "max": 1, "mode": "uniform"},
},
{
"order": order,
"control_points": torch.rand(n_ctrl_pts),
"knots": None,
},
]
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)
# Should fail if order is not a positive integer
with pytest.raises(AssertionError):
Spline(
order=-1, control_points=args["control_points"], knots=args["knots"]
)
# Should fail if control_points is not None or a torch.Tensor
def test_constructor_wrong():
with pytest.raises(ValueError):
Spline(
order=args["order"], control_points=[1, 2, 3], knots=args["knots"]
)
# Should fail if knots is not None, a torch.Tensor, or a dict
with pytest.raises(ValueError):
Spline(
order=args["order"], control_points=args["control_points"], knots=5
)
# Should fail if both knots and control_points are None
with pytest.raises(ValueError):
Spline(order=args["order"], control_points=None, knots=None)
# Should fail if knots is not one-dimensional
with pytest.raises(ValueError):
Spline(
order=args["order"],
control_points=args["control_points"],
knots=torch.rand(n_knots, 4),
)
# Should fail if control_points is not one-dimensional
with pytest.raises(ValueError):
Spline(
order=args["order"],
control_points=torch.rand(n_ctrl_pts, 4),
knots=args["knots"],
)
# Should fail if the number of knots != order + number of control points
# If control points are None, they are initialized to fulfill this condition
if args["control_points"] is not None:
with pytest.raises(ValueError):
Spline(
order=args["order"],
control_points=args["control_points"],
knots=torch.linspace(0, 1, n_knots + 1),
)
# Should fail if the knot dict is missing required keys
with pytest.raises(ValueError):
Spline(
order=args["order"],
control_points=args["control_points"],
knots={"n": n_knots, "min": 0, "max": 1},
)
# Should fail if the knot dict has invalid 'mode' key
with pytest.raises(ValueError):
Spline(
order=args["order"],
control_points=args["control_points"],
knots={"n": n_knots, "min": 0, "max": 1, "mode": "invalid"},
)
Spline()
@pytest.mark.parametrize("args", valid_args)
@pytest.mark.parametrize("pts", points)
def test_forward(args, pts):
# Define the model
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)
# Evaluate the model
output_ = model(pts)
assert output_.shape == pts.shape
# Compare with scipy implementation only for interpolant knots (mode: auto)
if isinstance(args["knots"], dict) and args["knots"]["mode"] == "auto":
check_scipy_spline(model, pts, output_)
yi = model(xi).squeeze()
scipy_check(model, xi, yi)
return
@pytest.mark.parametrize("args", valid_args)
@pytest.mark.parametrize("pts", points)
def test_backward(args, pts):
# Define the model
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
# Evaluate the model
output_ = model(pts)
loss = torch.mean(output_)
loss.backward()
assert model.control_points.grad.shape == model.control_points.shape
# 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])

180
tests/test_model/test_spline_surface.py
View File

@@ -1,180 +0,0 @@
import torch
import random
import pytest
from pina.model import SplineSurface
from pina import LabelTensor
# Utility quantities for testing
orders = [random.randint(1, 8) for _ in range(2)]
n_ctrl_pts = random.randint(max(orders), max(orders) + 5)
n_knots = [orders[i] + n_ctrl_pts for i in range(2)]
# Input tensor
points = [
LabelTensor(torch.rand(100, 2), ["x", "y"]),
LabelTensor(torch.rand(2, 100, 2), ["x", "y"]),
]
@pytest.mark.parametrize(
"knots_u",
[
torch.rand(n_knots[0]),
{"n": n_knots[0], "min": 0, "max": 1, "mode": "auto"},
{"n": n_knots[0], "min": 0, "max": 1, "mode": "uniform"},
None,
],
)
@pytest.mark.parametrize(
"knots_v",
[
torch.rand(n_knots[1]),
{"n": n_knots[1], "min": 0, "max": 1, "mode": "auto"},
{"n": n_knots[1], "min": 0, "max": 1, "mode": "uniform"},
None,
],
)
@pytest.mark.parametrize(
"control_points", [torch.rand(n_ctrl_pts, n_ctrl_pts), None]
)
def test_constructor(knots_u, knots_v, control_points):
# Skip if knots_u, knots_v, and control_points are all None
if (knots_u is None or knots_v is None) and control_points is None:
return
SplineSurface(
orders=orders,
knots_u=knots_u,
knots_v=knots_v,
control_points=control_points,
)
# Should fail if orders is not list of two elements
with pytest.raises(ValueError):
SplineSurface(
orders=[orders[0]],
knots_u=knots_u,
knots_v=knots_v,
control_points=control_points,
)
# Should fail if both knots and control_points are None
with pytest.raises(ValueError):
SplineSurface(
orders=orders,
knots_u=None,
knots_v=None,
control_points=None,
)
# Should fail if control_points is not a torch.Tensor when provided
with pytest.raises(ValueError):
SplineSurface(
orders=orders,
knots_u=knots_u,
knots_v=knots_v,
control_points=[[0.0] * n_ctrl_pts] * n_ctrl_pts,
)
# Should fail if control_points is not of the correct shape when provided
# It assumes that at least one among knots_u and knots_v is not None
if knots_u is not None or knots_v is not None:
with pytest.raises(ValueError):
SplineSurface(
orders=orders,
knots_u=knots_u,
knots_v=knots_v,
control_points=torch.rand(n_ctrl_pts + 1, n_ctrl_pts + 1),
)
# Should fail if there are not enough knots_u to define the control points
with pytest.raises(ValueError):
SplineSurface(
orders=orders,
knots_u=torch.linspace(0, 1, orders[0]),
knots_v=knots_v,
control_points=None,
)
# Should fail if there are not enough knots_v to define the control points
with pytest.raises(ValueError):
SplineSurface(
orders=orders,
knots_u=knots_u,
knots_v=torch.linspace(0, 1, orders[1]),
control_points=None,
)
@pytest.mark.parametrize(
"knots_u",
[
torch.rand(n_knots[0]),
{"n": n_knots[0], "min": 0, "max": 1, "mode": "auto"},
{"n": n_knots[0], "min": 0, "max": 1, "mode": "uniform"},
],
)
@pytest.mark.parametrize(
"knots_v",
[
torch.rand(n_knots[1]),
{"n": n_knots[1], "min": 0, "max": 1, "mode": "auto"},
{"n": n_knots[1], "min": 0, "max": 1, "mode": "uniform"},
],
)
@pytest.mark.parametrize(
"control_points", [torch.rand(n_ctrl_pts, n_ctrl_pts), None]
)
@pytest.mark.parametrize("pts", points)
def test_forward(knots_u, knots_v, control_points, pts):
# Define the model
model = SplineSurface(
orders=orders,
knots_u=knots_u,
knots_v=knots_v,
control_points=control_points,
)
# Evaluate the model
output_ = model(pts)
assert output_.shape == (*pts.shape[:-1], 1)
@pytest.mark.parametrize(
"knots_u",
[
torch.rand(n_knots[0]),
{"n": n_knots[0], "min": 0, "max": 1, "mode": "auto"},
{"n": n_knots[0], "min": 0, "max": 1, "mode": "uniform"},
],
)
@pytest.mark.parametrize(
"knots_v",
[
torch.rand(n_knots[1]),
{"n": n_knots[1], "min": 0, "max": 1, "mode": "auto"},
{"n": n_knots[1], "min": 0, "max": 1, "mode": "uniform"},
],
)
@pytest.mark.parametrize(
"control_points", [torch.rand(n_ctrl_pts, n_ctrl_pts), None]
)
@pytest.mark.parametrize("pts", points)
def test_backward(knots_u, knots_v, control_points, pts):
# Define the model
model = SplineSurface(
orders=orders,
knots_u=knots_u,
knots_v=knots_v,
control_points=control_points,
)
# Evaluate the model
output_ = model(pts)
loss = torch.mean(output_)
loss.backward()
assert model.control_points.grad.shape == model.control_points.shape