splinebox.multivariate.

MultivariateSpline#

class splinebox.multivariate.MultivariateSpline(M, basis_functions, closed=False, control_points=None, padding_functions=<function padding_function>)#

Spline in multiple independent variables.

A multivariate spline is defined as a tensor product of univariate splines, one for each variable. It can be evaluated, fitted to data, and used to generate meshes for bivariate splines.

Parameters:

Miterable of int: Number of knots for each variable.
basis_functionssplinebox.basis_functions.BasisFunction or iterable: The basis function(s) used to construct the spline. A single basis function is applied to all variables; otherwise an iterable with one basis function per variable must be provided.
closedbool or iterable of bool: Whether each variable is closed. A single boolean is broadcast to all variables.
control_pointsnumpy array, optional: The control points of the spline. The first nvariate axes correspond to the control point grid, and the last axis is the codomain dimension. Control points can be supplied directly as a NumPy array, or built with helpers such as splinebox.multivariate.tensor_product() for separable geometries. If None, the spline must be initialized later via knots or fit.
padding_functionscallable or iterable of callables: Function(s) used to pad knots for open splines. The default is splinebox.spline_curves.padding_function().

Attributes:

control_points: The control points \(c[k]\) as defined in equation (1).
half_support: Half the support of each basis function.
knots
ndim: Dimensionality of the codomain, i.e.
pad: Number of additional control points used for padding each open end.

Methods

`__call__`(t[, derivatives])	Evaluate the multivariate spline at the parameter values `t`.
`fit`(points[, t])	Fit the multivariate spline to a set of points by least squares.
`mesh`([step_t])

Raises:

ValueError: If M is not an iterable of integers, if basis_functions or closed do not have the expected length, or if padding_functions does not match the number of variables.
RuntimeError: If any entry of M is smaller than the support of the corresponding basis function.

Examples

Create a bivariate B-spline:

>>> import numpy as np
>>> import splinebox
>>> spline = splinebox.multivariate.MultivariateSpline(
...     M=(4, 5),
...     basis_functions=splinebox.B3(),
...     closed=(False, False),
... )

Set the control points directly. For open splines the control points have to be padded along each open dimension (one extra point on each side for B3):

>>> spline.control_points = np.random.rand(6, 7, 3)

Alternatively, a separable control-point grid can be built with splinebox.multivariate.tensor_product():

>>> control_points = splinebox.multivariate.tensor_product(
...     [np.sin(np.linspace(0, np.pi, m + 2)) for m in (4, 5)]
... )
>>> spline.control_points = control_points

Evaluate the spline on a grid of parameter values:

>>> t0 = np.linspace(0, 4, 5)
>>> t1 = np.linspace(0, 5, 6)
>>> t = np.stack(np.meshgrid(t0, t1, indexing="ij"), axis=-1)
>>> values = spline(t)

Multivariate splines