moderndid.BSpline

class moderndid.BSpline(x=None, internal_knots=None, boundary_knots=None, knot_sequence=None, degree=3, df=None)

Bases: SplineBase

B-spline basis functions.

The B-spline basis of degree \(d\) is defined by a sequence of knots \(t_0, t_1, \ldots, t_{m}\). The basis functions \(B_{i,d}(x)\) are defined recursively as

\[B_{i,0}(x) = 1 \quad \text{if } t_i \le x < t_{i+1}, \text{ and } 0 \text{ otherwise,}\]

\[B_{i,d}(x) = \frac{x - t_i}{t_{i+d} - t_i} B_{i,d-1}(x) + \frac{t_{i+d+1} - x}{t_{i+d+1} - t_{i+1}} B_{i+1,d-1}(x).\]

Parameters:

xarray_like, optional

The values at which to evaluate the basis functions.

internal_knotsarray_like, optional

The internal knots of the spline.

boundary_knotsarray_like, optional

The boundary knots of the spline. If not provided, they are inferred from the range of \(x\).

knot_sequencearray_like, optional

A full knot sequence. If provided, it overrides other knot specifications.

degreeint, default=3

The degree of the spline.

dfint, optional

The degrees of freedom of the spline. This determines the number of internal knots if they are not provided.

Methods

basis([complete_basis])	Compute B-spline basis functions.
derivative([derivs, complete_basis])	Compute derivatives of B-spline basis functions.
get_boundary_knots()	Get boundary knots.
get_degree()	Get polynomial degree.
get_internal_knots()	Get internal knots.
get_knot_sequence()	Get full knot sequence.
get_order()	Get spline order (degree + 1).
get_spline_df()	Get degrees of freedom.
get_x()	Get x values.
get_x_index()	Get x indices relative to knot sequence.
integral([complete_basis])	Compute integrals of B-spline basis functions.
set_boundary_knots(knots)	Set boundary knots and update the spline state.
set_degree(degree)	Set polynomial degree.
set_internal_knots(knots)	Set internal knots and update the spline state.
set_knot_sequence(seq)	Set knot sequence and update dependent properties.
set_order(order)	Set spline order.
set_x(x)	Set x values.

Attributes

boundary_knots	Boundary knots property.
degree	Degree property.
internal_knots	Internal knots property.
knot_sequence	Knot sequence property.
order	Return spline order.
spline_df	Degrees of freedom property.
x	X values property.
x_index	X index property.