scipy.interpolate.BPoly

class BPoly(c, x, extrapolate=None, axis=0)

Piecewise polynomial in terms of coefficients and breakpoints.

The polynomial between x[i] and x[i + 1] is written in the Bernstein polynomial basis:

S = sum(c[a, i] * b(a, k; x) for a in range(k+1)),

where k is the degree of the polynomial, and:

b(a, k; x) = binom(k, a) * t**a * (1 - t)**(k - a),

with t = (x - x[i]) / (x[i+1] - x[i]) and binom is the binomial coefficient.

Parameters

cndarray, shape (k, m, …)

Polynomial coefficients, order k and m intervals

xndarray, shape (m+1,)

Polynomial breakpoints. Must be sorted in either increasing or decreasing order.

extrapolatebool, optional

If bool, determines whether to extrapolate to out-of-bounds points based on first and last intervals, or to return NaNs. If ‘periodic’, periodic extrapolation is used. Default is True.

axisint, optional

Interpolation axis. Default is zero.

Attributes

xndarray

Breakpoints.

cndarray

Coefficients of the polynomials. They are reshaped to a 3-D array with the last dimension representing the trailing dimensions of the original coefficient array.

axisint

Interpolation axis.

Methods

__call__ extend derivative antiderivative integrate construct_fast from_power_basis from_derivatives

See also

PPoly : piecewise polynomials in the power basis

Notes

Properties of Bernstein polynomials are well documented in the literature, see for example [1] [2] [3].

References

[1]

https://en.wikipedia.org/wiki/Bernstein_polynomial

[2]

Kenneth I. Joy, Bernstein polynomials, http://www.idav.ucdavis.edu/education/CAGDNotes/Bernstein-Polynomials.pdf

[3]

E. H. Doha, A. H. Bhrawy, and M. A. Saker, Boundary Value Problems, vol 2011, article ID 829546, :doi:`10.1155/2011/829543`.

Examples

>>> from scipy.interpolate import BPoly
>>> x = [0, 1]
>>> c = [[1], [2], [3]]
>>> bp = BPoly(c, x)

This creates a 2nd order polynomial

\[\begin{split}B(x) = 1 \times b_{0, 2}(x) + 2 \times b_{1, 2}(x) + 3 \times b_{2, 2}(x) \\ = 1 \times (1-x)^2 + 2 \times 2 x (1 - x) + 3 \times x^2\end{split}\]

__init__(c, x, extrapolate=None, axis=0)

Methods

__init__(c, x[, extrapolate, axis])
antiderivative([nu])	Construct a new piecewise polynomial representing the antiderivative.
construct_fast(c, x[, extrapolate, axis])	Construct the piecewise polynomial without making checks.
derivative([nu])	Construct a new piecewise polynomial representing the derivative.
extend(c, x)	Add additional breakpoints and coefficients to the polynomial.
from_derivatives(xi, yi[, orders, extrapolate])	Construct a piecewise polynomial in the Bernstein basis, compatible with the specified values and derivatives at breakpoints.
from_power_basis(pp[, extrapolate])	Construct a piecewise polynomial in Bernstein basis from a power basis polynomial.
integrate(a, b[, extrapolate])	Compute a definite integral over a piecewise polynomial.

Attributes

c
x
extrapolate
axis