scipy.interpolate.BPoly#
- class scipy.interpolate.BPoly(c, x, extrapolate=None, axis=0)[source]#
Piecewise polynomial in terms of coefficients and breakpoints.
The polynomial between
x[i]
andx[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])
andbinom
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.
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
[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
\[\begin{split}B(x) = 1 \times b_{0, 2}(x) + 2 \times b_{1, 2}(x) + 3 \times b_{2, 2}(x) \\ = 1 \times (1-x)^2 + 2 \times 2 x (1 - x) + 3 \times x^2\end{split}\]- 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__
(x[, nu, extrapolate])Evaluate the piecewise polynomial or its derivative.
extend
(c, x)Add additional breakpoints and coefficients to the polynomial.
derivative
([nu])Construct a new piecewise polynomial representing the derivative.
antiderivative
([nu])Construct a new piecewise polynomial representing the antiderivative.
integrate
(a, b[, extrapolate])Compute a definite integral over a piecewise polynomial.
construct_fast
(c, x[, extrapolate, axis])Construct the piecewise polynomial without making checks.
from_power_basis
(pp[, extrapolate])Construct a piecewise polynomial in Bernstein basis from a power basis polynomial.
from_derivatives
(xi, yi[, orders, extrapolate])Construct a piecewise polynomial in the Bernstein basis, compatible with the specified values and derivatives at breakpoints.