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 outofbounds 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 [R0da78b0816f01] [R0da78b0816f02] [R0da78b0816f03].
References
 R0da78b0816f01
 R0da78b0816f02
Kenneth I. Joy, Bernstein polynomials, http://www.idav.ucdavis.edu/education/CAGDNotes/BernsteinPolynomials.pdf
 R0da78b0816f03
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
\[\begin{split}B(x) = 1 \times b_{0, 2}(x) + 2 \times b_{1, 2}(x) + 3 \times b_{2, 2}(x) \\ = 1 \times (1x)^2 + 2 \times 2 x (1  x) + 3 \times x^2\end{split}\] Attributes
 xndarray
Breakpoints.
 cndarray
Coefficients of the polynomials. They are reshaped to a 3dimensional array with the last dimension representing the trailing dimensions of the original coefficient array.
 axisint
Interpolation axis.
Methods
__call__
(self, x[, nu, extrapolate])Evaluate the piecewise polynomial or its derivative.
extend
(self, c, x[, right])Add additional breakpoints and coefficients to the polynomial.
derivative
(self[, nu])Construct a new piecewise polynomial representing the derivative.
antiderivative
(self[, nu])Construct a new piecewise polynomial representing the antiderivative.
integrate
(self, 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.