`scipy.interpolate._interpolate:BPoly`

source: /scipy/interpolate/_interpolate.py :1316

Signature

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

Members

Summary

Piecewise polynomial in the Bernstein basis.

Extended Summary

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

c : ndarray, shape (k, m, ...): Polynomial coefficients, order k and m intervals
x : ndarray, shape (m+1,): Polynomial breakpoints. Must be sorted in either increasing or decreasing order.
extrapolate : bool, 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.
axis : int, optional: Interpolation axis. Default is zero.

Attributes

x : ndarray: Breakpoints.
c : ndarray: 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.
axis : int: Interpolation axis.

Methods

__call__
extend
derivative
antiderivative
integrate
construct_fast
from_power_basis
from_derivatives

Notes

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

Array API Standard Support

BPoly has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ✅                     ⛔                   
JAX                   ⚠️ no JIT             ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

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

✓

This creates a 2nd order polynomial .. math:: 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