# scipy.interpolate.BarycentricInterpolator#

class scipy.interpolate.BarycentricInterpolator(xi, yi=None, axis=0)[source]#

The interpolating polynomial for a set of points

Constructs a polynomial that passes through a given set of points. Allows evaluation of the polynomial, efficient changing of the y values to be interpolated, and updating by adding more x values. For reasons of numerical stability, this function does not compute the coefficients of the polynomial.

The values yi need to be provided before the function is evaluated, but none of the preprocessing depends on them, so rapid updates are possible.

Parameters:
xiarray_like, shape (npoints, )

1-D array of x coordinates of the points the polynomial should pass through

yiarray_like, shape (…, npoints, …), optional

N-D array of y coordinates of the points the polynomial should pass through. If None, the y values will be supplied later via the set_y method. The length of yi along the interpolation axis must be equal to the length of xi. Use the `axis` parameter to select correct axis.

axisint, optional

Axis in the yi array corresponding to the x-coordinate values. Defaults to `axis=0`.

Notes

This class uses a “barycentric interpolation” method that treats the problem as a special case of rational function interpolation. This algorithm is quite stable, numerically, but even in a world of exact computation, unless the x coordinates are chosen very carefully - Chebyshev zeros (e.g., cos(i*pi/n)) are a good choice - polynomial interpolation itself is a very ill-conditioned process due to the Runge phenomenon.

Based on Berrut and Trefethen 2004, “Barycentric Lagrange Interpolation”.

Attributes:
dtype

Methods

 Evaluate the interpolating polynomial at the points x `add_xi`(xi[, yi]) Add more x values to the set to be interpolated `set_yi`(yi[, axis]) Update the y values to be interpolated