scipy.interpolate.

barycentric_interpolate

scipy.interpolate.barycentric_interpolate(xi, yi, x, axis=0, *, der=0, rng=None)

Convenience function for polynomial interpolation.

Constructs a polynomial that passes through a given set of points, then evaluates the polynomial. For reasons of numerical stability, this function does not compute the coefficients of the polynomial.

This function 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.

Parameters:

xiarray_like

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

yiarray_like

The y coordinates of the points the polynomial should pass through.

xscalar or array_like

Point or points at which to evaluate the interpolant.

axisint, optional

Axis in the yi array corresponding to the x-coordinate values.

derint or list or None, optional

How many derivatives to evaluate, or None for all potentially nonzero derivatives (that is, a number equal to the number of points), or a list of derivatives to evaluate. This number includes the function value as the ‘0th’ derivative.

rngnumpy.random.Generator, optional

Pseudorandom number generator state. When rng is None, a new numpy.random.Generator is created using entropy from the operating system. Types other than numpy.random.Generator are passed to numpy.random.default_rng to instantiate a Generator.

Returns:

yscalar or array_like

Interpolated values. Shape is determined by replacing the interpolation axis in the original array with the shape of x.

See also

BarycentricInterpolator

Barycentric interpolator

Notes

Construction of the interpolation weights is a relatively slow process. If you want to call this many times with the same xi (but possibly varying yi or x) you should use the class BarycentricInterpolator. This is what this function uses internally.

Examples

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We can interpolate 2D observed data using barycentric interpolation:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.interpolate import barycentric_interpolate
>>> x_observed = np.linspace(0.0, 10.0, 11)
>>> y_observed = np.sin(x_observed)
>>> x = np.linspace(min(x_observed), max(x_observed), num=100)
>>> y = barycentric_interpolate(x_observed, y_observed, x)
>>> plt.plot(x_observed, y_observed, "o", label="observation")
>>> plt.plot(x, y, label="barycentric interpolation")
>>> plt.legend()
>>> plt.show()

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