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Module « scipy.interpolate »

Fonction barycentric_interpolate - module scipy.interpolate

Signature de la fonction barycentric_interpolate

def barycentric_interpolate(xi, yi, x, axis=0, *, der=0, rng=None) 

Description

help(scipy.interpolate.barycentric_interpolate)

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
----------
xi : array_like
    1-D array of x coordinates of the points the polynomial should
    pass through
yi : array_like
    The y coordinates of the points the polynomial should pass through.
x : scalar or array_like
    Point or points at which to evaluate the interpolant.
axis : int, optional
    Axis in the `yi` array corresponding to the x-coordinate values.
der : int 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.
rng : `numpy.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
-------
y : scalar 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
--------
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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