Module « scipy.interpolate »

Fonction barycentric_interpolate - module scipy.interpolate

Signature de la fonction barycentric_interpolate

def barycentric_interpolate(xi, yi, x, axis=0) 

Description

barycentric_interpolate.__doc__

    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
        Points to evaluate the interpolator at.
    axis : int, optional
        Axis in the yi array corresponding to the x-coordinate values.

    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 : Bary centric 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 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()