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# scipy.interpolate.barycentric_interpolate

scipy.interpolate.barycentric_interpolate(xi, yi, x, axis=0, *, der=0)

  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.

    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.

    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`

    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()