# scipy.interpolate.Rbf

class scipy.interpolate.Rbf(*args, **kwargs)

  A class for radial basis function interpolation of functions from N-D scattered data to an M-D domain.

  Legacy

  This class is considered legacy and will no longer receive updates. This could also mean it will be removed in future SciPy versions. `Rbf` is legacy code, for new usage please use `RBFInterpolator` instead.

  Parameters:
    *args arrays

      x, y, z, …, d, where x, y, z, … are the coordinates of the nodes and d is the array of values at the nodes

    function str or callable, optional

      The radial basis function, based on the radius, r, given by the norm (default is Euclidean distance); the default is ‘multiquadric’:

          'multiquadric': sqrt((r/self.epsilon)**2 + 1)
          'inverse': 1.0/sqrt((r/self.epsilon)**2 + 1)
          'gaussian': exp(-(r/self.epsilon)**2)
          'linear': r
          'cubic': r**3
          'quintic': r**5
          'thin_plate': r**2 * log(r)

      If callable, then it must take 2 arguments (self, r). The epsilon parameter will be available as self.epsilon. Other keyword arguments passed in will be available as well.

    epsilon float, optional

      Adjustable constant for gaussian or multiquadrics functions - defaults to approximate average distance between nodes (which is a good start).

    smooth float, optional

      Values greater than zero increase the smoothness of the approximation. 0 is for interpolation (default), the function will always go through the nodal points in this case.

    norm str, callable, optional

      A function that returns the ‘distance’ between two points, with inputs as arrays of positions (x, y, z, …), and an output as an array of distance. E.g., the default: ‘euclidean’, such that the result is a matrix of the distances from each point in `x1` to each point in `x2`. For more options, see documentation of scipy.spatial.distances.cdist.

    mode str, optional

      Mode of the interpolation, can be ‘1-D’ (default) or ‘N-D’. When it is ‘1-D’ the data d will be considered as 1-D and flattened internally. When it is ‘N-D’ the data d is assumed to be an array of shape (n_samples, m), where m is the dimension of the target domain.

  See also

  `RBFInterpolator`

  Examples

      >>> import numpy as np
      >>> from scipy.interpolate import Rbf
      >>> rng = np.random.default_rng()
      >>> x, y, z, d = rng.random((4, 50))
      >>> rbfi = Rbf(x, y, z, d)  # radial basis function interpolator instance
      >>> xi = yi = zi = np.linspace(0, 1, 20)
      >>> di = rbfi(xi, yi, zi)   # interpolated values
      >>> di.shape
      (20,)

  Attributes:
    N int

      The number of data points (as determined by the input arrays).

    di ndarray

      The 1-D array of data values at each of the data coordinates xi.

    xi ndarray

      The 2-D array of data coordinates.

    function str or callable

      The radial basis function. See description under Parameters.

    epsilon float

      Parameter used by gaussian or multiquadrics functions. See Parameters.

    smooth float

      Smoothing parameter. See description under Parameters.

    norm str or callable

      The distance function. See description under Parameters.

    mode str

      Mode of the interpolation. See description under Parameters.

    nodes ndarray

      A 1-D array of node values for the interpolation.

    A internal property, do not use

  Methods

  `__call__`(*args) | Call self as a function.