# scipy.interpolate.Rbf¶

class scipy.interpolate.Rbf(*args)[source]

A class for radial basis function approximation/interpolation of n-dimensional scattered data.

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.

Examples

>>> from scipy.interpolate import Rbf
>>> x, y, z, d = np.random.rand(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. 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.

#### Next topic

scipy.interpolate.Rbf.__call__