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

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


*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 : 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:

def euclidean_norm(x1, x2):
    return sqrt( ((x1 - x2)**2).sum(axis=0) )

which is called with x1 = x1[ndims, newaxis, :] and x2 = x2[ndims, : ,newaxis] such that the result is a matrix of the distances from each point in x1 to each point in x2.


>>> 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