scipy.interpolate.Rbf

class scipy.interpolate.Rbf(*args)

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.