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 : 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, :]
andx2 = x2[ndims, : ,newaxis]
such that the result is a matrix of the distances from each point inx1
to each point inx2
.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
A
Methods
__call__
(*args)