cathy_tools.Rbf

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cathy_tools.Rbf#

class cathy_tools.Rbf(*args, **kwargs)[source]#

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

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.

Variables:

  • 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)

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,)
__init__(*args, **kwargs)[source]#

Methods

__init__(*args, **kwargs)

Attributes

A

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