RBFBlock#

class RBFBlock(neighbors=None, smoothing=0.0, kernel='thin_plate_spline', epsilon=None, degree=None)[source]#

Bases: Module

Radial Basis Function (RBF) interpolation layer. It need to be fitted with the data with the method fit(), before it can be used to interpolate new points. The layer is not trainable.

Note

It reproduces the implementation of scipy.interpolate.RBFBlock and it is inspired from the implementation in torchrbf.

Parameters:

neighbors (int) – Number of neighbors to use for the interpolation. If None, use all data points.
smoothing (float) – Smoothing parameter for the interpolation. if 0.0, the interpolation is exact and no smoothing is applied.
kernel (str) – Radial basis function to use. Must be one of linear, thin_plate_spline, cubic, quintic, multiquadric, inverse_multiquadric, inverse_quadratic, or gaussian.
epsilon (float) – Shape parameter that scaled the input to the RBF. This defaults to 1 for kernels in scale_invariant dictionary, and must be specified for other kernels.
degree (int) – Degree of the added polynomial. For some kernels, there exists a minimum degree of the polynomial such that the RBF is well-posed. Those minimum degrees are specified in the min_degree_funcs dictionary above. If degree is less than the minimum degree, a warning is raised and the degree is set to the minimum value.

property smoothing#

Smoothing parameter for the interpolation.

Return type:: float

property kernel#

Radial basis function to use.

Return type:: str

property epsilon#

Shape parameter that scaled the input to the RBF.

Return type:: float

property degree#

Degree of the added polynomial.

Return type:: int

fit(y, d)[source]#

Fit the RBF interpolator to the data.

Parameters:

y (torch.Tensor) – (n, d) tensor of data points.
d (torch.Tensor) – (n, m) tensor of data values.

forward(x)[source]#

Returns the interpolated data at the given points x.

Parameters:: x (torch.Tensor) – (n, d) tensor of points at which to query the interpolator
Return type:: (n, m) torch.Tensor of interpolated data.

static kernel_vector(x, y, kernel_func)[source]#

Evaluate radial functions with centers y for all points in x.

Parameters:

x (torch.Tensor) – (n, d) tensor of points.
y (torch.Tensor) – (m, d) tensor of centers.
kernel_func (str) – Radial basis function to use.

Return type:

(n, m) torch.Tensor of radial function values.

static polynomial_matrix(x, powers)[source]#

Evaluate monomials at x with given powers.

Parameters:

x (torch.Tensor) – (n, d) tensor of points.
powers (torch.Tensor) – (r, d) tensor of powers for each monomial.

Return type:

(n, r) torch.Tensor of monomial values.

static kernel_matrix(x, kernel_func)[source]#

Returns radial function values for all pairs of points in x.

Parameters:

x (torch.Tensor) – (n, d) tensor of points.
kernel_func (str) – Radial basis function to use.

Return type:

(n, n) torch.Tensor of radial function values.

static monomial_powers(ndim, degree)[source]#

Return the powers for each monomial in a polynomial.

Parameters:

ndim (int) – Number of variables in the polynomial.
degree (int) – Degree of the polynomial.

Return type:

(nmonos, ndim) torch.Tensor where each row contains the powers for each variable in a monomial.

static build(y, d, smoothing, kernel, epsilon, powers)[source]#

Build the RBF linear system.

Parameters:

y (torch.Tensor) – (n, d) tensor of data points.
d (torch.Tensor) – (n, m) tensor of data values.
smoothing (torch.Tensor) – (n,) tensor of smoothing parameters.
kernel (str) – Radial basis function to use.
epsilon (float) – Shape parameter that scaled the input to the RBF.
powers (torch.Tensor) – (r, d) tensor of powers for each monomial.

Return type:

(lhs, rhs, shift, scale) where lhs and rhs are the left-hand side and right-hand side of the linear system, and shift and scale are the shift and scale parameters.

static solve(y, d, smoothing, kernel, epsilon, powers)[source]#

Build then solve the RBF linear system.

Parameters:

y (torch.Tensor) – (n, d) tensor of data points.
d (torch.Tensor) – (n, m) tensor of data values.
smoothing (torch.Tensor) – (n,) tensor of smoothing parameters.
kernel (str) – Radial basis function to use.
epsilon (float) – Shape parameter that scaled the input to the RBF.
powers (torch.Tensor) – (r, d) tensor of powers for each monomial.

Raises:

ValueError – If the linear system is singular.

Return type:

(shift, scale, coeffs) where shift and scale are the shift and scale parameters, and coeffs are the coefficients of the interpolator