spharpy.interpolate#

Interpolation module for spherical data.

Classes:

SmoothSphereBivariateSpline(sampling, data)

Smooth bivariate spline approximation in spherical coordinates.

class spharpy.interpolate.SmoothSphereBivariateSpline(sampling, data, w=None, s=0.0001, eps=1e-16)[source]#

Bases: SmoothSphereBivariateSpline

Smooth bivariate spline approximation in spherical coordinates. The implementation uses the method proposed by Dierckx [1].

Parameters:

sampling (pyfar.Coordinates) – Coordinates object containing the positions for which the data is sampled
data (array, float) – Array containing the data at the sampling positions. Has to be real-valued.
w (array, float) – Weighting coefficients. The default is None, which sets the weighting coefficients to 1.
s (float, 1e-4) – Smoothing factor > 0 Positive smoothing factor defined for estimation condition: sum((w(i)*(r(i) - s(theta(i), phi(i))))**2, axis=0) <= s Default s=len(w) which should be a good value if 1/w[i] is an estimate of the standard deviation of r[i]. The default value is 1e-4
eps (float, 1e-16) – Sets the threshold used to determine the effective rank of the underlying linear system of equations. Values smaller than this threshold are treated as zero during the fitting process. Depends on the used data type and numerical precision. The default is 1e-16.

Note

This is a wrapper for scipy’s SmoothSphereBivariateSpline only using Coordinates objects as container for the azimuth and elevation angles. For detailed information see scipy’s documentation.

References

Examples

>>> n_max = 10
>>> sampling = spharpy.samplings.equalarea(
...     n_max, n_points=500, condition_num=np.inf)
>>> Y = spharpy.spherical.spherical_harmonic_basis_real(n_max, sampling)
>>> y_vec = spharpy.spherical.spherical_harmonic_basis_real(
...     n_max, Coordinates(1, 0, 0))
>>> data = Y @ y_vec.T
>>> data = np.sin(sampling.elevation)*np.sin(2*sampling.azimuth)
>>> interp_grid = spharpy.samplings.hyperinterpolation(35)
>>> data_grid = np.sin(interp_grid.elevation)*np.sin(2*interp_grid.azimuth)
>>> interpolator = interpolate.SmoothSphereBivariateSpline(
...     sampling, data, s=1e-4)
...
>>> interp_data = interpolator(interp_grid)

Methods:

`__call__`(interp_grid[, dtheta, dphi])	Evaluate the spline on a new sampling grid.
`get_coeffs`()	Get the coefficients of the spline.
`get_knots`()	Get the knots of the spline.
`get_residual`()	Get the residual of the spline.

__call__(interp_grid, dtheta=0, dphi=0)[source]#

Evaluate the spline on a new sampling grid.

Parameters:

interp_grid (pyfar.Coordinates) – Coordinates object containing a new set of points for which data is to be interpolated.
dtheta (int, optional) – Order of theta derivative. Default is 0.
dphi (int, optional) – Order of phi derivative. Default is 0.

get_coeffs()[source]#

Get the coefficients of the spline.

Returns:: coeffs – The coefficients of the spline. The shape is (n_coeffs_theta, n_coeffs_phi, n_coefficients). The coefficients are ordered by increasing degree and order.
Return type:: ndarray, float

get_knots()[source]#

Get the knots of the spline.

Returns:: knots – The knots of the spline. The first element is the knots in theta direction and the second element is the knots in phi direction.
Return type:: tuple of ndarray, float

get_residual()[source]#

Get the residual of the spline.

Returns:: residual – The residual of the spline, which is the sum of squared errors between the data and the spline evaluation.
Return type:: float