spharpy.interpolate

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)

Bases: SmoothSphereBivariateSpline

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

Parameters:

• sampling (spharpy.samplings.Coordinates, pf.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

• 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) – The eps valued to be considered for interpolator estimation. 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

[1]

P. Dierckx, “Algorithms for smoothing data on the sphere with tensor product splines,” p. 24, 1984.

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()	Return spline coefficients.
get_knots()	Return a tuple (tx,ty) where tx,ty contain knots positions of the spline with respect to x-, y-variable, respectively.
get_residual()	Return weighted sum of squared residuals of the spline approximation: sum ((w[i]*(z[i]-s(x[i],y[i])))**2,axis=0)

__call__(interp_grid, dtheta=0, dphi=0)

Evaluate the spline on a new sampling grid.

Parameters:

• interp_grid (spharpy.samplings.Coordinates, pf.Coordinates) – Coordinates object containing a new set of points for which data is to be interpolated.

• dtheta (int, optional) – Order of theta derivative

• dphi (int, optional) – Order of phi derivative

get_coeffs()

Return spline coefficients.

get_knots()

Return a tuple (tx,ty) where tx,ty contain knots positions of the spline with respect to x-, y-variable, respectively. The position of interior and additional knots are given as t[k+1:-k-1] and t[:k+1]=b, t[-k-1:]=e, respectively.

get_residual()

Return weighted sum of squared residuals of the spline approximation: sum ((w[i]*(z[i]-s(x[i],y[i])))**2,axis=0)