Subclasses

Subclass name Description
SlepianCap Class for Slepian functions concentrated within a spherical cap.
SlepianMask Class for Slepian functions concentrated in an arbitrary domain.

Initialization

Initialization method Description
x = Slepian.from_cap() Construct Slepian functions concentrated within a spherical cap.
x = Slepian.from_mask() Construct Slepian functions concentrated within an arbitrary region.

Attributes

Attribute Description
kind Either 'cap' or 'mask'.
coeffs Array of spherical harmonic coefficients of the rotated spherical-cap Slepian functions.
shannon The Shannon number, which approximates the number of well localized functions.
area Area of the concentration domain, in radians.
eigenvalues Concentration factors of the Slepian functions.
orders The angular orders for each of the spherical-cap Slepian functions.
lmax Spherical harmonic bandwidth of the Slepian functions.
theta Angular radius of the spherical-cap localization domain (default in degrees).
theta_degrees True (default) if theta is in degrees.
nmax Number of Slepian functions. Default is (lmax+1)**2.
nrot The number of best-concentrated spherical cap Slepian functions that were rotated and whose coefficients are stored in coeffs.
clat, clon Latitude and longitude of the center of the rotated spherical-cap Slepian functions (default in degrees).
coord_degrees True (default) if clat and clon are in degrees.
slepian_degrees Boolean or int array defining which spherical harmonic degrees were used to construct the Slepian functions.

Methods

Method Description
expand() Expand the input function in Slepian functions.
to_array() Return an array of the spherical harmonic coefficients for function alpha, where alpha=0 is the best concentrated, optionally using a different normalization convention.
to_shcoeffs() Return the spherical harmonic coefficients of function alpha, where alpha=0 is the best concentrated, as a new SHCoeffs class instance, optionally using a different normalization convention.
to_shgrid() Return as a new SHGrid instance a grid of function alpha, where alpha=0 is the best concentrated.
number_concentrated() Return the number of Slepian functions that have concentration factors greater or equal to a specified value.
degrees() Return an array containing the spherical harmonic degrees of the Slepian functions, from 0 to lmax.
spectra() Return the spectra of one or more Slepian functions.
rotate() Rotate the spherical cap Slepian functions, originally located at the North pole, to clat and clon and save the spherical harmonic coefficients in coeffs.
variance() Calculate the theoretical variance of the power of a function expanded in spherical-cap Slepian functions.
copy() Return a copy of the class instance.
plot() Plot the best concentrated Slepian functions using a simple cylindrical projection.
plot_spectra() Plot the spectra of the best concentrated Slepian functions.
info() Print a summary of the data stored in the Slepian instance.
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