Classes for localized spectral analyses.


Subclass name Description
SHWindowCap Class for windows concentrated within a spherical cap.
SHWindowMask Class for windows concentrated in an arbitrary domain.


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


Attribute Description
kind Either 'cap' or 'mask'.
coeffs Array of spherical harmonic coefficients of the rotated spherical-cap localization windows.
shannon The Shannon number, which approximates the number of well localized windows.
area Area of the concentration domain, in radians.
eigenvalues Concentration factors of the localization windows.
orders The angular orders for each of the spherical-cap localization windows.
weights Taper weights used with the multitaper spectral analyses. Default is None.
lmax Spherical harmonic bandwidth of the localization windows.
theta Angular radius of the spherical-cap localization domain (default in degrees).
theta_degrees True (default) if theta is in degrees.
nwin Number of localization windows. Default is (lmax+1)**2.
nwinrot The number of best-concentrated spherical cap windows that were rotated and whose coefficients are stored in coeffs.
clat, clon Latitude and longitude of the center of the rotated spherical-cap localization windows (default in degrees).
coord_degrees True (default) if clat and clon are in degrees.
taper_degrees Boolean or int array defining which spherical harmonic degrees were used to construct the windows.


Method Description
to_array() Return an array of the spherical harmonic coefficients for taper i, where i=0 is the best concentrated, optionally using a different normalization convention.
to_shcoeffs() Return the spherical harmonic coefficients of taper i, where i=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 taper i, where i=0 is the best concentrated window.
number_concentrated() Return the number of localization windows that have concentration factors greater or equal to a specified value.
degrees() Return an array containing the spherical harmonic degrees of the localization windows, from 0 to lmax.
spectra() Return the spectra of one or more localization windows.
rotate() Rotate the spherical cap tapers, originally located at the north pole, to clat and clon and save the spherical harmonic coefficients in coeffs.
coupling_matrix() Return the coupling matrix of the first nwin.
biased_spectrum() Calculate the multitaper (cross-) spectrum expectation of a localized function.
multitaper_spectrum() Return the multitaper spectrum estimate and uncertainty for the input SHCoeffs class instance.
multitaper_cross_spectrum() Return the multitaper cross-spectrum estimate and uncertainty for two input SHCoeffs class instances.
variance() Compute the theoretical variance of a windowed function for a given input power spectrum.
copy() Return a copy of the class instance.
plot_windows() Plot the best concentrated localization windows using a simple cylindrical projection.
plot_spectra() Plot the spectra of the best concentrated localization windows.
plot_coupling_matrix() Plot the multitaper coupling matrix.
info() Print a summary of the data stored in the SHWindow instance.
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