SHWindow class

Classes for localized spectral analyses.

Subclasses

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

Initialization

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.

Attributes

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.

Methods

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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