Slepian class

Classes for Slepian functions.

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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