Calculate the eigenfunctions of the spherical-cap concentration problem.

## Usage

tapers, eigenvalues, taper_order = SHReturnTapers (theta0, lmax)

## Returns

tapers : float, dimension (lmax+1, (lmax+1)**2)
The spherical harmonic coefficients of the (lmax+1)**2 localization windows. Each column contains the coefficients of a single window that possesses non-zero coefficients for the single angular order specified in taper_order. The first and last rows of each column correspond to spherical harmonic degrees 0 and lmax, respectively, and the columns are arranged from best to worst concentrated.
eigenvalues : float, dimension ((lmax+1)**2)
The concentration factors of the localization windows.
taper_order : integer, dimension ((lmax+1)**2)
The angular order of the non-zero spherical harmonic coefficients in each column of tapers.

## Parameters

theta0 : float
lmax : integer
The spherical harmonic bandwidth of the localization windows.

## Description

SHReturnTapers will calculate the eigenfunctions (i.e., localization windows) of the spherical-cap concentration problem. Each column of the matrix tapers contains the spherical harmonic coefficients of a single window and the corresponding concentration factor is given in the array eigenvalues. Each window has non-zero coefficients for only a single angular order that is specified in taper_order: all other spherical harmonic coefficients for a given window are identically zero. The columns of tapers are ordered from best to worst concentrated, and the first and last rows of each column correspond to spherical harmonic degrees 0 and lmax, respectively. The localization windows are normalized such that they have unit power.

## References

Wieczorek, M. A. and F. J. Simons, Localized spectral analysis on the sphere, Geophys. J. Int., 162, 655-675, 2005.

Simons, F.J., F.A. Dahlen, and M.A. Wieczorek, Spatiospectral concentration on a sphere, SIAM Review, 48, 504-536, 2006.