Calculate the eigenfunctions of the spherical-cap concentration problem.

## Usage

call SHReturnTapers (theta0, lmax, tapers, eigenvalues, taper_order, exitstatus)

## Parameters

theta0 : input, real*8
The angular radius of the spherical cap in radians.
lmax : input, integer
The spherical harmonic bandwidth of the localization windows.
tapers : output, real*8, 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 : output, real*8, dimension ((lmax+1)**2)
The concentration factors of the localization windows.
taper_order : output, integer, dimension ((lmax+1)**2)
The angular order of the non-zero spherical harmonic coefficients in each column of tapers.
exitstatus : output, optional, integer
If present, instead of executing a STOP when an error is encountered, the variable exitstatus will be returned describing the error. 0 = No errors; 1 = Improper dimensions of input array; 2 = Improper bounds for input variable; 3 = Error allocating memory; 4 = File IO error.

## 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.

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.