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.

## 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.

## See also

shreturntapersm, computedg82, computedm

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