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- The angular radius of the spherical cap in radians.
`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.

## See also

shreturntapersm, computedg82, computedm

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