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SHReturnTapers
Calculate the eigenfunctions of the spherical-cap concentration problem.
Usage
tapers
, eigenvalues
, taper_order
= pyshtools.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 intaper_order
. The first and last rows of each column correspond to spherical harmonic degrees 0 andlmax
, 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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