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SHReturnTapersM
Calculate the eigenfunctions of the spherical-cap concentration problem for a single angular order.
Usage
tapers
, eigenvalues
= pyshtools.SHReturnTapersM (theta0
, lmax
, m
)
Returns
tapers
: float, dimension (lmax
+1,lmax
+1)- The spherical harmonic coefficients of the
lmax+1
localization windows, arranged in columns. 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)- The concentration factors of the localization windows.
Parameters
theta0
: float- The angular radius of the spherical cap in radians.
lmax
: integer- The spherical harmonic bandwidth of the localization windows.
m
: integer- The angular order of the localization windows.
Description
SHReturnTapersM
will calculate the eigenfunctions (i.e., localization windows) of the spherical-cap concentration problem for a singular angular order. The spherical harmonic coefficients of each window are given in the columns of tapers
, and the corresponding concentration factors are given in eigenvaules
. 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
shreturntapers, computedg82, computedm
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