Calculate the eigenfunctions of the spherical-cap concentration problem for a single angular order.
call SHReturnTapersM (theta0
, lmax
, m
, tapers
, eigenvalues
, shannon
)
theta0
: input, real*8
: The angular radius of the spherical cap in radians.
lmax
: input, integer
: The spherical harmonic bandwidth of the localization windows.
m
: input, integer
: The angular order of the localization windows.
tapers
: output, real*8, 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 and lmax
, respectively, and the columns are arranged from best to worst concentrated.
eigenvalues
: output, real*8, dimension (lmax
+1)
: The concentration factors of the localization windows.
shannon
: output, optional, real*8
: The Shannon number, which is the trace of the concentration kernel.
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.
Wieczorek, M. A. and F. J. Simons, Localized spectral analysis on the sphere,
Geophys. J. Int.
, 162, 655-675.
Simons, F.J., F.A. Dahlen, and M.A. Wieczorek, Spatiospectral concentration on a sphere, SIAM Review
, 48, 504-536, 2006.