Calculate the eigenfunctions of the spherical-cap concentration problem.
call SHReturnTapers (theta0
, lmax
, tapers
, eigenvalues
, taper_order
)
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
.
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.
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.