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SHReturnTapersM

SHReturnTapersM -

Calculate the eigenfunctions of the spherical-cap concentration problem for a single angular order.

SYNOPSIS

SUBROUTINE SHReturnTapersM (

THETA0, LMAX, M, TAPERS, EIGENVALUES, SHANNON )

    REAL*8

    THETA0, TAPERS(LMAX+1), EIGENVALUES(LMAX+1)

    INTEGER

    LMAX, M

    REAL*8, OPTIONAL

    SHANNON

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.

ARGUMENTS

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) REAL*8, OPTIONAL

The shannon number, which is calculated as the trace of the concentration kernel.

SEE ALSO

shreturntapers(1), computedg82(1), computed0(1), computedm(1)

http://shtools.ipgp.fr/

REFERENCES

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.

COPYRIGHT AND LICENSE

Copyright 2012 by Mark Wieczorek <wieczor@ipgp.fr>.

This is free software; you can distribute and modify it under the terms of the revised BSD license.