# csdms-contrib/slepian_alpha

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 function nrmorl=addmup(nr,drk) % nrmorl=ADDMUP(nr,drk) % % Calculates the number of real spherical harmonic orders that belong to % an expansion from degree l=0 to L, OR vice versa. % For arrays where m=0:l. % % INPUT: % % nr The number of real spherical harmonic orders, OR % The degree of the expansion % drk 'a' the input is the degree, calculate the number [default] % 'r' the input is the number, calculate the degree % % OUTPUT: % % nrmorl The degree of the expansion, OR % The number of real spherical harmonic orders % % NOTE: % % addmup(-1) equals 0, which is just as well % % See also ADDMOFF, ADDMOUT % % Last modified by fjsimons-at-alum.mit.edu, 05/17/2011 % Calculates the number of real spherical harmonic orders % that belong to an expansion from degree l=0 to L - or vice versa. % Since m=0:l for real spherical harmonics, the number of orders per % degree is l+1. This program thus calculates % $\sum\limits_{l=0}^{L}(l+1)$ and its inverse, for a given L, using % analytical expressions. Works for matrices, vectors as well as % scalars. Note: degrees 0 and 1 are of course included. % Check the behavior for the negatives should you ever need those defval('nr',3) defval('drk','a') switch drk case 'a' nrmorl=1/2*(nr+1).^2+1/2*nr+1/2; % nrmorl=1/2*nr.^2+3/2*nr+1; case 'r' nrmorl=-3/2+1/2*sqrt(1+8*nr); if prod((round(nrmorl)==nrmorl)+0)==0 warning('Invalid entry - noninteger result') end otherwise error('Specify a valid option') end