# csdms-contrib/slepian_alpha

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 function R=rots(L,V,EM,gammas) % R=ROTS(L,V,EM,gammas) % % Makes a pole-rotation matrix for Slepian functions on axisymmetric % polar domains. It does this by combining non-zero orders. % % INPUT: % % L Bandwidth of the Slepian basis % V Eigenvalues of the Slepian basis % EM List of orders in which the basis is presented (by, e.g. GALPHA) % gammas List of radian angles over which you want to rotate each function % % OUTPUT: % % R A blocky rotation matrix to multiply into the G of GALPHA % % EXAMPLE: % % L=18; % [G,V,EM]=galpha(40,L,1,linspace(0,pi,50),linspace(0,2*pi,100),'global'); % R=rots(L,V,EM,rand(addmup(L),1)); GR=R*G; subplot(211); % imagesc(reshape(G(2,:),50,100)); subplot(212); imagesc(reshape(GR(2,:),50,100)); % % SEE ALSO: GALPHA % % Last modified by fjsimons-at-alum.mit.edu, 08/19/2008 defval('L',3) if length(V)~=length(EM) error('V and EM must be the same length') end if ~exist('V') || (exist('V') & isempty(V)) % Just to get some defaults going [G,V,EM]=galpha(40,L,1,0,NaN,'global'); end defval('gammas',pi/4) if length(gammas)==1 gammas=repmat(gammas,addmup(L),1); end % Which are the abs(orders) in question here? % EM=abs(EM(logical([1 ~~diff(abs(EM))]))); % Nope % The previous often backfire if for some reason two m=0 or two |m| % are in direct succession... the real discriminant is: EM=abs(EM(logical([1 ~~diff(V)]))); % Check the dimensions are right... difer(length(EM)-length(unique(V))) difer(length(EM)-length(gammas)) % Now construct the grand old rotation matrix % This growth might have to be optimized later R=[]; for index=1:length(EM) if EM(index)==0 lR=1; else gams=gammas(index); lR=[cos(gams) -sin(gams) ; sin(gams) cos(gams)]; end R=blkdiag(R,lR); end