glm2lmcosi.m

function lmcosi=glm2lmcosi(G,wot)
% lmcosi=GLM2LMCOSI(G,wot)
%
% From the output of GLMALPHA, extracts the wot'th column and produces a
% matrix of the form lmcosi suitable for input to PLM2XYZ or PLOTPLM
% etc. Since KERNELC works with unit-normalized harmonics and PLM2XYZ
% with 4*pi-normalized ones, we renormalize.  We didn't use to do this
% elsewhere, but from now on, it will matter. 
%
% SEE ALSO: PLOTSLEP, LOCALIZATION, KLM2LMCOSI
% 
% Last modified by fjsimons-at-alum.mit.edu, 07/11/2012

% Collect the output into a format that PLM2XYZ knows how to interpret
L=sqrt(size(G,1))-1;
[~,~,mz,lmcosi,~,~,~,~,~,ronm]=addmon(L);
tocofs=2*addmup(L); difer(tocofs-2*length(lmcosi),[],[],NaN)

% Construct the full matrix
lmcosi(tocofs+ronm)=G(:,wot);

% Renormalize so that when multiplied with 4pi-harmonics they have the
% same integral. Note that this has nothing special for the m=0 zonal
% coefficients - it's simply the last mile of the normalization. Check
% this using FIBONACCIGRID as suggested in GALPHA.
lmcosi(:,3:4)=lmcosi(:,3:4)/sqrt(4*pi);

% Remember that if you were to use YLM for rendering you'd have to add
% the (-1)^m phase factor which is missing from this.