function [V,C,dels,dems,XY]=localization(L,dom,N)
% [V,C,dels,dems,XY]=LOCALIZATION(L,dom,N)
%
% Returns bandlimited spectral eigenfunctions and their associated
% eigenvalues localized to a closed domain on the unit sphere.
%
% INPUT:
%
% L        Bandwidth, maximum angular degree
% dom      'patch', 'sqpatch', 'africa',  'eurasia',  'namerica', 
%          'australia', 'greenland', 'samerica', 'amazon', 'orinoco'
% N        The splining smoothness [default: 10] or
%          The parameters for 'patch' and 'dpatch' passed on to KERNELC
%
% OUTPUT:
%
% V        A list of all the eigenvalues 
% C        A cell array with cosine/sine coefficients eigenfunctions
% dels     Spherical harmonic degrees 
% dems     Spherical harmonic orders 
% XY       Coordinates of the outlines of the region
%
% EXAMPLE:
%
% [V,C,dels,dems]=localization(18,'amazon');
% plotplm([dels dems C{1}])
%
% This function uses KERNELC to compute the kernel.
% 
% Last modified by fjsimons-at-alum.mit.edu, 08/20/2006

% And study covariance?

% Default inputs
defval('L',18)
defval('dom','australia')
defval('N',10)

% Calculates the localization kernel for this domain
[Klmlmp,XY]=kernelc(L,dom,N);

% Calculates the eigenfunctions/values for this localization problem
[C,V]=eig(Klmlmp);
[V,isrt]=sort(sum(real(V),1));
V=fliplr(V);
C=C(:,fliplr(isrt));

% Sticks the cosine/sine coefficients back
% into the right place of LMCOSI
[dems,dels,mz,lmc,mzin]=addmon(L);
for index=1:size(C,2)
  CC{index}=reshape(insert(C(:,index),0,mzin),2,length(dems))';
end

% Make standard output
V=V(:);
C=CC;