# csdms-contrib/slepian_alpha

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 function [E,V,th,C]=sdwcapt2(TH,L,m,nth,vcut,grd) % [E,V,th,C]=SDWCAPT2(TH,L,m,nth,vcut,grd) % % Spherical harmonic localization to DOUBLE spherical polar cap: % spatially concentrated and optimally bandlimited solutions. % % INPUT: % % TH Angular extent of the spherical cap, in degrees % L Bandwidth % m Angular order of the required data window, -lL) error('Order cannot exceed degree') end % Filename of saved data fnpl=sprintf('%s/SDW-%i-%i-%i-%i.mat',... fullfile(getenv('IFILES'),'SDWCAPT2'),TH,L,nth,m); if exist(fnpl,'file')==2 eval(sprintf('load %s',fnpl)) disp(sprintf('%s loaded by SDWCAPT2',fnpl)) else [E,V,th,C,ngl1,ngl2,K]=sdwcap2(TH,L,m,nth,vcut,grd); % Use the "trick": expand truncated basis functions % Put on the black lines belt=[th>TH]&[th<180-TH]; E(belt,:)=0; if m==0 % Expand to Nyquist; watch for the factors! C2=th2pl(E,size(E,1)-1)*sqrt(4*pi); else C2=th2plm(E,size(E,1)-1,m); end % Don't need to do this, but it should return the zeroed input E! % Reexpand % E2=pl2th(C2,[],1); % Watch for the factors! % Now E with the zeroed portions and E2 should be identical % and the C2's are still orthogonal C=C2; % Output in degrees eval(sprintf('save %s E V L TH C th',fnpl)) end if grd==2 % Output on full grid if mor<=0 EE=E; clear E for index=1:size(EE,2) E{index}=EE(:,index)*cos(m*linspace(0,2*pi,nlon)); end end if mor>0 EE=E; clear E for index=1:size(EE,2) E{index}=EE(:,index)*sin(m*linspace(0,2*pi,nlon)); end end end