function swvals2d % SWVALS2D % % FIGURE 3 of SIMONS & WANG % % Makes a plot of the eigenvalues of the concentration problem to the % Cartesian disk while differentiating the orders. % % SEE ALSO: % % SWFRIED2D, SDWVALS % % Last modified by fjsimons-at-alum.mit.edu, 04/24/2009 % Prepare for plotting clf [ah,ha,H]=krijetem(subnum(2,2)); yls=[-0.1 1.1]; symbs={'o','x','s','+','v','*','^','d','<','>','p','h',... 'o','x','s','+','v','*','^','d'}; xmax=60; NN=[3 11 24 42]; % Do this for a variety of Shannon numbers for index=1:length(NN) clear E EV EM N=NN(index); % The upper of number of orders should "cover" all the cases down to % very low values M=11; % Calculate the radial functions but only care about the eigenvalues for m=0:M [E,EV{m+1}]=swdisk(m,N,2*N,[],NaN,'DV'); EM{m+1}=repmat(m,1,2*N); end % Sort them all according to their eigenvalue EV=[EV{:}]; EM=[EM{:}]; [EV,i]=sort(EV,'descend'); EM=EM(i); % Repeat the nonzero orders twice and take as many as you had dbl=~~EM+1; % The indexing sequence in the non-repeated vectors seq=gamini(1:length(EV),dbl); % Make the eigenvalue sequence with the repeats EV=gamini(EV,dbl); % Make the order sequence with the repeats EM=EM(seq); % Now do the plots axes(ah(index)) for ondi=1:length(EV) p(ondi,index)=plot(ondi,EV(ondi),symbs{EM(ondi)+1}); hold on end hold on plot([N N],yls,'k:') plot([0 xmax],[0.5 0.5],'k:') plot([0 xmax],[0 0],'k:') plot([0 xmax],[1 1],'k:') set(ah(index),'xlim',[0 xmax],'ylim',yls,'xgrid','off','ygrid','off',... 'xtickl',[1 10:10:xmax],'xtick',[1 10:10:xmax],... 'ytick',[0:0.25:1]) drawnow end % Save the cosmetics for the very end % Now make the plot beautiful axes(ah(4)) fb=fillbox([2 18 0.88 -0.05],'w'); for ondi=1:12 ypo=0+0.075*(ondi-1); pl(ondi,1)=plot(4,ypo,symbs{ondi}); hold on tl(ondi,1)=text(7,ypo,sprintf('m = %s %i','\pm',ondi-1),'FontS',8); end longticks(ah) set([p(~~p(:)) ; pl(~~pl(:))],'MarkerS',4,'MarkerF',grey,'MarkerE','k') axes(ha(1)) al(1)=ylabel('eigenvalue \lambda'); axes(ha(2)) al(2)=ylabel('eigenvalue \lambda'); axes(ha(2)) xl(1)=xlabel('rank'); axes(ha(4)) xl(2)=xlabel('rank'); nolabels(ha(3:4),2) nolabels(ah(1:2),1) serre(H',1/2,'down') serre(H,1/2,'across') for ind=1:4 xx(ind)=xtraxis(ah(ind),NN(ind),sprintf('N2D = %i',NN(ind))); end longticks(xx) set([xl al],'FontS',13) set([ ah],'FontS',12) fig2print(gcf,'portrait') figdisp([],[],[],1)