function D=kernelc2D(XY,XYP,K) % D=KERNELC2D(XY,XYP,K) % % This function is used to calculate the two-dimensional Cartesian % spatiospectral concentration, i.e. Bessel, kernel. % See Simons and Wang, J. Geomathematics 2011, Eq. 54 % % INPUT: % % XY [X(:) Y(:)] A two-column matrix with one set of coordinate pairs % XYP [XP(:) YP(:)] A two-column matrix with another set of points % K The wavenumber of the circular bandlimitation % % OUTPUT: % % D The desired spatiospectral localization kernel, a matrix of % [length(XY(:))-by-length(XYP(:))] % % SEE ALSO: % % LOCALIZATION2D % % Last modified by dongwang-at-princeton.edu, 02/22/2008 % Last modified by fjsimons-at-alum.mit.edu, 10/07/2008 t0=clock; % Make all the required combinations, i.e. the pairs of the unwrapped % pairs of points; switch order so the dimensions are right [XX,XXP]=meshgrid(XYP(:,1),XY(:,1)); [YY,YYP]=meshgrid(XYP(:,2),XY(:,2)); % Calculate the distance norm md=sqrt((XX-XXP).^2+(YY-YYP).^2); % Calculate the actual kernel, but watch out for zero division % So - not actually a singular kernel, right? warning off MATLAB:divideByZero D=K*besselj(1,K*md)/2/pi./md; warning on MATLAB:divideByZero % Supply the correct form of the kernel where the argument was zero. Note % that this is not necessarily on the diagonal - the matrix D might not % even be square D(find(md