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雨人007銀蟲 (小有名氣)
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[求助]
MATLAB 中有關griddata的計算原理，看不懂，求詳解！
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>>type griddata function [xi,yi,zi] = gdatav4(x,y,z,xi,yi) %GDATAV4 MATLAB 4 GRIDDATA interpolation % Reference: David T. Sandwell, Biharmonic spline % interpolation of GEOS-3 and SEASAT altimeter % data, Geophysical Research Letters, 2, 139-142, % 1987. Describes interpolation using value or % gradient of value in any dimension. xy = x(  + y(*sqrt(-1);% Determine distances between points d = xy(:,ones(1,length(xy))); d = abs(d - d.'); n = size(d,1); % Replace zeros along diagonal with ones (so these don't show up in the % find below or in the Green's function calculation). d(1:n+1:numel(d)) = ones(1,n); non = find(d == 0, 1); if ~isempty(non), % If we've made it to here, then some points aren't distinct. Remove % the non-distinct points by averaging. [r,c] = find(d == 0); k = find(r < c); r = r(k); c = c(k); % Extract unique (row,col) pairs v = (z(r) + z(c))/2; % Average non-distinct pairs rep = find(diff(c)==0); if ~isempty(rep), % More than two points need to be averaged. runs = find(diff(diff(c)==0)==1)+1; for i=1:length(runs), k = (c==c(runs(i))); % All the points in a run v(runs(i)) = mean(z([r(k);c(runs(i))])); % Average (again) end end z(r) = v; if ~isempty(rep), z(r(runs)) = v(runs); % Make sure average is in the dataset end % Now remove the extra points. z(c) = []; xy(c, = [];xy(:,c) = []; d(c, = [];d(:,c) = []; % Determine the non distinct points ndp = sort([r;c]); ndp(ndp(1:length(ndp)-1)==ndp(2:length(ndp))) = []; warning('MATLAB:griddata:NonDistinctPoints',['Averaged %d non-distinct ' ... 'points.\n Indices are: %s.'],length(ndp),num2str(ndp')) end % Determine weights for interpolation g = (d.^2) .* (log(d)-1); % Green's function. % Fixup value of Green's function along diagonal g(1:size(d,1)+1:numel(d)) = zeros(size(d,1),1); weights = g \ z( ;[m,n] = size(xi); zi = zeros(size(xi)); jay = sqrt(-1); xy = xy.'; % Evaluate at requested points (xi,yi). Loop to save memory. for i=1:m for j=1:n d = abs(xi(i,j)+jay*yi(i,j) - xy); mask = find(d == 0); if ~isempty(mask), d(mask) = ones(length(mask),1); end g = (d.^2) .* (log(d)-1); % Green's function. % Value of Green's function at zero if ~isempty(mask), g(mask) = zeros(length(mask),1); end zi(i,j) = g * weights; end end if nargout<=1, xi = zi; end |
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