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function [xi,yi,zi] = griddata(x,y,z,xi,yi,method)%GRIDDATA Data gridding.% ZI = GRIDDATA(X,Y,Z,XI,YI) returns matrix ZI containing elements% corresponding to the elements of matrices XI and YI and determined by% interpolation within the 2-D function described by the (usually)% nonuniformly-spaced vectors (X,Y,Z).%% XI can be a row vector, in which case it specifies a matrix with% constant columns. Similarly, YI can be a column vector and it% specifies a matrix with constant rows.%% [XI,YI,ZI] = GRIDDATA(X,Y,Z,XI,YI) returns the XI and YI formed% this way, which are the same as the matrices returned by MESHGRID.%% GRIDDATA uses an inverse distance method.%% See also INTERP2, INTERP1.

% Copyright (c) 1984-94 by The MathWorks, Inc.% $Revision: 5.3 $

% 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.

error(nargchk(5,5,nargin)) % Ignore method for now.

[msg,x,y,z,xi,yi] = xyzchk(x,y,z,xi,yi);

if length(msg)>0, error(msg); endxy = x(:) + y(:)*sqrt(-1);

% Determine distances between pointsd = 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:prod(size(d))) = ones(1,n);

non = find(d == 0);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) pairsv = (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 = find(c==c(runs(i))); % All the points in a runv(runs(i)) = mean(z([r(k);c(runs(i))])); % Average (again)

endendz(r) = v;

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if ~isempty(rep),z(r(runs)) = v(runs); % Make sure average is in the dataset

end

% Now remove the extra points.x(c) = [];y(c) = [];z(c) = [];xy(c,:) = [];xy(:,c) = [];d(c,:) = [];d(:,c) = [];

% Determine the non distinct pointsndp = sort([r;c]);ndp(find(ndp(1:length(ndp)-1)==ndp(2:length(ndp)))) = [];

disp(sprintf('Averaged %d non-distinct points. Indices are:', ...length(ndp)))

disp(ndp')end

% Determine weights for interpolationg = (d.^2) .* (log(d)-1); % Green's function.

% Fixup value of Green's function along diagonalg(1:size(d,1)+1:prod(size(d))) = zeros(size(d,1),1);weights = g \ z(:);

[m,n] = size(xi);zi = zeros(m,n);jay = sqrt(-1);xy = xy.';

% Evaluate at requested points (xi,yi). Loop to save memory.for i=1:mfor j=1:n

d = abs(xi(i,j)+jay*yi(i,j) - xy);

mask = find(d == 0);if length(mask)>0, d(mask) = ones(length(mask),1); endg = (d.^2) .* (log(d)-1); % Green's function.% Value of Green's function at zeroif length(mask)>0, g(mask) = zeros(length(mask),1); endzi(i,j) = g * weights;

endend

if nargout