How can I populate the rows of a difference matrix without using a for loop?

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Matthew Kehoe
Matthew Kehoe 2023-10-16
编辑： Matthew Kehoe 2023-10-18
I am creating Matlab code to construct the following matrix:
In my data, x and y are 101-dimensional real vectors and N is a vector of six real numbers. My Matlab implementation is
% Real inputs of length 101 for x,y and length 6 for X,Y
x = rand(1,101);
y = rand(1,101);
X = rand(6,1);
Y = rand(6,1);
n = length(x);
N = length(X);
G = zeros((N-1),2,n);
% Distance calculation
d = @(k) sqrt((X(k) - x).^2 + (Y(k) - y).^2); % L2 Norm / Euclidean distance
xdiff = @(k) (((X(1) - x) ./ d(1)) - ((X(k+1) - x) ./ d(k+1)));
ydiff = @(k) (((Y(1) - y) ./ d(1)) - ((Y(k+1) - y) ./ d(k+1)));
GBlock = @(k) [xdiff(k) ydiff(k)];
% This seems inefficient - is there a better alternative?
Z = all(G>=0,2);
for k = 1:size(G,1)
if Z(k)
G(k,:) = GBlock(k);
end
end
Creating Gblock followed by a for loop seems inefficient. Is there a way to vectorize this code and avoid writing a for loop?
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Matthew Kehoe
Matthew Kehoe 2023-10-17
编辑：Matthew Kehoe 2023-10-18
Yes, I incorrect indexed two locations of x and y. I have updated my original question.

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采纳的回答

Matt J
Matt J 2023-10-16
编辑：Matt J 2023-10-16
X=X(:);
Y=Y(:);
x=reshape(x,1,1,[]);
y=reshape(y,1,1,[]);
d=hypot( X - x , Y - y );
Diff=@(U,u) ((U(1)-u)./d(1,1,:)) - ((U(2:end) - u) ./ d(2:end,1,:));
G=[Diff(X,x), Diff(Y,y)];

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