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Extract only diagonal elements from matrix

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I have a matrix in one variable and a list of coordinates in another variable. Is there a way to extract only the matching pairs of coordinate from the matrix? I.e. X(1),Y(1); X(2), Y(2)...
I can extract all of the permutations (X1, Y1; X1 Y2 ...X2,Y1 ... etc) and then take the diagonal, but I was wondering if there was a simple solution I'm missing to only extract the matched pairs.
Thanks,
Will
%Data
mat = rand(100);
%Coordinates
x_coord = round(rand(10,1)*100);
y_coord = round(rand(10,1)*100);
%Extract coordinates
extracted_coord = diag(mat(x_coord,y_coord));

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Accepted Answer

Image Analyst
Image Analyst on 26 Jan 2021
You can do this, where m is your matrix, and v is the vector of extracted values from the x,y locations
v = zeros(1, length(X));
for k = 1 : length(X)
row = Y(k);
col = X(k);
v(k) = m(row, col);
end
Then just repeat with a scrambled x and y - I'm sure there is some function for that. Put the various v into a matrix and use eye() to extract the diagonal.

  3 Comments

Will Bassett
Will Bassett on 29 Jan 2021
I was hoping to find something without a for loop for speed, but this works well and gets the job done. Thanks!
It feels like the kind of thing that has a one line function for it, but perhaps not.
Image Analyst
Image Analyst on 29 Jan 2021
How long was it taking?
I did a million points and it took about 78 milliseconds. If I use 1000 points, it's 0.0003 seconds. Just how many points are you going to use, and what kind of speed do you require?
mat = rand(100);
[rows, columns] = size(mat)
numPoints = 1000000
X = ceil(rand(numPoints,1)*columns);
Y = ceil(rand(numPoints,1)*rows);
tic
v = zeros(1, length(X));
for k = 1 : length(X)
row = Y(k);
col = X(k);
v(k) = mat(row, col);
end
toc
Elapsed time is 0.078826 seconds.
Will Bassett
Will Bassett on 29 Jan 2021
It was taking several seconds for me, but I was using a 2k x 2k matrix and the time consuming thing for that (in my testing) was generating the matrix. Pulling the actual points took about the same as yours. I think the speed is just fine this way.
This is much faster than making the full matrix and diagonalizing as I was doing before.
Thanks

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