Find indices of points in meshgrid-like data

Hi,

I'm looking for an optimal solution to the following problem:

You are given a vector containing coordinates x,y for set of points e.g.:

A = [2 3; 3 4; 1 1];

given that the full-data is structured in a matrix form (meshgrid-like)

[X,Y] = meshgrid(1:5, 1:5);

find indices B, such that:

A = [X(B), Y(B)];

I am able to solve this problem simply by looping over all points in A and finding the index with

for pt = 1:size(A,1);
  index(pt) = find(A(pt,1)== X & A(pt,2) == Y);
end

However I'm not satisfied with the performance of this solution as I am running through ~50,000 data points around 300 times, and I'd love to replace the for loop with some vectorized formula.

Any help would be highly appreciated!

Thanks,

Alex

Answer 1

[Adam]

[~, index] = ismember( A, [X(:) Y(:)], 'rows' );

Not sure if that is any faster than a loop though. ismember is not a very performant function as, if I remember correctly, it contains quite a lot of checks that slow it down.

[Aleksander Marek]

It actually works really well, and gives improvement of about 10 times over the for loop.

Thanks a lot!

Answer 2

[Bish Erbas]

How about this?

A = [2 3; 3 4; 1 1];
[X,Y] = meshgrid(1:5, 1:5);
XIdxCell = arrayfun(@(x) find(X==x),A(:,1),'UniformOutput',false);
YIdxCell = arrayfun(@(x) find(Y==x),A(:,2),'UniformOutput',false);
XIdx = cell2mat(XIdxCell);
YIdx = cell2mat(YIdxCell);
A = [X(XIdx), Y(YIdx)]