MATLAB: Custom coordinates into an array

arrayMATLABsub2ind

Hi,

This problem is getting me really crazy right now.

I'm trying to figure a way to make this work elegantly.

A is a N x N x N x...x N array (N is repeated M times).

N and M are integers greater than 2.

Assume a given i in {1,…,M} and a given j in {1,…N}.

I'm looking for a way to design a function that will receive A,N,M,i,j and will return

A(:,:,...,:,j,:...,:)

where j is at the i-th coordinate.

I.E. all elements who have j as their i-th coordinate, stored into a Nx…xN (M-1 times) array.

I have spent hours trying to find an elegant way to do this.

and still haven't found a lot in matlab's doc (sub2ind might come in handy eventually)

I also tried to design ':,…,:,j,:,…:' as a string and tried to pass it as an argument to A() but it does not seem to work.

I'm a bit stuck in here and I could really use a tip on this !

Thank you for your time !

Best Answer

ii = repmat({':'},1,M);
ii(i) = {j};
out = A(ii{:});

Related Solutions

MATLAB: How to efficiently find the indices

sort is your friend:

First we sort the entries of A so that like entries are adjacent

[S, iSorted] = sort(A(:));

Then we find the markers - where the value changes, plus the endpoints

markers = [0; find(diff(S)); numel(A)];

All we need to do is find the entries of iSorted corresponding to each block.

for i = 1:numel(markers)-1
  uM(i) = S(markers(i)+1);
  I{i} = iSorted(markers(i)+1:markers(i+1));
end

MATLAB: Speed up for loop in this code for calculating mutual information (maybe using GPU computing)

For a 1000x1000 matrix, this is 6 times faster already:

% Version 1:
n  = size(X, 1);
X = X.';
Y = Y.';
dx = zeros(n, n);
dy = zeros(n, n);
for j = 1:n
   Xj = X(:, j);
   Yj = Y(:, j);
   for i = j+1:n
      dx(i,j) = sqrt(sum(bsxfun(@minus, X(:, i), Xj) .^ 2));
      dy(i,j) = sqrt(sum(bsxfun(@minus, Y(:, i), Yj) .^ 2));
      dx(j,i) = dx(i,j);
      dy(j,i) = dy(i,j);
   end
end
dz = max(dx, dy);

The original function took 29.5 sec (R2016b, Core2Duo, Win7/64), and the cleaned version 5.2 sec.

Here the data are processed columnwise, which is much faster because neighboring elements are accessed much faster in the memory. Then the comparison my max() is done outside the loop. And finally the resulting matrix is symmetric and you can omit the computation of X(:,i) and X(:,j) if you have the results for X(:,j) and X(:,i) already.

I tried to vectorized the inner loop:

% Version 2:
n  = size(X, 1);
X = X.';
Y = Y.';
dx = zeros(n, n);
dy = zeros(n, n);
for j = 1:n
   dx(j+1:n,j) = sqrt(sum(bsxfun(@minus, X(:, j+1:n), X(:, j)) .^ 2, 1));
   dy(j+1:n,j) = sqrt(sum(bsxfun(@minus, Y(:, j+1:n), Y(:, j)) .^ 2, 1));
   dx(j,j+1:n) = dx(j+1:n,j);
   dy(j,j+1:n) = dy(j+1:n,j);
end
dz = max(dx, dy);

But this takes 21 sec for 1000x1000 arrays. But for smaller 100x100 inputs it is faster: 1.2 sec instead of 2.2 sec (100 iterations).

Now you have an efficient function to start a parallelization or computation on the GPU. Maybe this is useful (I cannot test it):

% Version 3:
parfor v = 1:2
  if v == 1
    for j = 1:n
      dx(j+1:n, j) = sqrt(sum((X(:, j+1:n) - X(:, j)) .^ 2, 1));
      dx(j, j+1:n) = dx(j+1:n, j);
    end
  else
    for j = 1:n
      dy(j+1:n, j) = sqrt(sum((Y(:, j+1:n) - Y(:, j)) .^ 2, 1));
      dy(j, j+1:n) = dy(j+1:n, j);
    end
  end
end

But parfor for the inner loop will use more cores.

Best Answer

Related Solutions

MATLAB: How to efficiently find the indices

MATLAB: Speed up for loop in this code for calculating mutual information (maybe using GPU computing)

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