title: Use a vector to index a matrix without linear index
body: <p>G'day,
  I'm trying to find a way to use a vector of [x,y] points to index from a large matrix in MATLAB.
  Usually, I would convert the subscript points to the linear index of the matrix.(for eg. <a href="https://stackoverflow.com/questions/5904488/use-a-vector-as-an-index-to-a-matrix-in-matlab">Use a vector as an index to a matrix</a>) However, the matrix is 4-dimensional, and I want to take all of the elements of the 3rd and 4th dimensions that have the same 1st and 2nd dimension.  Let me hopefully demonstrate with an example:</p>
  
  <pre><code>Matrix = nan(4,4,2,2); % where the dimensions are (x,y,depth,time)
  Matrix(1,2,:,:) = 999; % note that this value could change in depth (3rd dim) and time (4th time) 
  Matrix(3,4,:,:) = 888; % note that this value could change in depth (3rd dim) and time (4th time) 
  Matrix(4,4,:,:) = 124;
  </code></pre>
  
  <p>Now, I want to be able to index with the subscripts (1,2) and (3,4), etc and return not only the 999 and 888 which exist in <code>Matrix(:,:,1,1)</code> but the contents which exist at <code>Matrix(:,:,1,2)</code>,<code>Matrix(:,:,2,1)</code> and <code>Matrix(:,:,2,2)</code>, and so on (IRL, the dimensions of <code>Matrix</code> might be more like <code>size(Matrix) = (300 250 30 200)</code></p>
  
  <p>I don't want to use linear indices because I would like the results to be in a similar vector fashion. For example, I would like a result which is something like:</p>
  
  <pre><code>ans(time=1)
  999 888 124
  999 888 124
  ans(time=2)
  etc etc etc
  etc etc etc
  </code></pre>
  
  <p>I'd also like to add that due to the size of the matrix I'm dealing with, speed is an issue here - thus why I'd like to use subscript indices to index to the data.</p>
  
  <p>I should also mention that (unlike this question: <a href="https://stackoverflow.com/questions/1146719/accessing-values-using-subscripts-without-using-sub2ind?rq=1">Accessing values using subscripts without using sub2ind</a>) since I want all the information stored in the extra dimensions, 3 and 4, of the i and jth indices, I don't think that a slightly faster version of <code>sub2ind</code> still would not cut it..</p>