Calculating means in large matrix using logical indexing

Hi there,

I have a large data matrix in which I want to calculate the average of elements satisfying certain conditions. The matrix has around 15 million rows.

There are two columns which are stored as a vector containing the conditions to be met:

elementIDs 15m x 1 (Containing the numbers 1 to 9664)
gridIDs 15m x 1 (Containing the numbers 1 to 3)

I want to know the average Reynolds number of each element in each grid. The Reynolds numbers are stored in:

Re 15m x 1 (Containing doubles)

The results are to be stored in a matrix with each element a row and each grid a column:

meanRe = 9664 x 3.

To illustrate this problem example I wrote the following:

% Initiate test data
n_rows = 150000 % In practice 15 000 000
elementIDs = randi(9664,n_rows,1);
gridIDs = randi(3,n_rows,1);
Re = rand(n_rows,1).*1000;
% Pre-allocate space
meanRe = zeros(9664,3);
% Timer
tic
% Loop over subsets to speed up the process
for kk = 1:3
  % Select subset using logical indexing
  Re_temp = Re(gridIDs==kk);
  elementIDs_temp = elementIDs(gridIDs==kk);
  % Loop over each element
  for ii = 1:9664
    % Calculate mean Reynolds using logical index
    meanRe(ii,kk) = mean(Re_temp(elementIDs_temp==ii));
    end
end
toc

Although for the amount of data the code runs fairly quick I still have to wait several minutes. Is their anyway to speed this code up significantly?

Answer 1

[Matt J]

 subs=[elementIDs, gridIDs];
 totals=accumarray(subs,Re);
 counts=accumarray(subs,ones(size(Re)));

 meanRe=totals./counts;

[Ernst Jan]

Great! I am wondering about the inner structure of this function.