Can I get rid of this for loop?

I have a matrix that has 3 columns that consist of -1, 0, and 1 (let's call them the "level columns"), and a fourth column that contains real numbers (call it the "data column"). For the level columns, I want to find the average of the "-1", "0", and "1" terms in the data column. So for the following matrix,

    -1    -1     0   837
    -1     0    -1   880
    -1     0     1   879
    -1     1     0   864
     0    -1    -1   834
     0    -1     1   833
     0     0     0   874
     0     0     0   875
     0     0     0   876
     0     1    -1   860
     0     1     1   859
     1    -1     0   829
     1     0    -1   872
     1     0     1   874
     1     1     0   856

the -1 average for column 1 would be 865. Is there a way that I can do that all at once, for each level column, and each level column value? Right now, I loop over the level columns and do this:

[mean(testMat(testMat(:,col) == -1,4)) mean(testMat(testMat(:,col) == 0,4)) mean(testMat(testMat(:,col) == 1,4))]

Is there a better way?

Thanks!

Answer 1

[Stephen23]

You cannot get rid of the for loop, but you can hide it inside a cellfun call. Note that my answer works for any number of columns, unlike the other solutions.

M = [...
-1    -1     0   837
-1     0    -1   880
-1     0     1   879
-1     1     0   864
 0    -1    -1   834
 0    -1     1   833
 0     0     0   874
 0     0     0   875
 0     0     0   876
 0     1    -1   860
 0     1     1   859
 1    -1     0   829
 1     0    -1   872
 1     0     1   874
 1     1     0   856 ];
%
[~,~,X] = cellfun(@unique,num2cell(M(:,1:end-1),1),'Uni',0);
N = cellfun(@(s)accumarray(s,M(:,end),[],@mean),X, 'Uni',0);
out = [N{:}]

creates this output matrix, where the rows correspond to [-1;0;1]:

>> out
out =
        865       833.25        861.5
     858.71       875.71       858.71
     857.75       859.75       861.25

Answer 2

[Star Strider]

I would use three concatenated accumarray calls:

M = [-1    -1     0   837
    -1     0    -1   880
    -1     0     1   879
    -1     1     0   864
     0    -1    -1   834
     0    -1     1   833
     0     0     0   874
     0     0     0   875
     0     0     0   876
     0     1    -1   860
     0     1     1   859
     1    -1     0   829
     1     0    -1   872
     1     0     1   874
     1     1     0   856];

   Result = [accumarray(M(:,1)+2, M(:,4), [], @mean),  accumarray(M(:,2)+2, M(:,4), [], @mean),  accumarray(M(:,3)+2, M(:,4), [], @mean)];

Result =
          865       833.25        861.5
       858.71       875.71       858.71
       857.75       859.75       861.25

Here, the columns correspond to those in ‘M(:,1:3)’ and the rows correspond to ‘[-1; 0; 1]’ respectively.

Answer 3

[Image Analyst]

If you have the Statistics and Machine Learning Toolbox, you can use grpstats(), but I don't know if it would be any more compact that what you're already doing.