Apply function to all rows in matlab

Question

I have a function, ranker, that takes a vector and assigns numerical ranks to it in ascending order. For example,
ranker([5 1 3 600]) = [3 1 2 4] or
ranker([42 300 42 42 1 42] = [3.5 6 3.5 3.5 1 3.5] .

I am using a matrix, variable_data and I want to apply the ranker function to each row for all rows in variable data. This is my current solution, but I feel there is a way to vectorize it and have it as equally fast :p

variable_ranks = nan(size(variable_data));
for i=1:1:numel(nmac_ids)
    variable_ranks(i,:) = ranker(abs(variable_data(i,:)));
end

Answer 1

If you place the matrix rows into a cell array, you can then apply a function to each cell.

Consider this simple example of applying the SORT function to each row

a = rand(10,3);
b = cell2mat( cellfun(@sort, num2cell(a,2), 'UniformOutput',false) );
%# same as: b = sort(a,2);

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You can even do this:

b = cell2mat( arrayfun(@(i) sort(a(i,:)), 1:size(a,1), 'UniformOutput',false)' );

Again, you version with the for loop is probably faster..

Answer 2

One way would be to rewrite ranker to take array input

sizeData = size(variable_data);

[sortedData,almostRanks] = sort(abs(variable_data),2);
[rowIdx,colIdx] = ndgrid(1:sizeData(1),1:sizeData(2));
linIdx = sub2ind(sizeData,rowIdx,almostRanks);
variable_ranks = variable_data;
variable_ranks(linIdx) = colIdx;

%# break ties by finding subsequent equal entries in sorted data
[rr,cc] = find(diff(sortedData,1,2) == 0);
ii = sub2ind(sizeData,rr,cc);
ii2 = sub2ind(sizeData,rr,cc+1);
ii = sub2ind(sizeData,rr,almostRanks(ii));
ii2 = sub2ind(sizeData,rr,almostRanks(ii2));
variable_ranks(ii) = variable_ranks(ii2);

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EDIT

Instead, you can just use TIEDRANK from TMW (thanks, @Amro):

variable_rank = tiedrank(variable_data')';

Answer 3

With collaboration from Amro and Jonas

variable_ranks = tiedrank(variable_data')';

Ranker has been replaced by the Matlab function in the Stat toolbox (sorry for those who don't have it),

[R,TIEADJ] = tiedrank(X) computes the ranks of the values in the vector X. If any X values are tied, tiedrank computes their average rank. The return value TIEADJ is an adjustment for ties required by the nonparametric tests signrank and ranksum, and for the computation of Spearman's rank correlation.

TIEDRANK will compute along columns in Matlab 7.9.0 (R2009b), however it is undocumented. So by transposing the input matrix, rows turn into columns and will rank them. The second transpose is then used to organize the data in the same manner as the input. There in essence is a very classy hack :p