Speed performance: Find all y-vector entries that have the same value in an x-vector of equal length.

Hi Guys,

imagine you have an x-vector

   x = [1 1 2 2 1 1];

as well as an y-vector of equal length.

    y = [1 2 3 4 5 6]

And you want to find out, which values the y-vector has at those indices where the x-vector has the value 1, as well as the y-vector values at those indices where the x-vector has the value 2. So that the solution for this example would be

solution = {[1 2 5 6], [3 4]} 

That is the first cell of 'solution' contains all y-values, that belong to the first unique x-value (1) & the second cell of it contains all y-values, that belong to the second unique x-value (2).

My ideas on how to implement this for vectors of any length are given below.

Does anybody has an idea, how to avoid the for-loop in approach A???

x = randi(10, 1, 100000);
y = randi(5, 1, 100000);

% Approach A:
tic 
xVals = unique(x); % get unique x values
tf = x == xVals';  % get true-or-false logical array (each row specifies where the n-th value of xVals occurs in x).
yVals = cell(1, size(tf,1)); % preallocate yVals
for i = 1:size(tf,1)
    yVals(i) = {y(tf(i,:))}; % Assign all y-values that belong to one xVal-entry to one cell.
end
toc

% Approach B: 
tic
[xs, id] = sort(x); % xsorted
ys = y(id); % sort y the same way x was sorted
[xVals, ia] = unique(xs);
% Divide the ys-vector into sections whose corresponding xs-indices have the same value in the xs vector.
yVals = mat2cell(ys, [1], [diff(ia)', length(ys)-sum(diff(ia))]); 
toc

% Runtimes:
%  x = randi(10, 1, 1000000);
%  y = randi(5, 1, 1000000);
%  A: Elapsed time is 0.100635 seconds.
%  B: Elapsed time is 0.149284 seconds. 

%  x = randi(100, 1, 1000000);
%  y = randi(5, 1, 1000000);
%  A: Elapsed time is 0.886396 seconds.
%  B: Elapsed time is 0.139918 seconds.

% Comparison
% A is faster than B if there are few different x-values (about 10-20). 
% The number of different x-values has high impact on speed of A.
% A is faster than B if x & y-vector are extremely long (> 100000).
% The vector length has low impact on speed of B.