How to improve the speed of computing trace in my code?

Hi all,

In my code there is a key function which cost the majority of computational power due to the large number of repetitive computations. Imagine I have 2 cell arrays 'respi' and 'respj' which contains results of SVD vectors:

>> respi

respi =

    1×10 cell array

    Columns 1 through 9

      {3×1 cell}    {3×1 cell}    {3×1 cell}    {3×1 cell}    {3×1 cell}    {3×1 cell}    {3×1 cell}    {3×1 cell}    {3×1 cell}

    Column 10

      {3×1 cell}

>> respi{1}

ans =

    3×1 cell array

      {242×5 double}
      {  5×5 double}
      {  3×5 double}

I have a function which takes respi and respj, compute and store the trace as follows

function otpt = uTuPartDemo(respi, respj)

otpt = zeros(length(respi), length(respj));

for iTr = 1:length(respi)
    u1 = respi{iTr}; % find the ith cell element.
    for jTr = 1:length(respj)
        u2 = respj{jTr}; % find the jth cell element
        otpt(iTr, jTr) = ... % compute the trace.
            trace((u2{3}' * u1{3}) * u1{2}' * (u1{1}' * u2{1}) * u2{2});
    end
end

And I need to run this function repetitively for many times as follows:

for i = 1:n % very large number, say n = 100000
    otpt = uTuPartDemo(respi, respj);
end

How can I improve the speed and efficiency of function uTuPartDemo? Many thanks!

Answer 1

[Pieter Hamming]

Presumably the trace calculation takes most time. Since you're only interested in the diagonals anyway, why not use the approach explained here. It should reduce your computational strain.

A minor other issue: you don't need to define u1 and u2. Instead of

 u1 = respi{iTr};
 u1{3}

Just use

 respi{iTr}{3}

It will save you a minor amount of memory.

[Xiaohan Du]

Hi Pieter,

Before trying this approach, I'd like to know if I need to recover the matrix before SVD (i.e. computing A = u1{1} * u1{2} * u1{3}', B = u2{1} * u2{2} * u2{3}'), then compute sum(A.*B',2)?