RE: [eigen] Matrix multiplication seems to be exceptionally slow in one specific case

[<Thijs.Kooi@xxxxxxxxxxxxx>]

Thanks for the feedback! Yes, you're right there is still a bug in there, I didn't get to debugging it. Compiling without without optimising also gives me an assertion error at runtime.

Thijs
________________________________________
From: Christoph Hertzberg [chtz@xxxxxxxxxxxxxxxxxxxxxxxx]
Sent: 16 June 2014 15:44
To: eigen@xxxxxxxxxxxxxxxxxxx
Subject: Re: [eigen] Matrix multiplication seems to be exceptionally slow in one specific case

Hi,

besides the already noted misuse of the auto keyword:
Your code does not run with assertions enabled, because you mix
expressions of different dimensions at several places (It's hard to find
out what you mean at some points, e.g. "M.row(n) - mu").

Furthermore, you can save some time if you use the
SelfAdjointEigenSolver (also saves the .real() conversions).
And if you store your M matrix the other way around, your for-loop will
be essentially a matrix-matrix product instead of 12498 matrix-vector
products.


Christoph

On 16.06.2014 15:14, Thijs.Kooi@xxxxxxxxxxxxx wrote:
> Hi,
>
> I am trying to implement a whitening transform using Eigen3, but I find that one of the matrix operations is extremely slow and I can't understand why. Below is the code:
>
>      MatrixXd M = convertToEigen(data);
>
>      MatrixXd mu = M.rowwise() - M.colwise().mean();
>      MatrixXd S = (mu.adjoint()*mu)/double(M.rows());
>
>      EigenSolver<MatrixXd> es(S, true);
>      auto V(es.eigenvalues());
>      auto U(es.eigenvectors());
>
>      V = V.cwiseSqrt().asDiagonal();
>      MatrixXd L(S.rows(), S.cols());
>      for(size_t d = 0; d < L.rows(); d++)
>          L(d, d) = 1./real(L(d, d));
>
>      MatrixXd Y(M.rows(), M.cols());
>      auto T = L*U.real().transpose();
>      for(size_t n = 0; n < M.rows(); n++)
>      {
>          Y.row(n) = T*(M.row(n) - mu);
>      }
>
>      Y = Y.transpose();
>
> I clocked some of the operations and find that the T*() inside the for-loop is the bottle neck, which takes about 0.047688 seconds on a 4th generation intel i7 and about the same time as the eigenvalue decomposition, which takes 0.049989 seconds, so that can't be right. M is a 12498 x 225 matrix, so T is 225 x 225 and so is mu.
> I am running Kubuntu 14.04, Eigen 3.2.0-8, which is in the repositories and all optimisation flags are turned on. Does anybody know what the problem is?
>
> Best regards,
> Thijs
>
> Het Radboudumc staat geregistreerd bij de Kamer van Koophandel in het handelsregister onder nummer 41055629.
> The Radboud university medical center is listed in the Commercial Register of the Chamber of Commerce under file number 41055629.
>


--
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Dipl.-Inf., Dipl.-Math. Christoph Hertzberg
Cartesium 0.049
Universität Bremen
Enrique-Schmidt-Straße 5
28359 Bremen

Tel: +49 (421) 218-64252
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Het Radboudumc staat geregistreerd bij de Kamer van Koophandel in het handelsregister onder nummer 41055629.
The Radboud university medical center is listed in the Commercial Register of the Chamber of Commerce under file number 41055629.