Re: [eigen] projects using Eigen2 ?

["Benoit Jacob" <jacob.benoit.1@xxxxxxxxx>]

One more remark: for what you're doing it's really much better if
christoffel is actually stored in row-major order as this makes the
rowwise sum do only contiguous memory accesses. Especially if n is
large enough (i guess it is say >= 10 otherwise you'd be using
fixed-size, right?) you'll benefit from vectorization.

Cheers,
Benoit

2008/12/6 Benoit Jacob <jacob.benoit.1@xxxxxxxxx>:
> Thanks, i'll add the link to the wiki.
>
> 2008/12/6 Timothy Hunter <tjhunter@xxxxxxxxxxxx>:
>> while the eigen-specific parts are located at:
>> http://personalrobots.svn.sourceforge.net/viewvc/personalrobots/pkg/trunk/controllers/control_toolbox/
>> (in include/ for the template code, src/serial_chain_model.cpp and
>> test/ for the test units)
>
> OK so I search occurences of "Eigen::" in this file and comment below:
>
>   90   Eigen::MatrixXd M(n,n);
>   91   NEWMAT::Matrix mass(n,n);
>   92   chain_->computeMassMatrix(kdl_q,kdl_torque_,mass);
>   93   for(int i=0;i<n;i++)
>   94     for(int j=0;j<n;j++)
>   95       M(i,j)=mass(i+1,j+1);
>
> Here, if the storage order (colmajor or rowmajor) (Eigen defaults to
> column-major) is the same for M and mass, instead of this double for
> loop, you are better off using a Eigen::Map as it will potentially
> vectorize.
>
> Something like  (using Eigen trunk):
> M = Eigen::MatrixXd::Map(mass.array_of_coefficients(), n, n);
>
> Now if mass is row-major, but it is a priority for you to optimize the
> copying from mass to M, then you can just declare M as a row-major
> matrix:
> Eigen::Matrix<double,Eigen::Dynamic,Eigen::Dynamic,Eigen::RowMajor> M(n,n);
>
>  102 //   ROS_DEBUG("5-");
>  103   for(int i=0;i<n;i++)
>  104     for(int j=0;j<n;j++)
>  105       for(int k=0;k<n;k++)
>  106         Q(i,j)+=christoffel(i*n+j+1,k+1)*kdl_q_dot(j);
>
> When I see this i want to cry "use Eigen expressions" but it's
> nontrivial as you're mixing Eigen with NEWMAT matrices.
> Again, assuming that you know the storage order of NEWMAT, you can get
> away with a Eigen::Map. Assuming it's column-major:
> Eigen::Map<Eigen::MatrixXd>
> map_christoffel(christoffel.array_of_coefficients(), n*n, n);
> for(int i=0;i<n;i++)
>  for(int j=0;j<n;j++)
>    Q(i,j) += map_christoffel.row(i*n+j).sum() * kdl_q_dot(j);
>       // notice that you were doing unnecessary multiplications in
> the inner loop as kdl_q_dot(j) didn't depend on k
>
> Now from here we can see a further simplification using
> rowwise().sum() and a dot product:
>
> #include<Eigen/Array>
> Eigen::Map<Eigen::MatrixXd>
> map_christoffel(christoffel.array_of_coefficients(), n*n, n);
> for(int i=0;i<n;i++)
>  Q.row(i) += map_christoffel.rowwise().sum().segment(i*n,n).dot(kdl_q_dot);
>
> Here I'm handling kdl_q_dot as a Eigen:: vector, i know that's not the
> case, but assuming it's stored contiguously in memory you can handle
> that again with a Eigen::Map.
>
> As you can see using Eigen expressions you go from 3 for loops down to
> 1. Assuming that the compiler isn't confused by that c++ abstraction,
> normally you can get much better performance. Do benchmark it before
> using it in production as we sometimes have bad surprises, depending
> on the version of GCC, sometimes complex expressions are poorly
> optimized.
>
> I'll stop here for now:)
>
> Cheers,
> Benoit
>

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