Re: [ublas] [ublas-dev] poor vector/matrix-proxy performance

From: Peter Schmitteckert (peter_at_[hidden])
Date: 2005-08-25 01:08:03

Dear Gunter,

On Wed, 24 Aug 2005, Gunter Winkler wrote:

> The table lists the times for performing the cholesky decomposition of
> different matrix types and sizes. The first line of each block shows the
> decomposition time of a dense matrix (only accessing the lower triangle). The
> second line uses a (lower) triangular_matrix. This should at least be as fast
> as the dense case but takes 3 times as long. The third line show the times
> for a banded matrix with (at most) 50 bands below the diagonal. (If the
> banded matrix has all maximal possible bands it is even slower than the
> triangular matrix.)
>
> I suspect the matrix rows/columns and vector ranges to be the source of the
> slow down. So I have to do more research on that.

Just as a hint, in my application I suffer large performance problems
from various matrix_assign calls, which are very pronounced on
the Itanium architecture.

> see http://www.bauv.unibw-muenchen.de/~winkler/ublas/examples/
>
> Do you have an idea how to reduce the slow down?

I've changed the following lines to be able to compile
with boost_1_33:

    // use dense matrix
    ublas::matrix<DBL> A ( ublas::zero_matrix<DBL>(size, size) );
    ublas::matrix<DBL> T (size, size);
    ublas::matrix<DBL> L (size, size);

    //A = ublas::zero_matrix<DBL>(size, size);

and compiled with

g++-3.3 -I /home/peter/Boost/boost-stable -O2 -g -pg cholesky_test.cpp  -o C

then a

./C 100
qprof C > Q.out

Most of the time is spend in the access function like operator [], (),
element etc. And the timinig indictaed, that the access for the
triangular matrices is more expensive then for the normal.

Of course, I made the usual mistake and repeated the profiliung with

g++-3.3 -DNDEBUG -I /home/peter/Boost/boost-stable -O2 -g -pg cholesky_test.cpp  -o C

Now I find that most of the time is spent in

 time   seconds   seconds    calls  ms/call  ms/call  name
 45.46      0.45     0.45        1   450.05   563.67  void
boost::numeric::ublas::indexing_matrix_assign<boost::numeric::ublas::scalar_assign,
boost::numeric::ublas::matrix<double,
boost::numeric::ublas::basic_row_major<unsigned int, int>,
boost::numeric::ublas::unbounded_array<double, std::allocator<double> > >,
boost::numeric::ublas::matrix_matrix_binary<boost::numeric::ublas::matrix<double,
boost::numeric::ublas::basic_row_major<unsigned int, int>,
boost::numeric::ublas::unbounded_array<double, std::allocator<double> > >,
boost::numeric::ublas::matrix_unary2<boost::numeric::ublas::matrix<double,
boost::numeric::ublas::basic_row_major<unsigned int, int>,
boost::numeric::ublas::unbounded_array<double, std::allocator<double> > >,
boost::numeric::ublas::scalar_identity<double> >,
boost::numeric::ublas::matrix_matrix_prod<double, double, double> >
>(boost::numeric::ublas::matrix<double,
boost::numeric::ublas::basic_row_major<unsigned int, int>,
boost::numeric::ublas::unbounded_array<double, std::allocator<double> >
>&,
boost::numeric::ublas::matrix_expression<boost::numeric::ublas::matrix_matrix_binary<boost::numeric::ublas::matrix<double,
boost::numeric::ublas::basic_row_major<unsigned int, int>,
boost::numeric::ublas::unbounded_array<double, std::allocator<double> > >,
boost::numeric::ublas::matrix_unary2<boost::numeric::ublas::matrix<double,
boost::numeric::ublas::basic_row_major<unsigned int, int>,
boost::numeric::ublas::unbounded_array<double, std::allocator<double> > >,
boost::numeric::ublas::scalar_identity<double> >,
boost::numeric::ublas::matrix_matrix_prod<double, double, double> > >
const&, boost::numeric::ublas::row_major_tag)

Interestingly, -funroll-loops seems to help the first version slightly,
but not the second one.

Best regards,
Peter