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From: Johan Jansson (johanjan_at_[hidden])
Date: 20030217 06:58:11
On Sat, 8 Feb 2003, Joerg Walter wrote:
> Hi Johan,
>
[...]
> On 32bit systems the upper dimensions for sparse_matrix are 65535 x 65535
> due to the internal mapping of (i, j) > (i * size2+j) (or (i + j * size1).
> I've added a corresponding check to the debug version.
>
> For larger dimension consider to use compressed_matrix (FORTRAN CRS/CCS
> format) or coordinate_matrix (FORTRAN COO format) please. I'm also assuming
> you're checking the boost_1_29_0 release, so you'll probably have to look
> into the current CVS version for these (many changes).
>
[...]
>
> Using the experimental (means undocumented ;( axpy_prod() functions one
> achieves the correct complexity.
>
[...]
>
> Alexei Novakov's benchmarks show an overhead of around 100% for the better
> ublas sparse matrix vector multiply implementations currently. He proposed
> an improvement of sparse matrix iterators already, which we'll tackle
> immediately after the upcoming 1_30_0 release.
>
> Thanks for your feedback,
>
> Joerg
>
>
Hi Joerg,
Thanks for all your info. I've run the tests with a Boost from CVS (from
january 31st), compressed_matrix and axpy_prod, and the results give
roughly the same speed as our implementation, and ca. 30% better memory
efficiency. Great! The DNDEBUG flag also seems critical, without it
performance is terrible (quadratic).
Alexei's proposed optimizations seem interesting. I tried the axpy_prod
you provided, but it didn't give any significant change. I trust your
figures however.
I will propose that we start using ublas as soon as the linear complexity
functions appear in the stable branch.
I provide our benchmark below for reference (with the timing calls, and
other dependencies stripped out):
Thanks,
Johan
 #include <iostream> #include <boost/numeric/ublas/config.hpp> #include <boost/numeric/ublas/vector.hpp> #include <boost/numeric/ublas/vector_sparse.hpp> #include <boost/numeric/ublas/matrix.hpp> #include <boost/numeric/ublas/matrix_sparse.hpp> #include <boost/numeric/ublas/io.hpp> #include <boost/numeric/ublas/operation.hpp> #define N 1000000 using namespace boost::numeric::ublas; namespace ublas = boost::numeric::ublas; typedef boost::numeric::ublas::compressed_matrix<double> uBLASSparseMatrix; typedef ublas::vector<double> uBLASVector; int main() { cout << "Benchmark for linear algebra in uBLAS" << endl; cout << "" << endl; cout << "Creating a vector with " << N << " elements" << endl; uBLASVector x(N); cout << "Creating another vector with " << N << " elements" << endl; uBLASVector y(N); cout << "Creating a " << N << " x " << N << " matrix" << endl; uBLASSparseMatrix A(N, N); cout << "Assembling" << endl; for (int i = 0; i < N; i++) { A(i,i) += 2.0; if ( i > 0 ) A(i, i  1) += 1.0; if ( i < (N1) ) A(i, i + 1) += 1.0; } cout << "Multiplying: y = A*x" << endl; axpy_prod(A, x, y); } 
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