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http://www.guwi17.de/ublas/matrix_sparse_usage.html

Example:

std::valarray<RealType> vax(size); std::valarray<RealType> vay(size); vax += vay; boost::numeric::ublas::vector<RealType> ux(size); boost::numeric::ublas::vector<RealType> uy(size); ux += uy;

The first assigned seems to be at least twice as fast as the second assignment, although the same algorithm is used. Why? UBLAS always expects that the right hand side of an expression can have common storage with the left hand side, i.e. that there is aliasing. Thus uBLAS first evaluates the right hand side into a temporary vector and then applies the changes to the left hand side. *(Update: uBLAS automatically assumes the absence of aliasing when lhs and rhs are simple containers. uBLAS can not automatically decide when the rhs is a general vector or matrix expression.)*

If you know for sure that there is no aliasing, you have to explicitly state it, either by using `noalias()` or the corresponding `*_assign()` member function.

ux .plus_assign( uy ); noalias( ux ) += uy;

$ g++-3.4 -o sample83 sample83.cpp -I $HOME/include/ -DNDEBUG -O2 -g \ -L /usr/lib/3dnow -lcblas -latlas -march=athlon -funroll-loops $ ./sample83 500 2>/dev/null size of double matrices - 500x500*500x500 (2005-06-11) prod axpy opb block goto atlas rkc rck krc kcr crk ckr RRR 2.77 1.38 1.73 0.48 0.46 0.12 1.69 3.76 2.06 7.09 2.96 7.11 RRC 1.56 1.73 1.74 0.47 0.47 0.12 3.51 1.83 2.84 7.14 1.9 7.09 RCR 6.04 1.42 1.71 0.49 0.45 0.13 1.76 6.61 2.03 4 6.69 3.08 RCC 2.63 2.77 1.73 0.48 0.45 0.12 3.53 2.96 2.81 4.03 3.9 3.03 CRR 2.61 2.63 1.73 0.48 0.46 0.12 3.04 3.78 4.05 2.81 2.91 3.44 CRC 1.13 1.69 1.76 0.48 0.46 0.13 6.98 1.9 7.01 2.86 1.85 3.45 CCR 6.05 1.62 1.73 0.49 0.47 0.11 3.07 6.66 4 1.99 6.66 1.77 CCC 2.75 1.59 1.72 0.49 0.46 0.13 6.99 3.02 6.98 2.04 3.86 1.72(first column gives storage orientation of X, A and B, other columns present times on an Athlon XP (1466MHz) for X += A*B using different products) source:

Users on the mailing list replied:

- An important design goal of ublas is to be as general as possible. Otherwise blas are very special. So AFAIR we decided not to invest to much time into connecting ublas and blas, but to concentrate on correctness of the algorithms. I think the consense was first to provide an easy to use interface and (long long time later ;-) maximize performance.

- Performance is important, and without high performance I would not be allowed to use the super-computers I have access to, but correctness is more important. And please be aware, that there are vendor supplied BLAS implementations which are just very lazy with accuracy, especially on the Itanium 2, so a reliable implementation is crucial for me to check the correctness of the code. And yes, I do get different results, depending on the BLAS implementation I use in the case I work with not-so well conditioned matrices, and it is _not_ a bug in my code.

Results for other data types

size of float matrices - 500x500*500x500 prod axpy opb block goto atlas rkc rck krc kcr crk ckr RRR 1.14 0.86 0.99 0.46 0.45 0.11 1.02 2.65 1.29 4.56 1.66 4.39 RRC 0.86 0.96 1.01 0.45 0.43 0.1 2.24 1.18 1.4 4.58 1.25 4.42 RCR 3.5 0.91 0.98 0.47 0.44 0.11 1.06 4.36 1.25 2.6 4.46 1.54 RCC 1.01 1.28 1 0.45 0.44 0.1 2.28 1.48 1.34 2.64 2.62 1.5 CRR 1.03 1.1 1.01 0.45 0.43 0.1 1.49 2.7 2.66 1.35 1.61 2.19 CRC 0.88 0.94 1.02 0.44 0.43 0.11 4.36 1.27 4.5 1.37 1.19 2.17 CCR 3.5 0.93 0.98 0.47 0.44 0.1 1.54 4.38 2.62 1.21 4.41 1.06 CCC 1.05 0.88 0.99 0.45 0.43 0.11 4.4 1.6 4.51 1.24 2.55 1.04

**Q**: Why can't I initialize a vector from `zero_vector`?

typedef ublas::zero_vector<double> zero_vec; typedef ublas::vector<double> Vector; std::size_t N = 5; Vector vec(zero_vec(N)); // compile error

**A**: This syntax declares a function taking one argument, a `zero_vec` named `N`, and
returning `Vector`. You have to make it not look like a function:

Vector vec((zero_vec(N))); // extra brackets Vector vec = zero_vec(N);

**Q**: how can I get a row out as a STL vector if I have data in a STL vector, how do I get it into a ublas vector/matrix?

**A**: You can always use `std::copy(ublas_container.begin(), ublas_container.end(), stl_container.begin());`
and `std::copy(stl_container.begin(), stl_container.end(), ublas_container.begin());` if they have the same size.

**Q**: Why is ublas so slow when I use 3x3 matrices and vectors of size 3?

**A**: Because the main development was on (large) dynamic sized matrices and sparse or structured matrices. For small fixed size linear algebra you should have a look at tvmet[2].

**Q**: I get compile errors with potrs, symm, symv, syrk, ...

**A**: The ublas::symmetric_matrix uses packed storage but the above functions require a dense matrix. Try to use the TP, SP ord HP versions of your BLAS-lib. LAPACK usually operates on dense matrices.

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