Hi,

I like your ideas. But i am not sure what you mean with 1. and 2.
The problem I see is, that uBLAS right now doesn't offer the desired quality and speed for single core, let alone multi core. Therefore I will focus on the internal infrastructure instead of motivating new algorithms.

short description:
1. Rock solid implementation of the BLAS algorithms( "compute kernels")
2. Rewriting of the expression mechanic.
2.1 automatic use of the compute kernels for the operations
2.2 automatic optimisation of expressions

long description
1. Rock solid implementation of the BLAS algorithms: matrix x vector and matrix x matrix in all useful combinations (sparse/sparse dense/dense dense/sparse ... triangular/dense...etc there are a lot), but also: matrix assignment. uBLAS will not be compared in #Features but in runtime compared to Armadillo/Eigen/Atlas/GotoBlas. Having a fast implementation of this is also crucial for multi-core and distributed computations. Also all higher level decompositions (Cholesky, LU, SVD, RankDecomp,...) and triangular solvers rely on fast BLAS.

2. Rewriting of the expression mechanic. The way uBLAS is implemented right now, writing

noalias(A)+=prod(B,C)+D
or
vec = prod(prod<matrix>(B,C),vec2);

is in most cases a bad decision. The second expression wouldn't even compile without the template parameter.
What I would like to have is the following:

2.1 automatic use of the fast algorithms. That is the above expression should be translated to
axpy_prod(B,C,A,false);
noalias(A) +=D;

right now the matrix_assign algorithms are used which do a terrible job on prod(B,C).

2.2 automatic optimization of expressions. The second expression above is really inefficient. First the matrix-matrix prod is evaluated and the result is afterwards used for a single matrix-vector prod.

now compare to this:
prod(B,prod<vector>(C,d));

only 2 matrix-vector products are performed which might save 99% of the FLOPS of the first expression. So it would be better if this would be transformed automatically. Normally the user could do that himself but sometimes it is not possible. Consider a Conjugate Gradient Solver:

x=CG(A,b);

a usual pattern of A is A=XX^T+c*Identity. CG uses internally only matrix-vector products - and possibly not many of them. Therefore you don't want to compute A because it is a) slow b) might require more memory than is available. Without expression optimizations it would be impossible to write a good CG that could do that.

Greetings,
Oswin

On 07.12.2013 11:38, David Bellot wrote: