You should be able to do it if you want to convert a sparse to a dense matrix like

.. matrix<double>( my_sparse_matrix) ..

we just don't want surprise implicit conversions.


Date: Thu, 28 Jan 2016 02:09:10 +0100
Subject: Re: [ublas] Matrix multiplication performance

Referring to the point 1:

1. It is called  only if both arguments are dense matrices, or one dense matrix and one dense vector. We should disable any implicit conversions to avoid surprises like converting a sparse matrix to a dense one

I think that it should be possible uncompress partially spare matrices in small buffers, use SIMD for calculations and then assign the result to result matrix.

Joaquim Duran

2016-01-27 16:18 GMT+01:00 nasos <>:
We would definitely like to adopt an implementation like this. We need though to make sure:

1. It is called  only if both arguments are dense matrices, or one dense matrix and one dense vector. We should disable any implicit conversions to avoid surprises like converting a sparse matrix to a dense one

2. We should provide extensive benchmarks for a large range of matrix sizes.

3. We should setup benchmarks that find optimal sizes for the micro and meso kernels. These benchmarks may be slow and we may want to find a way to publish optimal sizes for various architectures. Maybe just include them in a readme file.

4. We should provide an interface to compile with these optimal sizes. Provide fallback when these are not provided

5. ublas is one of the fastest libraries for small matrices. Because I think the most prevalent use of dense multiplication is on small matrices ( geometric transformations etc.) we need to make sure this stays that way.

Concerning 3, please note that my experience is that there is not a single combination that is optimal for all matrix sizes and this is reflected in the previous developments in the fast matrix multiplication branch on github. I hope we can find a good compromise.

I will  create a branch with the aim to create an implementation that embodies 1-4 and uses Michael's work. I apologize for not having a lot of time to invest in this endeavor atm but I think if I make an outline of the integration requirements we can work it out through pull requests. When things are setup I will be running benchmarks on various architectures and compilers ( currently I have access to clang, gcc, intel and msvc)


On 01/26/2016 07:39 PM, Michael Lehn wrote:

On 23 Jan 2016, at 18:53, palik imre <> wrote:

Hi All,

what's next?  I mean what is the development process for ublas?

Now we have a C-like implementation that outperforms both the mainline, and the branch version (axpy_prod).  What will we do with that?

As far as I see we have the following options:

1) Create a C++ template magic implementation out of it.  But for this, at the least we would need compile-time access to the target instruction set.  Any idea how to do that?

2) Create a compiled library implementation out of it, and choose the implementation run-time based on the CPU capabilities.

3) Include some good defaults/defines, and hope the user will use them.

4) Don't include it, and do something completely different.

What do you think?

At the moment I am not sure, but pretty sure, that you donít have to rewrite uBLAS to support good performance.  uBLAS is a pretty fine
library and already has what you need.  So just extend it. At least for 383 lines of code :-)

As I was pretty busy the last days, so I could not continue until today.  I made some minimal modifications to adopt the GEMM implementation
to take advantage of uBLAS:

- The GEMM frame algorithm and the pack functions now work with any uBLAS matrix that supports element access through the notation A(i,j)
- Only for matrix C in the operation C <- beta*C + alpha*A*B it requires that the matrix is stored row-major or col-major.  The other matrices can
be expressions. Here I need some help to get rid of this ugly lines of code:

    TC *C_ = &C(0,0);
    const size_type incRowC = &C(1,0) - &C(0,0);
    const size_type incColC = &C(0,1) - &C(0,0);

- Things like the following should work without performance penalty (and in particularly without creating temporaries):
  blas::axpy_prod(3*A1+A2, B1 - B2, C, matprodUpdate)
- And matrices A and B can be symmetric or whatever.  Of course if A or B is triangular a specialized implementation can take advantage
- The storage format does not matter.  You can mix row-major and col-major, packed, Ö

Here is the page for this:

Please note, creating the benchmarks for the symmetric matrix-matrix product really takes long because the current uBLAS implementation seems
to be much slower than for general matrices.  So I reduced the problem size for now.  It would be helpful if some people could reproduce the benchmarks
and also check different cases:

- different expressions
- different element types, e.g. A with floats, B with double etc.  At the moment there is only a micro kernel for double.  The performance depends on the
common type of A and B.  So with complex<..> the reference implementation.  But the performance should at least be constant in this case.

It would in particular be nice to have benchmarks from people with an Intel Sandybridge or Haswell as the micro kernels are optimized for these
architectures.  If interested I can extend the benchmarks to compare with Intel MKL.  For Linux there is a free non-commercial version available.



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