RE: [eigen] Intel (R) MKL IE SpBLAS support in Eigen

Hi All,

First of all appreciate your interest in integration of sparse kernels in Eigen.

Please see my comments below

I also tried:

vec1_dense.noalias() += column_major_sparse * vec2_dense

Since this operation is not supported by mkl_sparse_optimize, the overhead is null here, but for some very sparse matrices (5 nnz/col) mkl_sparse_d_mv is about x2 slower than Eigen, while for denser matrices both implementations achieve the same speed.

[akalinki] That’s sound strange. Can I ask you which MKL version do you use for your testing and what architecture is the target? We implemented matvec support in IE SparseBlas couple of years ago and significantly improve its performance during this year. Can I ask you also about the size of matrix, so I will be able to check it on my side?

I just tried your patch with:

vec1_dense.noalias() += row_major_sparse * vec2_dense

and I observe a very significant drop of performance (almost x10) compared to pure Eigen (with -fopenmp) if this operation is performed only once, or very few times... Changing the 'expected_calls' parameter from 10 to 1 does not reduce the performance drop due to mkl_sparse_optimize. If I repeat this operation hundreds of times, then both Eigen and MKL achieve the same level of performance for this particular operation and the matrices I tried (1M^2 Laplacian, bi-Laplacian, and tri-Laplacian matrices).

So I still believe that silently and unconditionally falling back to IE SpBLAS is not the right approach. It could be that calling MKL's SpBLAS is never a loss (we have to bench), but that's clearly not the case of the optimize step. So, clearly, the optimize step must be explicitly activated on user selected expressions only.

[akalinki] This can be an issue for an older version of MKL, because initially we spent additional time on doing hints/optimize when calling this every time. Starting from MKL2018u3 we’re planning to remove this overhead – if you want we can share eng. build to check performance on same binaries.

Also about poor performance of SparseBlas matvec functionality in comparison with Eigen built-in one: all these cases we interpret as issue that need to be investigated and should be fixed on our side. So I don’t think that we need to add any dispatch on Eigen level between built-in kernels and ours – all this stuff should be hidden in MKL libraries.

And back to the main question of this topic – we have customers who use Eigen on Intel processors and are interested in optimizing their code. Implementation of new SparseMatrix type will forced them to rewrite the code, that sometimes can be impossible due to different reasons. That’s why we are asking to find the way how we can just extend current SparseMatrix type to support MKL functionality.

Thanks,

Alexander Kalinkin,

PhD, Team leader, Architect or of Sparse components in Intel®MKL

From: Gael Guennebaud [mailto:gael.guennebaud@xxxxxxxxx]
Sent: Friday, April 6, 2018 5:06 AM
To: eigen <eigen@xxxxxxxxxxxxxxxxxxx>
Subject: Re: [eigen] Intel (R) MKL IE SpBLAS support in Eigen

I also tried:

vec1_dense.noalias() += column_major_sparse * vec2_dense

gael.

On Fri, Apr 6, 2018 at 1:42 PM, Gael Guennebaud <gael.guennebaud@xxxxxxxxx> wrote:

I just tried your patch with:

vec1_dense.noalias() += row_major_sparse * vec2_dense

and I observe a very significant drop of performance (almost x10) compared to pure Eigen (with -fopenmp) if this operation is performed only once, or very few times... Changing the 'expected_calls' parameter from 10 to 1 does not reduce the performance drop due to mkl_sparse_optimize. If I repeat this operation hundreds of times, then both Eigen and MKL achieve the same level of performance for this particular operation and the matrices I tried (1M^2 Laplacian, bi-Laplacian, and tri-Laplacian matrices).

So I still believe that silently and unconditionally falling back to IE SpBLAS is not the right approach. It could be that calling MKL's SpBLAS is never a loss (we have to bench), but that's clearly not the case of the optimize step. So, clearly, the optimize step must be explicitly activated on user selected expressions only.

gael

Best regards,

Maria

From: Gael Guennebaud [mailto:gael.guennebaud@xxxxxxxxx]
Sent: Thursday, April 5, 2018 2:54 PM
To: eigen <eigen@xxxxxxxxxxxxxxxxxxx>
Subject: Re: [eigen] Intel (R) MKL IE SpBLAS support in Eigen

On Thu, Apr 5, 2018 at 11:00 PM, Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx> wrote:

On 2018-04-05 15:31, Edward Lam wrote:

Would it be useful to incorporate lambda's into the interface to avoid begin/end pairs? So from the user side, we would write code like this instead:

1) Analyze and run

     SimplicialLDLT<MklSparseMatrix<double>> llt(A);
     int it = 0;
     for (int it = 0; ...; ++it) {
         if (it == 0)
             llt.matrixL().sparseAnalyzeAndRun(100, [&] { llt.solve(b); });
         else
             llt.solve(b);
         // ...
     }

2) Analyze only

     SimplicialLDLT<MklSparseMatrix<double>> llt(A);
     llt.matrixL().sparseAnalyze(100, [&] { llt.solve(b); });
     // and solve as usual

For more complicated algorithms, one can always outline the lambda and pass it into the analysis.

That would certainly clean up things a lot. Having to call
A.beginXY();
doStuff();
A.endXY();
is a very C-stylish API, which is error-prone (e.g., one of the calls might not get called, because it is masked by a wrong if-condition, or due to an exception, which is caught only outside).
This can usually be avoided with proper C++ constructs.

The advantages of the begin/end pair are that 1) this keeps the API minimal, and 2) the user can easily wrap them to accommodate its taste and usages. To avoid all sorts of redundancies, one could even write a free function on top the begin/end pair to do:

while(...) {

optimize_if(iter==0, 100, [&]{x=llt.solve(b);}, llt.matrixL());

}

and with variadic templates:

while(...) {

optimize_if(iter==0, 100, [&]{x=LU.solve(b);}, LU.matrixL(), LU.matrixU());

}

Actually, this last example is not conceivable at the moment because the factors in SparseLU are not stored in a standard compressed format, we would need to add an option to tell SparseLU to turn them to regular SparseMatrix and to use them for solving.

Anyways, all these variants are essentially syntactic sugar/implementation details, and at this stage I'm more concerned about possible shortcomings in the general approach. Is it flexible enough? I'm also not fan of introducing a MklSparseMatrix inheriting SparseMatrix, but I don't have a better offer for now that is generic and easily applicable to decompositions.

gael

However, if this is required, I would suggest to add this method not only to matrices but also to the decomposition (and pass it through to the internal matrices). Otherwise, this does not scale for decompositions which use more than one matrix (like SparseLU). And we could even let the sparseAnalyze() functions return a proxy to the decomposition which would allow writing something like:

x = llt.sparseAnalyzeAndRun(100)->solve(b);
// equivalent to
llt.sparseAnalyzeAndRun(100, [&]{x=llt.solve(b);});

or
{
auto llt_ = llt.sparseAnalyzeAndRun(100);
x = llt_-> solve(b);
y = llt_-> matrixL() * c;
} // destructor of llt_ calls `endAnalyze`

The naming of this method is still debatable, of course.
And I have no idea what actually happens inside MKL when it 'analyzes' an operation (after how many iterations do you actually benefit from the overhead of analyzing the operation?)

Christoph

Cheers,
-Edward

On 4/5/2018 8:01 AM, Gael Guennebaud wrote:

Thank you for opening this discussion on the public mailing list.

So let's discuss about the public API, which currently is not very convenient as already noticed by others. Issues are:

(i1) - Storing MKL's handle in SparseMatrix breaks ABI and does not sounds very generic.
   - We need a way to control:
(i2) - which operations are going to be analyzed/optimized,
(i3) - and specify the 'expected_calls' parameter.

In order to discuss these issues, let's consider the following typical pattern: (e.g., non-linear optimization, eigenvalues, ...)

SimplicialLDLT<SparseMatrix<double> > llt(A);

while(...) {
   ...
x = llt.solve(b);
...
}

Here the triangular L factor is going to be used for triangular and transposed-triangular solves dozens to hundreds of time but only the user of SimplicialLDLT knowns that, not SimplicialLDLT, nor SparseMatrix. Moreover, the user does not own the SparseMatrix that we want to analyze/optimize for. Other patterns are likely easier to handle, so let's focus on it for now.

Regarding (i1), I would suggest to introduce a new type, say MklSparseMatrix<> that would enhance SparseMatrix<> through inheritance. Then for (i2) and (i3) we could imagine something like:

MklSparseMatrix::beginAnalysis(Index expected_calls) const {
// turn *this to compressed mode
// create handle
// store expected_calls
// enable recording mode
}
MklSparseMatrix::endAnalysis() const {
// disable recording mode
// [optional] call mkl_sparse_optimize
}

All states in MklSparseMatrix would be mutable.

Between a pair of beginAnalysis/endAnalysis each call to a supported operation would trigger calls to mkl_sparse_set_*_hint()/mkl_sparse_optimize.
Optionally, we could even add a "dryrun" mode for which no operation would be performed, only calls to mkl_sparse_set_*_hint() and then mkl_sparse_optimize would be called in endAnalysis(). This way mkl_sparse_optimize() would be called only once.

And that's it. Our example would look-like:

SimplicialLDLT<MklSparseMatrix<double> > llt(A);
int it=0;
while(...) {
   ...
   if(it==0) llt.matrixL().beginAnalysis(100);
x = llt.solve(b);
if(it==0) llt.matrixL().endAnalysis();
...
++it;
}

or using a "dry-run" mode:

SimplicialLDLT<MklSparseMatrix<double> > llt(A);

llt.matrixL().beginAnalysis(100, DryRun);
x = llt.solve(b); // permutation and division by the diagonal matrix D would still be performed, but calls to actual triangular solves would be by-passed
llt.matrixL().endAnalysis();

while(...) {
   ...
   x = llt.solve(b);
...
}

If someone directly deal with the factor L, then we could follow the same pattern or copy the SparseMatrix factor L to a MklSparseMatrix:

SimplicialLLT<SparseMatrix<double> > llt(A);

MklSparseMatrix L(llt.matrixL());
L.beginAnalysis(100,DryRun);
y = L.triangularView<Lower>() * x;
L.endAnalysis();
while(...) {
   ...
y = L.triangularView<Lower>() * x;
...
}

This design in quite general and expendable to any sparse-optimizers, even built-in ones in the future.

In contrast to the current proposal, only selected operations would be passed to MKL (need to use a MklSparseMatrix + begin/end recording phase).

What do you think?

gael

On Tue, Apr 3, 2018 at 11:39 PM, Zhukova, Maria <maria.zhukova@xxxxxxxxx <mailto:maria.zhukova@xxxxxxxxx>> wrote:

    Hello Eigen community,

    My name is Maria Zhukova and I’m a software development engineer at Intel ®
    MKL Sparse team.

    My team is interested in contributing into Eigen, so I’ve investigated our
    possibilities and so far this is what I have:
    Eigen support different operations for sparse matrices stored in CSR and CSC
    format which can be implemented on a basis of IE SpBLAS kernels (please,
    refer to
https://software.intel.com/en-us/mkl-developer-reference-c-inspector-executor-sparse-blas-routines
<https://software.intel.com/en-us/mkl-developer-reference-c-inspector-executor-sparse-blas-routines>
    for the general idea of interfaces)
    , basically we want to implement calls to our IE SpBLAS into next
    operations:____

                     SparseMatrix + SparseMatrix (mkl_sparse_?_add)
                     SparseMatrix * DenseVector (mkl_sparse_?_mv)____

                     SparseMatrix * DenseMatrix   (mkl_sparse_?_mm)____

                     SparseMatrix * SparseMatrix (mkl_sparse_spmm),
    and Triangular solve (mkl_sparse_?_trsv).____

    I’ve already started with implementation of sparse_time_dense_impl_mkl
    kernel which is based on mkl_sparse_?_mv (included in patch).____

    This is how it will look like for user:
    *#include <Eigen/SpBLASSupport> *<-- *NEW:* IE SpBLAS include module ____

    void main () {
     SparseMatrix<double, RowMajor> A;
     Matrix<double, Dynamic, 1> x, y;

     A.makeCompressed(); /* Convert matrix A into CSR/CSC format */
    *A.createSparseHandle();*/* *NEW*: is used to create handle required for all
    IE SpBLAS routines */____

    // support of IE SpBLAS is here
    y = beta*y + alpha*A*x; /* call to mkl_sparse_?_mv with operation =
    SPARSE_OPERATION_NON_TRANSPOSE */
    y = beta*y + alpha*A.transpose()*x; /* call to mkl_sparse_?_mv with
    operation = SPARSE_OPERATION_TRANSPOSE */
    y = beta*y + alpha*A.adjoint()*x; /* call to mkl_sparse_?_mv with operation
    = SPARSE_OPERATION_CONJUGATE_TRANSPOSE */____

    *A.destroySparseHandle();* /* *NEW*: is used to delete created handle */
    }____

    __ __

    I’ve attached a draft patch including all necessary changes and would like
    to hear your feedback.
    Please, let me know if you have any questions and comments.____

    __ __

    Best regards,
    Maria____

    __ __

    __ __

    __ __

--
Dr.-Ing. Christoph Hertzberg

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