[petsc-users] I am wondering if there is a way to implement SPMM

[Matthew Knepley]

On Tue, Aug 4, 2015 at 5:31 AM, Cong Li <solvercorleone at gmail.com> wrote:

> Actually, I am trying to implement s-step krylov subspace method.
> I want to extend the Krylov subspace by s dimensions by using monomial,
> which can be defined as C={X, AX, A^2X, ... , A^sX},  in one loop. So, my
> plan now is to firstly calculate the recurrence, which is P_n(x)=xP_n-1(x),
> and then use the results to update the items in C. And then, in the next
> loop of Krylov subspace method, the C will be updated again. This means I
> need to update C in every iteration.
> This continues till the convergence criteria is satisfied.
>
> I suppose A is huge sparse SPD matrix with millions of rows, and X is
> tall-skinny dense matrix.
>
> Do you still think MATNEST is a good way to define C.
>
> Actually I am wondering if there is a way to do SPMM by using a submatrix
> of C and also store the result in a submatrix of C.  If it is possible, I
> think we can remove some of cost of data movement.
> For example, C=[c_1, c_2,.., c_s], and I want to use the result of A*c_1
> to update c_2, and then use he result of A*c_2(updated) to update c_3 and
> so on.
> I don't need the intermediate result separately, such as the result of
> A*c_1, A*c_2. And I only need the final C.
> Is there any SPMM function or strategies I can use to achievement this?
>

So there are two optimizations here:

  1) Communication: You only communicate every s steps. If you are solving
a transport dominated problem, this can make sense.
      For elliptic problems, I think it makes no difference at all.

  2) Computation: You can alleviate bandwidth pressure by acting on
multiple vectors at once.

I would first implement this naively with a collection of Vecs to check
that 1) makes a difference for your problem.
If it does, then I think 2) can best be accomplished by using a TAIJ matrix
and a long Vec, where you shift the
memory at each iterate.

  Thanks,

     Matt


> Thanks
>
> Cong Li
>
>
>
> On Tue, Aug 4, 2015 at 6:46 PM, Patrick Sanan <patrick.sanan at gmail.com>
> wrote:
>
>> On Tue, Aug 04, 2015 at 06:09:30PM +0900, Cong Li wrote:
>> > I am sorry that I should have explained it more clearly.
>> > Actually I want to compute a recurrence.
>> >
>> > Like, I want to firstly compute A*X1=B1, and then calculate A*B1=B2,
>> > A*B2=B3 and so on.
>> > Finally I want to combine all these results into a bigger matrix
>> C=[B1,B2
>> > ...]
>> >
>> > Is there any way to do this efficiently.
>> With no other information about your problem, one literal solution might
>> be to use MATNEST to define C once you have computed B1,B2,..
>> However, this invites questions about what you plan to do with C and
>> whether you require explicit representations of some or all of these
>> matrices, and what problem sizes you are considering.
>> >
>> >
>> >
>> > On Tue, Aug 4, 2015 at 5:45 PM, Patrick Sanan <patrick.sanan at gmail.com>
>> > wrote:
>> >
>> > > On Tue, Aug 04, 2015 at 03:42:14PM +0900, Cong Li wrote:
>> > > > Thanks for your reply.
>> > > >
>> > > > I have an other question.
>> > > > I want to do SPMM several times and combine result matrices into one
>> > > bigger
>> > > > matrix.
>> > > > for example
>> > > > I firstly calculate AX1=B1, AX2=B2 ...
>> > > > then I want to combine B1, B2.. to get a C, where C=[B1,B2...]
>> > > >
>> > > > Could you please suggest a way of how to do this.
>> > > This is just linear algebra, nothing to do with PETSc specifically.
>> > > A * [X1, X2, ... ] = [AX1, AX2, ...]
>> > > >
>> > > > Thanks
>> > > >
>> > > > Cong Li
>> > > >
>> > > > On Tue, Aug 4, 2015 at 3:27 PM, Jed Brown <jed at jedbrown.org> wrote:
>> > > >
>> > > > > Cong Li <solvercorleone at gmail.com> writes:
>> > > > >
>> > > > > > Hello,
>> > > > > >
>> > > > > > I am a PhD student using PETsc for my research.
>> > > > > > I am wondering if there is a way to implement SPMM (Sparse
>> > > matrix-matrix
>> > > > > > multiplication) by using PETSc.
>> > > > >
>> > > > >
>> > > > >
>> > >
>> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatMatMult.html
>> > > > >
>> > >
>>
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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