[petsc-users] [dev at libelemental.org] Re: The product of two MPIDENSE matrices

S V N Vishwanathan vishy at stat.purdue.edu
Tue Oct 1 20:03:20 CDT 2013

> You can use MatTransposeMatMult with an MPIAIJ and a MPIDENSE.  (This
> is the standard case mentioned earlier, and I don't understand what
> Elemental is offering you in this situation.  Do you have other dense
> matrices running around?)

Perhaps I should give a bit of background on what we are trying to
achieve and the experts in the lists can give us some advice.

We are trying to find a k rank approximation to a n x m x p tensor
T. Here, n, m, p are of the order of millions but k is very small,
typically somewhere between 10 and 100. Also T is extremely sparse (nnz
is typically around 500 million or so).

Let A (size n x k), B(m x k) and C (p x k) be the factors. 

We are flattening the tensor along each of the three dimensions and
representing them as three matrices T1 (size n x mp), T2 (size m x np)
and T3 (size p x mn), all in MPIAIJ format.  

One of the intermediate computations that we perform is form the k x k
matrix A^T A. Another computation that we perform is to compute A^T T1.

If we set A to be MPIDENSE then PETSc cannot compute A^T A. So we
thought about using Elemental. But now the issue we are running into is
that we cannot form A^T T1 if A is of type MATELEMENTAL. 

Also somewhere in our code, we form a k x k matrix, collect it in one of
the processors and invert it and broadcast it back to all the other
processors. We need to use Cholesky or LU factorization for this



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