On a more serious note, Matt and I have discussed the use of PETSc for sparse multidimensional array computations for dimensions greater than 2, also known as tensor computations. The associated paper describing previous work with dense arrays is
http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-210.html. There was even an unsuccessful SciDAC application proposal that described how PETSc could be used for that domain when sparsity is important. To start, all we'd need is sparse matrix x sparse matrix multiplication, which I hear the multigrid folks also need. Sparse times dense is also important. Sparse tensor factorization would also help, but I get that there are enough open math questions there that it might be impractical to try to implement something in PETSc in the near future.
Maybe I am just biased because I spend all of my time reading
www.nextplatform.com, but I hear machine learning is becoming an important HPC workload. While the most hyped efforts related to running inaccurate - the technical term is half-precision - dense matrix multiplication as fast as possible, I suspect that more elegant approaches will prevail. Presumably there is something that PETSc can do to enable machine learning algorithms. As most of the existing approaches use silly programming models based on MapReduce, it can't be too hard for PETSc to do better.