Ref. on compilation of abstract mixed dense-sparse matrix operations

Does anybody have some references on the following problem:


I have multi-dimensionnal matrices that have complex mixed dense and
sparse storage schemes. The storage is defined by equations so a dense
storage would be a j0=i*step+offset type relation and sparse structures
are defined with extra index vectors (or matrices) like j0 = s[i]. Being
multi-dimensional, a single matrix can mix in a abitrary fashion the dense
and sparse equations.


I want to compile operations involving these matrices.


Obviously I need to solve the equations that describe the different matrix
structure given the constraints of the operations. I am currently working
on this in a very direct heuristic rule way. I find the dependency
relations and then try to match patterns and when all failes generate a
very inefficient code.


I have found literature on specific sparsity structure compilation (the
typical parallelize fortran stuff) but nothing on a general formulation of
the problem. Does anybody have any references?
__________________________________________________________________


James Litsios Phone: +41 1/632 60 92
Integrated Systems Laboratory Fax: +41 1/252 09 94
ETH Zurich E-Mail:litsios@iis.ee.ethz.ch
CH-8092 Zurich, Switzerland
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