On May 14, 2014, at 10:40 AM, Jens Axel Søgaard <[email protected]> wrote:
> 2014-05-13 23:24 GMT+02:00 Matthias Felleisen <[email protected]>: >> On May 13, 2014, at 4:19 PM, Neil Toronto <[email protected]> wrote: >>> We need a predicate like >>> >>> (: flonum-matrix? (All (A) (-> (Matrix A) Boolean : (Matrix Flonum)))) >> >> >> I think in our world of types we could even have >> >> (: flonum-matrix? (All (A) (-> (Matrix A) Boolean : (TriangularMatrix A)))) >> >> and such and then dispatch to even more special solvers. It's kind of like a >> number hierarchy generalization. Just a thought. > > I think it was a mistake to represent matrices simply as naked arrays. > > If the representation were > > (struct matrix (representation-type representation properties)) > > then one could take advantage of the properties of the matrix. > > E.g. for a symmetric matrix it is enough to store the upper triangular > part (the same goes for a triangular matrix). > > This would also allow mixing computation between ones representated > as two dimensional arrays and LAPACK ones. > > Problems using a dispatch based on inspecting the matrix values: > * there are two many interesting properties to check > (symmetric, hermition, upper/lower-triangular, sparse) > * times saved is less than the time used to check > (consider the case of adding two symmetric matrices) In a typed world you could probably get rid of _almost all_ run-time costs. That's what I am saying. You provide constructors that create matrices of the right kind, the overloaded functions on matrices come with types such as +'s to keep track of properties where possible, and when you claim a regular Matrix is a Triangle, you pay -- but that's pay as you go and convenient in occurrence typing. I am sure computational scientists will understand the last step, and Vincent can help them -- Matthias ____________________ Racket Users list: http://lists.racket-lang.org/users
