Dag Sverre Seljebotn wrote: > I need a convenient matrix class for some numerical work. SciPy doesn't > accept GPL code and besides I heavily dislike the NumPy matrix class. So > why not put my efforts into improving Sage (or at least write something > Sage-compatible for myself)... > > In particular I need to Cholesky-factor Hermitian matrices (possibly > sparse and possibly million-by-million elements), and it would be nice > to be able to abstract away which library does the factorization (dense > or sparse) from case to case by simpling passing "sparse=True" to the > matrix function... > > Here's the list of I need (I think) -- thoughts? Would you accept this > into Sage, or should I just write my own custom class? Is it allowed to > only submit new features over RDF and CDF or should any new API item > work on all parents to be accepted? > > (Apologies if some of this is already in, I'm mostly ignorant about the > Sage matrix classes): > > 1) Efficient sparse matrix class for RDF and CDF. (I don't think this > exist currently? At least I get > sage.matrix.matrix_generic_sparse.Matrix_generic_sparse which doesn't > feel right.)
This would simply use SciPy's sparse matrix classes. > > 2) I haven't checked but I think converting all my sparse values to a > Python dict to get it into a Sage matrix would be too slow, at least it > is wasteful. So I'd like something like > > matrix(CDF, I=I, J=J, V=V, sparse=True) > > where I, J, and V are vectors containing respectively rows, columns, and > values, element by element. > > 3) Support for declaring a matrix as Hermitian (or symmetric), and then > only store half of it. Something like > > sage: a = matrix(..., hermitian=True) > sage: a[1,0] = 1+1j > sage: print a[0,1] > (1-1j) > > or perhaps > > sage: a = matrix(..., hermitian='upper') > sage: a[1,0] = 1+1j > Traceback... > ... > ValueError: Matrix is defined by its upper-triangular elements only > > This would allow storing only half the elements (and probably trigger > Cholesky solving for log_determinant etc.). > > 4) Explicit diagonal matrices. And probably explicit > lower/upper-triangular matrices as well (with efficient back-solving etc.) > > sage: a = matrix(CDF, ..., diagonal=True) > sage: a[1,0] = 2 > Traceback... > ... > ValueError: Assigning outside of diagonal on a diagonal matrix > > and similar for matrix(..., lower=True) and ...upper=True... > > 5) Call CHOLMOD to do sparse Cholesky, either through cvxopt or more > likely through a recent wrapper by Nathaniel Smith. CHOLMOD is already > in Sage through cvxopt. > > -- Dag Sverre -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
