Dag Sverre Seljebotn wrote: > I'm in the process of writing a PermutationMatrix class (applications: > friendly interface to permuted decompositions, etc.): > > sage: P = permutation_matrix([0, 2, 1]); P > [1 0 0] > [0 0 1] > [0 1 0] > sage: parent(P) > Full MatrixSpace of 3 by 3 sparse matrices over Integer Ring > sage: P * A # calls A.matrix_from_rows([0, 2, 1]) > ...and so on > > > My goal is to allow to treat a permutation (stored efficiently) as much > as possible like an (immutable) sparse matrix. When doing this I'm > growing aware of some issues with matrices and mutability. > > 1) A matrix transpose() is currently always mutable in all > implementations. This is a rather huge issue here. Would it be OK to > have the transpose of an immutable matrix always be immutable, unless > mutable=True is passed? > > Having P.transpose() be mutable requires conversion to a less efficient > mutable matrix loosing the permutation-ness. This has a few other > applications as well (caching transposes, automatically making use of > matrix decompositions already computed for the transpose). > > 2) In the same spirit, change_ring sometimes returns an immutable matrix > (if no change was needed and self is returned), and sometimes not: > > Always returns a copy (unless self is immutable, in which case > returns self). > > This is hardly a useful IMO -- would it be OK to change it so that one > had to pass mutable=True to get a mutable matrix, and otherwise it was > always immutable? This would allow PermutationMatrix to change rings to > another permutation matrix.
Essential correction: A.change_ring(..) would always return a matrix with the same mutability status as A, unless the mutable flag is set. This makes it consistent with my proposal for transpose. Dag Sverre > > 3) Perhaps more controversial: Allow immutability to propagate. > Currently, "2*P*A" can be much slower than "2*(P*A)" because "2*P" must > be a mutable matrix. If the product of two immutable matrices, or an > immutable matrix with a scalar, was itself immutable, this would be > trivial to speed up (2*P would be a new "permutation matrix" simply > returning 2 instead of 1). > > Again, this might have applications to cached matrix decompositions > (transform existing decompositions rather than recompute), though I'm > not sure if that is useful. > -- 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
