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.
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
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