Hi Martin,
On 12 Jul., 19:48, Martin Albrecht <martinralbre...@googlemail.com>
wrote:
> As far as I know it's the fastest implementation for medium size primes (16
> bits or so). For very small primes one can do better
But actually linbox is already much faster over GF(3) than what is
currently done in Sage.
> It's a shame we are not using the libraries we ship to full potential but so
> far no one stepped up (me included) to fix this situation.
OK, but how much work would be needed? It appears to me that there is
only very little overhead in calling the linbox routines (via
sage.libs.linbox.linbox), since the data of a Matrix_modn_dense is
already stored in the same format used by linbox (namely mod_int **).
In particular, I wounder about your statement that the memory
consumption would increase. Is that because of internal linbox
computations?
Here is how linbox is wrapped (see
sage.matrix.matrix_modn_dense.Matrix_modn_dense._multiply_linbox):
...
self._init_linbox()
sig_on()
linbox.matrix_matrix_multiply(ans._matrix, B._matrix,
B._nrows, B._ncols)
sig_off()
self._init_linbox() seems rather light-weight, and
linbox.matrix_multiply is also a very thin wrapper of the linbox
routines. Similarly, one proceeds with other routines (computing
echelon form and so on)
Actually I think it would even be easy enough to call the linbox
routines directly (without using the sage.libs.linbox.linbox wrapper,
thus avoiding all overhead). Since I need fast matrix arithmetics over
finite fields, I have some motivation to rewrite _mul_ accordingly.
But one question: Can linbox deal with non-prime finite fields?
Cheers,
Simon
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