#15104: Special case modn_dense matrix operations to improve performance
-------------------------------------+-------------------------------------
       Reporter:  nbruin             |        Owner:
           Type:  enhancement        |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.2
      Component:  linear algebra     |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Nils Bruin         |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/SimonKing/ticket/15104           |  0f008f9266e3ed6fbd67e7f3d357474825bdb160
   Dependencies:                     |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by SimonKing):

 * commit:  a908e28159a544ca33f03dcbf0e8def3cfe9a60e =>
     0f008f9266e3ed6fbd67e7f3d357474825bdb160


Comment:

 With your branch, I got
 {{{
 sage: k=GF(17)
 sage: A=matrix(k,100,101,[k.random_element() for i in range(100*101)])
 sage: B=matrix(k,100,100,[k.random_element() for i in range(100*100)])
 sage: %timeit At=A.transpose()
 10000 loops, best of 3: 68.5 us per loop
 sage: %timeit Bt=B.transpose()
 10000 loops, best of 3: 48.7 us per loop
 }}}
 With the additional commits that I have just pushed, I get
 {{{
 sage: k=GF(17)
 sage: A=matrix(k,100,101,[k.random_element() for i in range(100*101)])
 sage: B=matrix(k,100,100,[k.random_element() for i in range(100*100)])
 sage: %timeit At=A.transpose()
 10000 loops, best of 3: 49.9 us per loop
 sage: %timeit Bt=B.transpose()
 10000 loops, best of 3: 49.3 us per loop
 }}}
 So, looks like progress.

 My changes are: I added a lazy attribute to matrix spaces, returning the
 transposed matrix space, and I am using it in `.new_matrix()`. This has
 the advantage that it is a generic method used by different custom
 implementations of `.transpose()`. Hence, there should be a speed-up for
 all types of matrices, not only for `Matrix_modn_dense_float`.
 ----
 New commits:
 
||[http://git.sagemath.org/sage.git/commit/?id=5487c67cc851fe4febec8e61c04a526986d074f0
 5487c67]||{{{Trac 15104: Faster creation of transposed matrix' parent}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=0f008f9266e3ed6fbd67e7f3d357474825bdb160
 0f008f9]||{{{Trac 15104: Add a test for the new lazy attribute}}}||

--
Ticket URL: <http://trac.sagemath.org/ticket/15104#comment:18>
Sage <http://www.sagemath.org>
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