#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/nbruin/ticket/15104 | a908e28159a544ca33f03dcbf0e8def3cfe9a60e
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by nbruin):
Some timings. I changed `dense_template.transpose` to use the given parent
for square matrices.
With this inner copy loop:
{{{
for i from 0 <= i < ncols:
for j from 0 <= j < nrows:
M._entries[j+i*nrows] = self._entries[i+j*ncols]
}}}
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: 30.3 us per loop
sage: %timeit Bt=B.transpose()
100000 loops, best of 3: 11 us per loop
}}}
As you can see, parent creation overhead is still the main thing.
With this inner loop
{{{
for i from 0 <= i < ncols:
for j from 0 <= j < nrows:
M._matrix[i][j] = self._matrix[j][i]
}}}
I get:
{{{
sage: %timeit At=A.transpose()
10000 loops, best of 3: 35.8 us per loop
sage: %timeit Bt=B.transpose()
100000 loops, best of 3: 15.8 us per loop
}}}
as one of the better timings. Depending on the matrix creation, but
consistent with that fixed, I was also seeing `23.4 us`, which I guess
happens if the `._matrix` pointer array is unfortunately allocated in
memory relative to `_entries` (cache thrashing perhaps).
I've also tried:
{{{
Midx=0
for i from 0 <= i < ncols:
selfidx=i
for j from 0 <= j < nrows:
M._entries[Midx]=self._entries[selfidx]
Midx+=1
selfidx+=ncols
}}}
which was not really distinguishable from the first solution, but if
anything, slightly slower. So my guess is that a multiplication is not
something to worry about on modern CPUs.
--
Ticket URL: <http://trac.sagemath.org/ticket/15104#comment:15>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
