On Mon, Feb 13, 2012 at 9:59 AM, Pierre <pierre.guil...@gmail.com> wrote: > I see. Well I *do* have hundreds of 2x2 matrices to multiply out so > i'm better off storing them as numpy matrices throughout... thanks for > your explanations though. > > Pierre
You might consider using Cython and writing a custom 2x2 matrix class. It wouldn't be difficult... so I'll write one right now and respond with the benchmarks. -- William > > On 13 fév, 18:32, Robert Bradshaw <rober...@math.washington.edu> > wrote: >> On Sun, Feb 12, 2012 at 4:30 PM, Nils Bruin <nbr...@sfu.ca> wrote: >> > On Feb 12, 1:39 pm, Pierre <pierre.guil...@gmail.com> wrote: >> >> i think zz above might still be considered as a 1 x 1 matrix instead >> >> of a complex number, somehow, and this may be slowing things down. >> > No, that's not the problem. It's simply that numpy's default complex >> > number type is apparently a bit slower for individual element >> > arithmetic. It may well be that you're mainly measuring overhead, >> > though, so you should really test in a more representative situation >> > before committing to a particular implementation choice. numpy does >> > allow arbitrary types in its arrays. I doubt they're as optimized as >> > its own types, but you can try: >> >> > sage: A= MatrixSpace(CDF, 2).random_element() >> > sage: B= MatrixSpace(CDF, 2).random_element() >> > sage: %timeit A*B >> > 625 loops, best of 3: 11.8 µs per loop >> > sage: import numpy >> > sage: AA= numpy.array(A); BB= numpy.array(B) >> > sage: %timeit AA.dot(BB) >> > 625 loops, best of 3: 1.28 µs per loop >> > sage: AAA= numpy.array(A,dtype=type(A[0,0])); BBB= >> > numpy.array(B,dtype=type(B[0,0])) >> > sage: %timeit AAA.dot(BBB) >> > 625 loops, best of 3: 2.33 µs per loop >> > sage: z=A[0,0] >> > sage: %timeit z*z >> > 625 loops, best of 3: 101 ns per loop >> > sage: zz=AA[0,0] >> > sage: %timeit zz*zz >> > 625 loops, best of 3: 253 ns per loop >> > sage: zzz=AAA[0,0] >> > sage: %timeit zzz*zzz >> > 625 loops, best of 3: 107 ns per loop >> > sage: type(z); type(zz); type(zzz) >> > <type 'sage.rings.complex_double.ComplexDoubleElement'> >> > <type 'numpy.complex128'> >> > <type 'sage.rings.complex_double.ComplexDoubleElement'> >> >> With such small matrices (and elements), you're essentially measuring >> overhead rather than arithmetic here. Of course if you have lots of >> small matrices, that may be a relavant thing to measure. As the matrix >> size grows, they should be the same, as multiplying CDF matrices >> simply defers to multiplying numpy matrices. >> >> sage: A= MatrixSpace(CDF, 200).random_element() >> sage: B= MatrixSpace(CDF, 200).random_element() >> sage: %timeit A*B >> 125 loops, best of 3: 7.31 ms per loop >> sage: AA= numpy.array(A); BB= numpy.array(B) >> sage: %timeit AA.dot(BB) >> 125 loops, best of 3: 7.34 ms per loop >> >> - Robert > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
