On Mon, Feb 13, 2012 at 10:06 AM, William Stein <wst...@gmail.com> wrote: > 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.
+1, exactly what I was going to consider. Depending on how naturally it fits your problem, you could also consider packing your 2x2 matrices into larger arrays (e.g. representing n 2x2 matrices by a 4 x n matrix and manually doing the multiplication) so you can your computations in a "vectorized" form. >> 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 -- 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
