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 On 13 fév, 18:32, Robert Bradshaw <[email protected]> wrote: > On Sun, Feb 12, 2012 at 4:30 PM, Nils Bruin <[email protected]> wrote: > > On Feb 12, 1:39 pm, Pierre <[email protected]> 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 [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
