David Joyner wrote:
> Going form a vague memory:
> My colleague was arguing that one should not teach
> a course in scientific programming using Sage
> because it was so slow in doing some very simple
> things. Apparently if A is a vector or matrix in matlab
> (ie, an array or real numbers) and f is a function
> (eg, a sin or a polynomial), then f(A) is both
> easy for the student to write and also super
> optimized. He doubted Sage could do that.
> So for large sized arrays with thousands of entries,
> matlab would leave Sage in the dust.
>
> My only argument, if I remember, was that his
> argument did not make intuitive sense. I said that
> though I didn't know off the top of my head
> how to write down the evaluation of a function
> on a matrix in an optimized way, there must exist one.
> With scipy used in industry for serious number-crunching,
> it must be possible.
Indeed. With numpy and scipy, it is pretty easy.
sage: a=random_matrix(ZZ,3)
sage: a
[ -1 0 1]
[ 0 0 -72]
[ -1 -1 0]
sage: a_npy=a.numpy()
sage: a_npy
array([[ -1, 0, 1],
[ 0, 0, -72],
[ -1, -1, 0]])
sage: sin(a_npy)
array([[-0.84147098, 0. , 0.84147098],
[ 0. , 0. , -0.25382336],
[-0.84147098, -0.84147098, 0. ]])
sage:
However, Sage does not have extremely good integration between the
symbolics and matrices just yet, so you do something like:
sage: a.apply_map(sin)
[ -sin(1) 0 sin(1)]
[ 0 0 -sin(72)]
[ -sin(1) -sin(1) 0]
You might also be interested in http://www.scipy.org/NumPy_for_Matlab_Users
Thanks,
Jason
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