On my system, for this example sage takes .36 seconds, and
mathematica takes 3.86 seconds, so sage is about 10 times faster.
-MH
On Dec 3, 10:42 am, Jason Grout <[EMAIL PROTECTED]> wrote:
> William Stein wrote:
> > On Dec 3, 2007 8:13 AM, Bill Hart <[EMAIL PROTECTED]> wrote:
> >> I did try to check that Mathematica was getting the right answer, but
> >> I had no luck. I don't know how to convert a mathematica matrix into
> >> ordinary matrix form in SAGE, so when I do the comparison it always
> >> just says false.
>
> > Damn it -- you're right. This isn't the first time I've been bitten by
> > this. Mathematica is just doing the componentwise product!
>
> > sage: mm = mathematica(n)
> > sage: n
> > [ 1/20 -1/10 1/20]
> > [ -1/10 -37/15 47/30]
> > [ 1/20 67/30 -77/60]
> > sage: mm^2
> > {{1/400}, {1/100}, {1/400}, {1/100}, {1369/225}, {2209/900}, {1/400},
> > {4489/900}, {5929/3600}}
> > sage: n^2
> > [ 3/200 53/150 -131/600]
> > [ 8/25 1439/150 -147/25]
> > [ -57/200 -419/50 3089/600]
>
> > Why the frick do so many mathematical software systems define
> > A^n for A a matrix to be componentwise powering. Other programs,
> > e.g., numpy define A*B on numpy arrays to be componentwise
> > multiplication.
>
> > So -- does anybody know how to raise a matrix to a power in
> > Mathematica, since I sure don't.
>
> Mathematica treats matrices as lists of lists. Since the product of a
> list and another list is the component-wise product, the "*" means
> hadamard multiplication.
>
> You probably want the "." operator, which does matrix multiplication:
>
> > {{1, 0}, {0, 1}}.{{1, 2}, {3, 4}}
>
> > {{1, 2}, {3, 4}}
>
> or Dot[{{1,0},{0,1}}, {{1,2},{3,4}}]
>
> Yes, this has bitten me several times too. You could also use:
>
> MatrixPower[{{1,2,3},{4,5,6},{7,8,9}}, 20000]
>
> to compute the matrix product power. For benchmarking, this is probably
> the function to use.
>
> -Jason
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/
-~----------~----~----~----~------~----~------~--~---
