Dan Drake wrote:
> On Sun, 07 Jun 2009 at 11:12AM -0700, paramaniac wrote:
>> Is there a possibility/workaround in Sage to compute the element-wise
>> multiplication of two matrices? In Matlab there's the .* operator, but
>> Matlab is useless in my case since I need a symbolic result.
>
> There's no operator that I know of for that, but you can convert your
> matrices to lists, multiply, and convert back:
>
> sage: x,y,z,w = var('x y z w')
> sage: a = matrix(SR, 2, 2, [x, y, z, w])
> sage: b = matrix(SR, 2, 2, [1+x, 1+y, 1+z, 1+w])
> sage: a.list()
> [x, y, z, w]
> sage: b.list()
> [x + 1, y + 1, z + 1, w + 1]
>
> Now make a list of corresponding pairs of entries with zip() and
> multiply:
>
> sage: [ x*y for x, y in zip(a.list(), b.list()) ]
> [(x + 1)*x, (y + 1)*y, (z + 1)*z, (w + 1)*w]
>
> ...and make a matrix out of the new list:
>
> sage: matrix(2, 2, [ x*y for x, y in zip(a.list(), b.list()) ])
>
> [(x + 1)*x (y + 1)*y]
> [(z + 1)*z (w + 1)*w]
>
> You can easily put that sequence of steps into a function. You may need
> to fiddle a bit with the rows and columns bits, and maybe add a ring
> argument if you need to specify what ring the matrix should be over.
>
> def componentwise_multiply(a, b, rows, cols):
> return matrix(rows, cols, [x*y for x, y in zip(a.list(), b.list())])
You can also turn this into a custom infix operator, if you want. That
would mean that your code would depend on a definition, but it could
make your function a lot easier to use. See
http://sagenb.org/home/pub/565 for an example using the above code.
This is based on the code developed in the thread
http://groups.google.com/group/sage-devel/browse_thread/thread/100de89e7d402134/fe89570b403344ae
(that code probably should get into Sage; it makes some calculations
very, very easy to write down...)
The trac ticket for incorporating this decorator is
http://trac.sagemath.org/sage_trac/ticket/6245
Thanks,
Jason
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