On 08/02/2011 10:10 AM, Matthew Rocklin wrote:
Start of a wiki-page is here if people want to go this route. I put
down the things that I think about.
https://github.com/sympy/sympy/wiki/Matrix-Expressions
I'm also happy to continue the conversation over e-mail.
What would be a good next step? How can I stimulate activity on this
topic?
On Sat, Jul 30, 2011 at 8:02 AM, Matthew Rocklin <mrock...@gmail.com
<mailto:mrock...@gmail.com>> wrote:
I see that Andy just posted while I was writing. I'll post anyway
although Ii thnk maybe the wiki page is a better start.
It seems like we have a few people who want to contribute to the
same concept. Should we put something on the master branch so that
people can start adding to it?
What would a general framework for matrix expressions look like
that could handle most of the use-cases? What are the use cases?
So far we have
* Expression that may contain matrices as atomic symbols
* Expression that may contain immutable matrices
* Derivatves of symbols
* Derivatves over indices?
* Block matrices
On Sat, Jul 30, 2011 at 1:40 AM, Tim Lahey <tim.la...@gmail.com
<mailto:tim.la...@gmail.com>> wrote:
On Sat, Jul 30, 2011 at 2:31 AM, Mateusz Paprocki
<matt...@gmail.com <mailto:matt...@gmail.com>> wrote:
> I'm sure that, sooner or later, those approaches will have
to be merged,
> because those are really two views of a very similar (if not
the same)
> problem domain. My original motivation came from reading
lecture notes
> for undergraduates about the finite element method. As
usually there was an
> introduction to basics of algebra needed to understand the
later material,
> and my question was why it must be so hard to do it in SymPy
(if possible at
> all). My branch is about "symbolic matrices" with explicit
content. However,
> I don't see any problem with allowing transition between
those two views
> (well at least in one direction). Suppose we have expr =
Eq(A*x, b), where
> A, x, b are matrices/vectors of appropriate shape. First, I
would like to be
> able to manipulate the expression alone, check various
shapes (and ask SymPy
> if it makes sense), etc. Then I would like to write
something like
> expr.expand(fullform=True) and get the same but with
MatrixExpr with
> explicit indexed symbols or values (if entities like zeros
or ones matrix
> was used in expr). Then I would like to make further
transformation on this
> "full form".
I would like to do things like differentiate c^T*A*c with
respect to
the vector c. It's a common thing for finite elements. But I'd
also
like block matrices. However, if you have symbolic matrix
expressions,
you can put them in a matrix and then perform standard matrix
calculations on that and you'd have block matrix support. So,
as long
as that's possible, there's no problem.
I've got by handling differentiating matrix-vector expressions in
Maple using their non-commutative support along with hacking
together
handling the transpose and differentiation of it. But, I'd
like proper
support.
If Sympy could support block matrices, that would be extremely
useful
in control theory (where they're used all the time).
Cheers,
Tim.
--
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo
http://about.me/tjlahey
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I looked at your wiki page and since you teach linear algebra you might
find the following book interesting -
http://www.amazon.com/Linear-Geometric-Algebra-Alan-Macdonald/dp/1453854932
also if you have not already done so you should look at the
documentation for the geometric algebra module for sympy.
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