[Maxima] Why I think lapack matrices should not be converted to list-of-lists.

sen1 at math.msu.edu sen1 at math.msu.edu
Wed Jan 3 10:53:44 CST 2007


If it is not too silly, I think it would be good to have both floats
and bigfloats supported, perhaps in separate packages. It might take
a lot longer to run, but, in some cases, the user might be willing to wait.

  There are a number of applications of moderate size, say matrices of
   order up to 500x500 where knowing the bigfloat answers might be
   useful.

-sen


   On Wed, 3 Jan 2007, Richard Fateman wrote:

>
>
>> -----Original Message-----
>> From: maxima-bounces at math.utexas.edu [mailto:maxima-
>> bounces at math.utexas.edu] On Behalf Of Raymond Toy
> ....>
>>     Robert> I think the Lisp arrays should be copied back into Maxima
>> matrices.
>>
>
>
> Just to point out what may help inform this discussion:
>
> It is not at all that hard -- and in fact is done in Mathematica, I believe
> -- to support another type of matrix (or more...). Namely large numerical
> matrices are stored in Mathematica NOT at lists of lists. This makes it
> possible to mimic  programs like matlab at full speed (in fact, as fast as
> matlab or faster).
>
> A full commitment to numerical matrix computation would provide the full
> complement of representation possibilities, including triangular,
> tridiagonal, symmetric, sparse, ...  double, complex
>
> I suggest the following:
>
> (a) a new maxima "head" or "operator"  which would be (say) ddmatrix for
> dense matrix of real double floats, e.g.  ((ddmatrix 10 20 simp) <a lisp
> matrix compatible with C>)
> (b) display programs for this. Naturally it would be unusual to see ALL of a
> large matrix in a 2-D display, since the typical entry would itself take 16+
> character spaces.
> (c) setting and accessing functions ... i.e.  a[p,q] as a value and a[p,q]:
> ...
>
> (d) conversion to and from ddmatrix to list-of-lists.
>
>
> Note that (d) at least must be written anyway.
>
>
> Also some policy that might automatically convert to a ddmatrix --when
> possible-- for the first use of a matrix in lapack functions etc,  and
> automatic conversion to a list-of-lists when necessary by setting a location
> to a symbol.
>
> What is the payoff, since conversion is in any case linear time and the
> lapack stuff is quadratic or worse?  Well, the overhead of converting each
> matrix repeatedly inside a loop or even inside a single matrix expression
> like A.B.transpose(A) ... would be painful.
>
> And if you want Maxima to compete head-on with Matlab, you can do it this
> way.
>
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>

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