Arjen Markus This page is meant for collecting ideas on how to deal with numerical analysis in Tcl.
The rationale
There are quite a few attempts to implement numerical analysis methods in Tcl, but so far there is no framework (conceptual or otherwise) that you can readily use. Everybody tries to do it in his or her own way.
If we look at our Perl and Python colleagues, they have PDL (Perl Data Language) and Numpy (or Numarray it seems to be called nowadays). There is no equivalent to my knowledge in Tcl, though there are quite extensive packages like la and NAP that might classify as such.
The basic problem
Numerical methods often deal with collections of data:
One could think of nested lists (see Playing APL for an example) to represent them, but the la package uses plain lists for good reasons:
Standard libraries exist in both C and Fortran for many problems (think of: Lapack and FFT libraries for instance). We can access these via small wrappers, generated via SWIG or Critcl and in fact a few such wrappers already exist.
The solution?
We should decide what the best methods are for dealing with numerical data and create an easy to use framework out of this. The design issues are:
My first guess is that we need a hybrid solution:
Lars H: I'd suggest using a flat list to hold the numerical data, with a separate "shape specification" that tells commands (that bother about the shape of data) how to treat it. I recall Fortran has some operation which e.g. allows you to say that the thing declared as a 6x6 matrix should be treated as a 36 element vector, or even 4x9 matrix. Saying "it's all basically vectors, but with a shape specification" makes that kind of thing easy.
As for how to handle the Tcl <-> binary conversions, I'd suggest making the string representation of the thing like a vector of numbers, or like a list containing such a thing. E.g. a 2x2 identity matrix might be
{2 2} {1.0 0.0 0.0 1.0}where the {2 2} part specifies the shape and the rest is the data. Note that this wouldn't have to be a list-of-lists-of-numbers as Tcl_Objs, but could be a single object of some new type whose string representation just happens to be possible to parse as lists. (In practice one shouldn't apply list operations on it, because that would discard the internal representation as "numerical array", but being able to do this anyway can be very useful when debugging.)
AM Your solution comes very close to what several packages are doing (I wanted to keep the discussion open by not proposing a "definite" solution :) But yes, it is the sort of solution you can find a lot.
DKF: Actually, for an N-dimensional matrix, your printed representation only needs to state N-1 dimensions, since you have the overall number of items "for free".
AM In Clustering data I use an approach with a list of lists, where each sublist represents the "coordinates" of the data point. As the algorithm only needs the data point by point and does not do anything "across" points, this works very well.