Re: [boost] [rfc] A light weight statically typed matrix template class (again?)

From: Andreas Harnack (ah.boost.04_at_[hidden])
Date: 2007-12-17 13:13:09

I'm not pretending to be an expert in Linear Algebra or in 
numerical computing and I certainly wouldn't dare to submit a 
full scale Linear Algebra library. (Though in all modesty, I 
probably could take one about 2/3 of the people out there 
working as professional programmers.) I'm just a computer 
engineer how thinks that matrices could be a very useful and 
handy tool in many situation, yet any time I reach out for it in 
my (standard) toolbox it's just not there. And if I go to the 
next DIY-market all I got offered is a whole range of highly 
sophisticated CNC-all-in-one solutions, that are very shiny and 
properly do an excellent job, but just won't fit into my modest 
workshop, where I just want to, let's say, drill a few holes. 
See my problem? And from what I read from the posts (this one as 
well as earlier ones) there are a few people out there feeling 
the same way.

If you think that this doesn't belong to the standard, then 
please allow me to ask one question: Why is there a complex 
number class in the standard and what does it actually do? 
Complex numbers are useful in many situations, as matrices are, 
yet the complex number class doesn't support a single one of 
them. Or is there a function in the library to find the roots of 
a polynomial or one to transform a signal sample from the time 
to the frequency domain? No, and I think it shouldn't. So why is 
everybody so keen to have a function to find eigenvalues in a 
matrix class, which comes down to exactly the same problem? 
Actually the complex number class does next to nothing. It is 
essentially a structure of two equally typed elements, about the 
most primitive data structure one could think off. It only 
forwards a few operators of the base type, which are already 
available in the language or in some other library. By far the 
most complex function in the complex number class is the input 
operator. And yet, the class is there, it's in the standard and 
it is useful. (Well, at least it doesn't hurt.)

All I'm trying to propose is to do the same thing with a 
two-dimensional array, about the second primitive data structure 
one could think of. (The third actually, one-dimensional arrays 
would come second, but it turned out that a matrix class without 
a dedicated vector class is more useful then vice versa and, 
after all, vectors are already in the standard too, though they 
do almost ignore the algebraic aspect of vectors.) This is not 
supposed to be an all-in-one solution, it shall only provide the 
most elementary stuff. By most elementary I mean operations, 
that are already there, somewhere in the standard. That's the 
reason I'm not too bothered about numerical problems. Adding two 
matrices doesn't impose more problems than folding a 
Plus-functor to a vector. It won't solve any equations, but 
matrices are not only about that.

Andreas