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

From: Kevin Lynch (krlynch_at_[hidden])
Date: 2007-12-07 12:24:01

Andreas Harnack wrote:
> Hi @,
> 
> shouldn't there be at least an elementary matrix class available
> in the standard? I notice there have been some discussions in
> the past, but there doesn't seem to be anything in the pipeline.

You're likely to find that such a thing would be a huge disappointment 
(cf valarray :-)

Doing numerics "right" is REALLY hard, particularly when it comes to 
matrix operations.  Anything that manages to pass the hurdles of 
standardization is likely to be:

1) underspecified to the point of worthlessness. This is not a shot at 
the Committee ... it's just a really hard problem to do right,

2) missing key functionality for most subsets of the C++ user community. 
  Unfortunately, it won't be the SAME missing functionality for 
different those different subgroups :-)   For instance, you may only 
need the ability to multiply small matrices together, but I need to do 
Gauss-Jordan elimination, my neighbor only needs to find eigenvalues, 
and his cousin only needs to find matrix permutations.  Where do you 
draw the line on what is "simple" enough to go into your "simple" matrix 
class?

3) so slow and numerically unstable as to be worthless for most serious 
uses.  Naive implementations are really BAD news on these fronts.  This 
is an enormous QOI issue, and reasonable implementations need to be 
implemented by numerics experts, not your garden variety programmer (I 
know just enough to know how much I don't know).

To see just how difficult a problem this is, you might want to survey 
the attempts to implement matrix functionality in C++:  ublas, Blitz, 
MTL, POOMA, and a host of others.  All of them are enormous efforts, 
they all make different trade offs, all of them are missing key 
functionality, and all of them provide different performance and 
correctness guarantees.

-- 
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