[boost] thinking about a "small matrix" library

From: Dave Steffen (steffend_at_[hidden])
Date: 2001-08-19 12:37:21

Ralf W. Grosse-Kunstleve writes:
 > I am thinking about implementing a "small matrix" library for
 > 2-dimensional arrays. (This would be similar to boost::array,
 > i.e. the small matrices will usually live on the stack to avoid
 > the dynamic memory allocation overhead.)

 Yeah, I've had some thoughts about this too.  Eventually this
 will/can/would/should be part of the Boost matrix library (which
 AFAIK will be == MTL version 3).

 > One requirement is to have operators for *heterogeneous*
 > arithmetic operations, e.g. multiplication. E.g. something
 > like:
 > 
 > template <class LR, class L, class R>
 > matrix<LR> operator*(const matrix<L>& lhs, const matrix<R>& rhs)
 > {
 >   // return the product
 > }
 > 
 > Is there a mechanism in C++ to define a table for the result type LR
 > depending on the types of L and R?

 Yes, use traits. 
 
 > For example, if L=int and R=int, the result type LR=int, but for
 > L=double and R=int the result type should be LR=double, etc.

 Quick example:

 template <class L, class R> struct MatrixOpTraits 
 { ... possible default result? ... };

 template <> struct MatrixOpTraits<int,int> 
 { typedef int Result; };

 template <> struct MatrixOpTraits<double,int> 
 { typedef double Result; };

 Then, e.g.

 template <class R, class L> inline
 MatrixOpTraits<R,L>::Result  // there's the return type
 operator * (const Matrix<R>& A, const Matrix<L>& B)
 { ... }

 On another subject, lots of cool things can be done if the size of
 the vectors/matrices is known at run time.  Template metaprogramming
 techniques can be used to effectively unroll the loops at
 compile-time, so that (for example) given 3-vectors a,b, and c, the
 line

 c = a + b;

 expands (via template metaprogramming magic) to

 c[0] = a[0] + b[0];
 c[1] = a[1] + b[1];
 c[2] = a[2] + b[2];

 which is typically something the compiler's optimizer can go crazy
 with.

--------------------------------------------------------------------------
Dave Steffen                      Wave after wave will flow with the tide
Numerica, Inc.                      And bury the world as it does
steffend_at_[hidden]          Tide after tide will flow and recede
                                    Leaving life to go on as it was...
                                                        - Peart / RUSH
"The reason that our people suffer in this way.... 
is that our ancestors failed to rule wisely".   -General Choi, Hong Hi