[boost] 2D Matrix

From: Jason Kraftcheck (kraftche_at_[hidden])
Date: 2006-11-07 20:26:42

Hi,

I have written a simple 2D matrix template where the extents of the matrix are
template parameters.  The multi_array container and the uBLAS matrix class both
provide matrices of fixed dimension (template parameter for multi_array and 2
for uBLAS) but variable extents.  I think my matrix definition is complementary
to these. There are several advantages to having an array of fixed extents; but
the implementation is, of course, unusable when the extents are not known at
compile-time.

If the extents of the matrix are part of the type, the compiler can enforce
correct matrix extents for operations, avoiding the cost of runtime checks.  For
example:
  double b[3][2] = { ... };
  matrix<3,3> A(2.0); // 2 * identity
  matrix<3,2> B(b);
  matrix<2,3> C;
  matrix<3,2> D;
  D = A * B; // OK
  C = A * B; // compile error - mismatched types
  C = transpose(B) * A; // OK
Optimizing compilers can trivially unroll the loops used to define the
operations.  Use of this class does not require heap allocation.  The storage
required for the matrix is the minimal possible (assuming no assumptions about
the values of the elements.)  An array of matrices can be "serialized" to an
array of doubles with a single reinterpret_cast.

The proposed implementation is unsuitable for very large matrices: defining the
element storage as a contiguous array may be problematic, most of the
performance gains become insignificant, and the implicit copying will become
significant.

I've attached my current implementation.  In it's current form, it is unsuitable
for inclusion in Boost.  I will fix any required issues if there is any interest
in including it in Boost.  The things that need to be changed (that I'm aware
of) are:
 o license - GPL is not acceptable for Boost
 o naming (namespace and class name)
 o change explict 'double' for element type to a template parameter
Some other changes that should probably be done before inclusion:
 o implement inverse for other than 2x2 and 3x3 matrices
 o more efficient determinant implementation for larger matrices
 o LU factorization
 o QR factorization

In timing tests using G++ 4.1 on a Linux/Pentium4 platform, the performance of
the arithmetic operations was equivalent to those of a special 3x3 matrix
implementation with all operations explicitly unrolled (the 'old' implementation
this one was to replace.)

Is there any interest in including such a matrix definition in Boost?

Is there already an effort to include something equivalent?  I searched back a
few years in the mailing list archive and didn't notice anything.

Any suggested changes (other than those I listed above) for the attached
implementation?