matrix type caching, triangualar and Cholesky solvers

[John W. Eaton]

On 27-Apr-2006, David Bateman wrote:

| Here is a patch that allows whether a full matrix is upper, lower or
| positive definite to be probed, cached and the method of solving linear
| equations with this matrix with the "/" or "\" operators automatically
| chosen based on this information. This seems to be about 40% for
| positive definite matrices and about 100 times for triangular matrices
| using atlas on my machine. I tried to test all possible cases of the use
| of this code before submitting it, but as there is no testing code
| whatsoever for the "\" and "/" full operators yet, it wasn't easy to
| propose appropriately adapted test code in the absence existing test code.
| 
| This should supersede the chol.oct file from octave-forge and the
| ov-tri-mat type as well.. John do you want it committed?

I'd say yes, but I have a couple of questions.

In ltsolve, you have

  if (typ == MatrixType::Permuted_Lower)
    {
      (*current_liboctave_error_handler)
          ("Permuted triangular matrix not implemented");
    }

Does the current code handle this case or is this something that would
fail now?  I guess there is no way to actually generate this case
(other than manually tagging a matrix), so it is OK? 

What is the intended usage of the MatrixType::info function?  Why does
it use the warning handler?

| Does someone else want to try it out?

That might be good too.

jwe