> Define what you mean by upper triangular form. The result appears to
> be obtained from performing elementary row operations on A, and is a
> triangular matrix.
>
> This issue was discussed at length in bug 1064238 "triangularize gives
> wrong results."
> (http://sourceforge.net/tracker/?group_id=4933&atid=104933&func=detail&aid=1064238)
Does anybody know what the return value of triangularize is supposed to be?
The documentation doesn't say, the code doesn't have comments,
and I can't puzzle it out from looking at the code (src/matrix.lisp).
I can think of at least three forms of triangular decompositions
(LU, QR, and Cholesky). If we can't figure out what triangularize does,
I'm inclined to cut it and use specific functions if/when they become
available.
There is an LU decomposition in share/linearalgebra/ (and none others
that I can find). I wrote a Cholesky decomposition a while back but
didn't commit it (just laziness on my part). There doesn't appear to be
a QR decomposition.
Maybe Fred can tell us what variety of triangularization he's looking for.
For what it's worth,
Robert Dodier