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[Lapack] LDL decomposition in SYTRF

Hi LAPACK team,

I was recently playing around with the SYTRF group of routines, which from
what I can tell perform the LDL decomposition. I was thinking these
routines should be faster than the Cholesky decomposition (in POTRF),
because as far as I know the decompositions are essentially the same except
that the LDL decomposition avoids taking square roots (and does some
pivoting, which I wasn't expecting).

However, what I've found is that SYTRF is much slower than POTRF, on my
machine about 20 times slower for a 5000 by 5000 float64 matrix. Is this to
be expected? I realize that SYTRF is more general, in that it does not
require inputs to be positive definite, but I had still hoped it would be
faster than POTRF, and certainly not so much slower.

Are there any other routines that expose an LDL decomposition that is
essentially the same as the Cholesky decomposition but without the square
roots? Or is POTRF my best bet for solving positive-definite symmetric

Eric Hunsberger
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