Ed Pozharski wrote:
On Wed, 2010-09-22 at 22:46 +0200, Gerard DVD Kleywegt wrote:
...constraints are just a special case of restraints in the limit
of infinite weights
If you impose "infinitely strong" NCS
restraints,
But "in the limit" means that the restrained refinement can be made to
approach the results of constrained refinement as close as one wishes by
appropriately increasing the weights. If the fact that in the case of
infinity the point itself can't be reached is somehow problematic, then
derivatives, delta-function, fractal geometry and many other useful
mathematical constructs should be thrown out.
I think the round-off problem Ian mentioned is simply a limitation of
our computers (or compilers). If the energy term for NCS is 10^7 times
any other energy term, then when they get added up the effect of the
xray term, geometry, etc is lost in the round-off (assuming real*4
arithmetic). I've actually seen this in CNS, going too high on the
ncs-weigts leads to some very distorted geometry.
For the sake of a thought experiment we can assume the refinement
is implemented with infinite-precision arithmetic. And for actually
taking the limit, if things seem to have converged with increasing
ncs weight before the refinement goes to pot because of roundoff,
maybe we are already close enough to infinity.
Gerard DVD Kleywegt wrote:
In practice this is not true, of course. If you impose "infinitely
strong" NCS restraints, any change to a thusly restrained parameter by
the refinement program will make the target function infinite, so
effectively your model will never change. This is very different from
the behaviour under NCS constraints and the resulting models in these
two cases will in fact be very easily distinguishable.
Only if the refinement is looking at one atom at a time (off-diagonal
terms in the 2n'd derivative matrix are ignored?). Two ncs-related atoms
can move in agreement with the ncs-restraint without penalty from the
near-infinite ncs-weight, and will if by doing so they improve the
agreement with the X-ray data?
eab
