Hi Nikolai,
I have seen the same thing with the different dispersion data sets in
the relax test suite. The numerical model from the Maple expansion
appears to be rock solid. Well, at least your implementation which is
now in relax. It's only disadvantage is computation time - though
much faster than the standard numeric solutions (also in relax), it is
still much slower than the analytic models. But if you take the CR72
model result as a starting point for optimisation - as is performed in
the auto-analysis of relax - then that disadvantage pretty much
disappears. One exception is if the CR72 model result is no good,
then it'll take a lot more time to reach the real minimum.
If it holds for all timescales and populations, then Andy's model
should theoretically find the same result as the numerical result. It
would take a comprehensive study over the entire parameter space to
demonstrate that this holds everywhere, but this is unfortunately
missing from the paper. But as it is an analytic model rather than
numeric model, then it will have the advantage of speed. So if it
were to be added to relax and someone is interested, it should be very
easy to perform a fair comparison of speed and accuracy between all
the different models. Speed is also very much implementation
dependent and small rearrangements of the order in which calculations
are preformed can make an order of magnitude difference. So I don't
understand where the factor of 130 mentioned in the abstract comes
from. Anyway, if Andy's model finds the same parameter values and
errors as the numerical models (excluding the off-resonance effects)
then it could theoretically replace all 2-site analytic and numeric
CPMG dispersion models.
Regards,
Edward
Re: Paper describing exact solution of CMPG, 130 faster than numerical solution