[Ifeffit] Fwd: problems with setting parameters in new Artemis (Demeter 0.9.16)
bravel at bnl.gov
Fri Feb 28 07:47:37 CST 2014
On 02/28/2014 07:52 AM, Cristina Alonso Escobar wrote:
> 1.- How can I restrain "a" ? I tried to manually add a restraint, but I
> do not know how to make an interval restraint...( 0<a<1)
> 2.- If you select "restrain" and after in the math expression "build
> restrain from ..."
> What is the meaning of scale by?
> Why the program duplicate the restrain (i.e restrain- a and restrain-
> res_a - 1* penalty (a, 0, 1)?
> I think I am not doing well because the value of my parameter "a" is
> suspiciously always 0.
In Artemis and in Ifeffit, a "constraint" is a mathematical relation
between parameters. A "restraint" is a math expression which is
evaluated and added in quadrature to chi-square when the fit is
The "penalty" function has this functional form:
penalty(a, min, max) = 0 for min < a < max
penalty(a, min, max) = a-max for a > max
penalty(a, min, max) = min-1 for a < min
This is useful as a restraint because it assesses no penalty in the
evaluation of chi-square when a is "well-behaved", i.e. between min
and max. As a deviates from its range, the penalty increases linearly
by its excursion out of range.
This will serve the purpose of a restraint. Since it is added in
quadrature to chi-square, it has no impact on chi-square as long as a
stays within range. It can, however, leave its range so long as there
is a compensating improvement in the quality of the fit.
The "scale" term is needed because you want the restraint to be
significant on the scale of chi-square. If the restraint is too
small, then the fit will not be sensitive to it and a will not be
encouraged to stay within its range. If the restraint is too big,
then a will not be allowed out of range even if that would improve the
quality of fit.
As a rule of thumb, I find that the square root of chi-square in the
absence of the restraint is about the right size for the scaling
factor. So if, chi-square without the restraint is 400,
set scale = 20
restrain my_res = scale * penalty(a, 0 , 1)
A few additional points:
1. The restraint I described above is linear in its excursion out of
bounds. You can make it quadratic very simply:
set scale = 20
restrain my_res = scale * (penalty(a, 0 , 1))**2
2. You don't have to use the penalty function. Any expression can be
a restraint and get added in quadrature to chi-square. Here's a
talk Matt gave many years ago in which he explains restraints very
clearly. At the end he also gives an example of restraint that
does not use the penalty function.
3. There is another way in Artemis (and Ifeffit) to set a boundary on
a parameter value:
guess b = 0.5
def a = max(0, min(1, b))
This sets hard-wall boundaries on a. This is not as attractive as
you might think, however. Because the boundaries are hard walls,
if the fit is pushing the value beyond one of the walls, error
bars can no longer be computed. This is because values outside
the hard-wall boundaries do not change the fit, thus the
covarience matrix cannot be calculated, and error bars cannot be
determined. Restraints are an improvement on hard wall boundaries
in that they allow error bars to be evaluated. You can make a
restraint behave somewhat like a hard wall by making the scaling
4. You said "I think I am not doing well because the value of my
parameter 'a' is suspiciously always 0." I find that that sort of
thing is usually trying to tell me something about my fit. In
your case, I would encourage you to think about how a is used in
the fit. You think that a should be bigger than 0, but perhaps
the fit is trying to tell you either that your assumption is
mistaken or that your fitting model has a mistake. Just something
to think about ....
5. There is hope for better things on the horizon. Larch has a much
more robust way of restraining parameter values than does Ifeffit.
Artemis is not ready to begin using Larch, but it will one of
these days. Then you will have access to much richer tools for
defining fitting parameters. Something to look forward to....
Bruce Ravel ------------------------------------ bravel at bnl.gov
National Institute of Standards and Technology
Synchrotron Science Group at NSLS --- Beamlines U7A, X24A, X23A2
Upton NY, 11973
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