smk78
commented
4 years ago I would say that providing an extrapolation which does not comply with the mathematics of how the invariant is defined is just plain wrong and it should be removed!
If we want to offer an alternative to the Guinier, then I would suggest Vonk's function, as implemented in the original Corfunc:
C Vonk model
sigy=0.
sigxsqu=0.
sigxsquy=0.
sigx4=0.
DO j=start,chanend
C Get sums
temp=xdata(j)**2
sigy=sigy+ydata(j)
sigxsqu=sigxsqu+temp
sigxsquy=sigxsquy+temp*ydata(j)
sigx4=sigx4+temp*temp
END DO
C Calculate parameters
npts=(chanend-start+1)
h2=(sigxsqu*sigy-npts*sigxsquy)/(npts*sigx4-(sigxsqu**2))
h1=(sigy+h2*sigxsqu)/npts
C Get chi squ.
chisqu=0.
DO j=start,chanend
chisqu=chisqu+(ydata(j)-h1+h2*xdata(j)*xdata(j))**2
END DO
chisqu=chisqu/nptsThe references for this are actually at the bottom of the SasView Corfunc help file (although it is not actually implemented in SasView Corfunc; the references are there because they also discuss correlation functions).
In fact, the Vonk extrapolation could be implemented for both analyses.
butlerpd
lucas-wilkins
There invariant perspective currently allows for calculating the invariant from the data with options to also estimate the low q and high contributions to the invariant from the curve at lower q than qmin and higher q than q max. This is done by fitting the last n points to a power law for high Q (some form of Porod) and a Guinier at low Q. Currently there is also the option to use a power law extrapolation to low Q. It is not at all clear why this low Q power law is an option. By definition a power law must diverge at q=0 meaning Q_star is infinite. Practically, it means that the experimental curve does not go to low enough Q to capture the full structure in which case the invariant is calculation is invalid. Only if one has a true Guinier region have you reached the full structural data. I realize for Geosciences this is often used even in the absence of a Guinier but in that case in principle they are measuring to very low Q not extrapolating and presumably assuming the the remaining low Q contribution is negligible?
If we remove the option, note that the unit tests based on data in
sasinvariant/test/utest_use_cases.pyhave been removed while those insasinvariant/test/utest_data_handling.pymostly remain but have notes in the doc strings about removing should we need to remove the feature.