hello, On 9 March 2016 at 23:20, Linus Torvalds <[email protected]> wrote: > > NOTE! R is not entirely happy about the non-linear fit of the Helium > curve: the fit is *so* precise that it failes the R relative-offset > convergence criterion. That is apparently generally a sign of > artificial data. > > > That is probably because Lubomir generated them from the linear mix of > two polynomial fits, rather than a linear mix of the original data. But > maybe the original data was artificial?
that's a good observation. the table (data set) for helium which i provided was only for consistency with the rest of the gases. *it is* the output of the polynomial, which i forgot to mention. the polynomial itself is a linear mix between two polynomials formed by fitting two different data sets. the resulting polynomial is quite good for the fact that the helium Z behaves almost linearly for our range of interest. the source which wasn't consistent was the helium experimental data: https://shareok.org/bitstream/handle/11244/2062/6614196.PDF?sequence=1 (in-document page 108). the pressure samples differ between the two examined helium temperatures which i've picked; for instance: T = 323.15°K, P = 540.204 atm, Z = 1.22738 PV/RT P = 319.943 atm, Z = 1.13754 PV/RT ... T = 319.943°K, P = 534.047 atm, Z = 1.26914 PV/RT P = 312.114 atm, Z = 1.16070 PV/RT ... so unlike the other book, which had samples for Z at the exact same pressures for all experimental temperatures, the experimental data here was taken at varying pressures, for some reason, quite possibly due to a equipment limitation - e.g. a manual sample-and-hold technique, of sorts. i'm not sure we can improve much on our end-result polynomial given these inconsistencies, but even if we do it might still end up being pretty close to what we currently have. of course, it would have been *much* better if the first book (which is apparently a *goto* resource) simply had the values for helium at the exact 300°K. i have never used R or much of Matlab, so perhaps Robert has the means to review / test the script. lubomir -- _______________________________________________ subsurface mailing list [email protected] http://lists.subsurface-divelog.org/cgi-bin/mailman/listinfo/subsurface
