I’ve improved my initial code greatly. You can find it here: http://bazaar.launchpad.net/~jfcaron/+junk/my_steffen/files
You can compile it into GSL by adding in the interpolation/Makefile references to “steffen.c”, “steffen.lo”, and “steffen.Plo” exactly where there are currently references to “akima.*”. I’ve tried adding an “integ” method, but I’m afraid I don’t even understand the workings of the integ methods for the existing interpolation types. I couldn’t just copy from the akima.c integ method because they use a build-in spline calculation function (which I also don’t understand). Reading uncommented C code is pretty hard. My test program shows that the integration method isn’t obviously broken, but it fails the tests I wrote in interpolation/test.c The actual interpolation and derivatives seem to work and pass the tests. I’ve not used github before, so I guess my next move should be to learn the basics and start using that, since otherwise describing my additions & changes are hard to follow. In the meantime, is anyone able to explain how the heck the “integ” methods work? Jean-François On Mar 20, 2014, at 11:30 , Patrick Alken <[email protected]> wrote: > Yes that green curve is rather strange and doesn't seem much better than the > cubic spline. I like simplicity too so lets proceed with importing the > steffen code. > > On 03/20/2014 12:18 PM, Jean-François Caron wrote: >> Definitely an advantage of a) is that it is conceptually simple. b) is 44 >> pages while a) is only 7. Even if b) is somehow mathematically superior, I >> like the idea of understanding the tools that I am using (and being able to >> explain it to my academic supervisor/conference attendees). >> >> The MESA astrophysics library (C++ unfortunately) actually includes both >> types, and has a little graph to show differences: >> http://mesa.sourceforge.net/interp_1D.html >> >> Actually their graph is confusing, blue is supposed to be a), green b), but >> the green curve isn’t piece-wise monotonic between the data points. I’m >> starting to think maybe Stetten and Huynh mean different things when they >> say “monotonic”. I’ll try to read Huynh’s paper to see if they define what >> they are trying to do. Steffen is pretty clear about his technique being a >> for an interpolating function that is monotonic between data points - i.e. >> the interpolating function doesn’t change sign between data points, and >> extrema can only occur at said data points. >> >> Jean-François >> >> On Mar 20, 2014, at 11:03 , Patrick Alken <[email protected]> wrote: >> >>> I see question 1) is answered by section 4 of Steffen's paper - the method >>> works on all data sets, and preserves monotonicity in each interval, which >>> is nice. They also state that method (c) has some serious drawbacks. >>> >>> Unfortunately paper (b) doesn't reference (a) and so its difficult to tell >>> whether (b) offers any advantage over (a) >>> >>> On 03/20/2014 11:52 AM, Patrick Alken wrote: >>>> Hi, I'm moving this discussion over to gsl-discuss which is more suited >>>> for development issues. >>>> >>>> I have 2 naive questions which you may be able to answer since you've >>>> been working on this code. >>>> >>>> 1) If the Steffen algorithm is applied to non-monotonic data, will it >>>> still provide a solution or does the method encounter an error? >>>> >>>> 2) Earlier on the GSL list it was mentioned that there are 3 different >>>> methods for interpolating monotonic data: >>>> >>>> (a) M.Steffen, "A simple method for monotonic interpolation in one >>>> dimension", Astron. Astrophys. 239, 443-450 (1990). >>>> >>>> (b) H.T.Huynh, "Accurate Monotone Cubic Interpolation", SIAM J. Numer. >>>> Anal. 30, 57-100 (1993). >>>> >>>> (c) Fritsch, F. N.; Carlson, R. E., "Monotone Piecewise Cubic >>>> Interpolation", SIAM J. Numer. Anal. 17 (2), 238–246 (1980). >>>> >>>> I haven't looked at (c) but it seems that (a) and (b) both use piecewise >>>> cubic polynomials and preserve monotonicity. Do you happen to know if >>>> one method is superior to the other? If one method is significantly >>>> better than the other two it would make more sense to include that one >>>> in GSL. >>>> >>>> Patrick >>>> >>>> On 03/20/2014 11:37 AM, Jean-François Caron wrote: >>>>> Yes, I didn’t bother doing the integration function at the time because I >>>>> was having trouble just compiling. I will add the integration function, >>>>> and re-write the eval and deriv/deriv2 functions to use Horner’s scheme >>>>> for the polynomials. I can generate some comparison graphs using fake >>>>> data like in Steffen’s paper, that sounds easy enough. >>>>> >>>>> I’ll look at the interpolation/test.c file and see if I can come up with >>>>> similar tests. >>>>> >>>>> Thanks for offering to help with the integration into GSL itself. I >>>>> don’t know a lot of the procedures (or even politics sometimes!) involved. >>>>> >>>>> Jean-François >>>>> >>>>> On Mar 20, 2014, at 10:22 , Patrick Alken <[email protected]> >>>>> wrote: >>>>> >>>>>> I did notice you talking about 1.6 in your earlier messages, but assumed >>>>>> it was a typo and you meant 1.16, oops. >>>>>> >>>>>> On 03/20/2014 11:11 AM, Jean-François Caron wrote: >>>>>>> My original problem was that I wanted to add an interpolation type to >>>>>>> GSL. Specifically I want monotonic cubic-splines following the >>>>>>> description in Steffen (1990): >>>>>>> http://adsabs.harvard.edu/full/1990A%26A...239..443S >>>>>> I took a quick look at your code earlier and it looks pretty nice. I >>>>>> noticed you commented out the _integ function - is this something you >>>>>> could add to make it feature complete with the other interpolation types? >>>>>> >>>>>> It is important to add automated tests for this. Can you look at >>>>>> interpolation/test.c and design similar tests for your new method? Also >>>>>> I think it would be nice to add a figure to the manual illustrating the >>>>>> differences between cubic, akima, and your new steffen method (similar >>>>>> to the figures in the Steffen paper). This would help users a lot when >>>>>> trying to decide what method to use. Do you happen to have a dataset >>>>>> which shows a nice contrast like Figs 1, 3 and 8 from that paper? >>>>>> >>>>>> When everything is ready I would be happy to add it to GSL, as we are >>>>>> already planning to update the interpolation module for the next >>>>>> release. When I find some time I want to import the 2D interpolation >>>>>> extension discussed previously, and also add Hermite interpolation. >>>>>> >>>>>> It would be easiest for us if you could clone the GSL git repository and >>>>>> make your changes there. You could make a new branch called 'steffen' or >>>>>> something and publish it to github, or just send a patch file to me, >>>>>> whichever is easiest. >>>>>> >>>>>> Patrick >>>>>> >>>>>> On Mar 19, 2014, at 18:40 , Dave Allured - NOAA Affiliate >>>>>> <[email protected]> wrote: >>>>>>>> More data. I tried the same plain build recipe, GSL 1.16 on our test >>>>>>>> machine which is at Mac OS 10.9.3. Got another perfect build, no make >>>>>>>> check errors, no PPC-related issues. Outputs on request, please be >>>>>>>> specific. >>>>>>>> >>>>>>>> CC=clang >>>>>>>> CFLAGS=-g >>>>>>>> ./configure --prefix /Users/dallured/Disk/3rd/gsl/1.16.os10.9 >>>>>>>> >>>>>>>> mac27:~/Disk/3rd/gsl/1.16.os10.9 57> sw_vers >>>>>>>> ProductName: Mac OS X >>>>>>>> ProductVersion: 10.9.3 >>>>>>>> BuildVersion: 13D17 >>>>>>>> >>>>>>>> mac27:~/Disk/3rd/gsl/1.16.os10.9/src 36> \ >>>>>>>> ? grep -i '# [a-z]' ../logfiles/make-check.0319a.log | sort | uniq -c >>>>>>>> 45 # ERROR: 0 >>>>>>>> 45 # FAIL: 0 >>>>>>>> 42 # PASS: 1 >>>>>>>> 3 # PASS: 2 >>>>>>>> 45 # SKIP: 0 >>>>>>>> 42 # TOTAL: 1 >>>>>>>> 3 # TOTAL: 2 >>>>>>>> 45 # XFAIL: 0 >>>>>>>> 45 # XPASS: 0 >>>>>>>> >>>>>>>> mac27:~/Disk/3rd/gsl/1.16.os10.9 62> \ >>>>>>>> ? grep -c -i ppc logfiles/*319a*log >>>>>>>> logfiles/configure.0319a.os10.9.log:0 >>>>>>>> logfiles/install.0319a.log:0 >>>>>>>> logfiles/make-check.0319a.log:0 >>>>>>>> logfiles/make.0319a.log:0 >>>>>>>> >>>>>>>> mac27:~/Disk/3rd/gsl/1.16.os10.9 65> \ >>>>>>>> ? grep -i ppc src/config.h src/config.log src/config.status >>>>>>>> src/config.h:/* #undef HAVE_GNUPPC_IEEE_INTERFACE */ >>>>>>>> src/config.log:HAVE_GNUPPC_IEEE_INTERFACE='' >>>>>>>> src/config.status:S["HAVE_GNUPPC_IEEE_INTERFACE"]="" >>>>>>>> >>>>>>>> --Dave >>>>>>>> >>>>>>>> On Wed, Mar 19, 2014 at 5:27 PM, Jean-Francois Caron >>>>>>>> <[email protected]> >>>>>>>> wrote: >>>>>>>>> Dave is correct, I am using an "i686" 64-bit x86 mac. For some reason >>>>>>>>> it is still looking for the PPC mac header file. The ./configure >>>>>>>>> stage correctly identifies my system, so it's a bit strange. Also GSL >>>>>>>>> installs without errors when I do it from MacPorts, and MacPorts >>>>>>>>> doesn't seem to do anything other than ./configure && make, from my >>>>>>>>> reading of the portfile. >>>>>>>>> >>>>>>>>> When I get back to my Mac, I will look at the NOTES file to see if >>>>>>>>> anything needs to be done for 10.9. >>>>>>>>> >>>>>>>>> Jean-François >
