I merged the steffen code into the master branch and updated the NEWS file
Patrick
On 04/03/2014 03:53 PM, Jean-François Caron wrote:
Looks good to me.
Jean-François
On Apr 3, 2014, at 14:51 , Patrick Alken <[email protected]> wrote:
Ok I used your new text and modified it slightly to say that the method uses
piecewise cubic polynomials in each interval:
----
Steffen's method guarantees the monotonicity of the interpolating function
between the given data points. Therefore, minima and maxima can only occur
exactly at the data points, and there can never be spurious oscillations
between data points. The interpolated function is piecewise cubic
in each interval. The resulting curve and its first derivative
are guaranteed to be continuous, but the second derivative may be
discontinuous.
----
Does this look ok?
I added your name to test.c
Patrick
On 04/03/2014 01:58 PM, Jean-François Caron wrote:
Hi Patrick, yes feel free to change the example dataset. I used it because
it’s the same as I put into the test.c code, and other interpolation methods
used randomly-generated data.
For the description in the docs, I might recommend a different wording:
@deffn {Interpolation Type} gsl_interp_steffen
Steffen’s method guarantees the monoticity of the interpolating function
between the given data points. Thus minima and maxima can only occur
exactly at the data points, and there can never be spurious oscillations
between data points.
The interpolated function and its first derivative are guaranteed to be
continuous,
but the second derivative may be discontinuous.
@end deffn
Thanks for supporting my work! I’m very excited to be officially contributing to
an open-source project. Could you check the copyright & attribution parts of
the code files that I modified? I’m not sure what is correct, but I see author’s
names and dates. I added mine to the steffen.c, but should I add it also to test.c
and the others?
Jean-François
On Mar 31, 2014, at 15:24 , Patrick Alken <[email protected]> wrote:
I couldn't reproduce the figure in Steffen's paper, so I found another dataset
which nicely illustrates oscillation issues with Akima:
J. M. Hyman, Accurate Monotonicity preserving cubic interpolation,
SIAM J. Sci. Stat. Comput. 4, 4, 1983.
The dataset is simpler than your randomly generated plot and I think its a
little easier to compare the different methods.
I added an example program and a figure to the manual (in the steffen branch).
I am hoping to finish everything up and merge into master by the end of the
week.
Thanks again,
Patrick
On 03/31/2014 02:37 PM, Patrick Alken wrote:
Ok I made a new branch 'steffen' in the GSL repository with your latest
changes, thanks for all your work on this. I still want to update the
docs a little and do some more testing on my own before merging it into
master. I made a blurb about gsl_interp_steffen in the docs:
----
@deffn {Interpolation Type} gsl_interp_steffen
Steffen's method for monotonic interpolation (not allowing minima or
maxima
to occur between adjacent data points). The resulting curve is
piecewise cubic on each interval with the slope at each grid point
chosen to ensure monotonicity and prevent undesired oscillations. The
first-order derivative is everywhere continuous.
@end deffn
----
Can you read this and make sure I haven't said anything inaccurate? Or
let me know any suggestions you think its important to add for the users
benefit to understand what this method does.
Thanks,
Patrick
On 03/27/2014 11:17 AM, Jean-François Caron wrote:
By the way, my the second test function in interpolation/test.c uses
randomly-generated data points, but actually serves to nicely illustrate the
difference between major non-linear interpolation methods. See the linked
graph for a comparison of the interpolation for those data using my
implementation of steffen, and the existing GSL akima and cubic spline methods.
https://github.com/jfcaron3/gsl-steffen-devel/blob/steffen/interpolation/compare.pdf
(I couldn’t send a pdf to the mailing list, and I don’t know how to view a pdf
on github’s website, but I guess you can just get the image when you clone the
repo.)
While the cubic spline and akima methods preserve continuity of the second
derivatives, they are not monotonic and can have oscillations that are often
undesireable. The steffen method sacrifices continuity of the second
derivative (but maintains it for the first) in order to maintain monoticity,
which also eliminates weird oscillations. In Steffen’s paper, there is also an
example graph where the akima method is unstable (a very small change in one
data point makes a large change in the interpolated function), while the
steffen method is stable by construction.
Jean-François
On Mar 27, 2014, at 01:10 , Patrick Alken <[email protected]> wrote:
The code is looking very good - I will try to find time in the next few days to
do some tests and import it into GSL
Thanks
Patrick
________________________________________
From: [email protected] [[email protected]] On
Behalf Of Jean-François Caron [[email protected]]
Sent: Wednesday, March 26, 2014 7:10 PM
To: [email protected]
Subject: Re: Compiling & Testing New Interpolation Type
I have now fixed the problems with the tests and added a more robust test with
lots of data points. I am effectively ready to give a pull request from my
github repo. Let me know what I need to do to facilitate this.
Jean-François
On Mar 25, 2014, at 15:51 , Jean-François Caron <[email protected]> wrote:
Git and Github weren’t as intimidating as I expected. I have a repo here with
the “steffen” branch including my changes:
https://github.com/jfcaron3/gsl-steffen-devel
The Savannah git repo didn’t include a configure script, and I got my modified
GSL+Steffen code to compile by directly modifying interpolation/Makefile AFTER
running ./configure, so I’m not sure how to compile the files cloned from my
github repo. At least it’s easier to see the changes now.
Jean-François
On Mar 25, 2014, at 14:56 , Jean-François Caron <[email protected]> wrote:
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
