PHYSICS
542
Applications of Numerical Methods in
Physics
R. J. Wilkes
Exercises #6 (there is no #5)
(Not to be handed in; answers with next set)
1. Fit a parabola through the following data set:
x
y
sy
-0.6
5.0
2.0
-0.2
3.0
1.0
0.2
5.0
1.0
0.6
8.0
2.0
Computer Demonstration
On the class website, go to exercises/, and download the code
for fitdemo.f, intgdemo.f, medfitdemo.f and fit.dat into your
filespace.
Compile fitdemo.f and medfitdemo.f on UW's homer or dante linux
machines:
> /usr/bin/gfortran -o fitdemo fitdemo.f
> /usr/bin/gfortran -o medfitdemo medfitdemo.f
(the option is lower case "oh", not zero)
or on any machine that has gnu fortran
(open source) g77:
> gf77 -o fitdemo fitdemo.f
Fitdemo uses a data file that has the following format: line 1 = npts,
followed by x,y,sigma, one data point per line. This program fits the
data using linear least squares.
When the program asks for the filename, enter
fit.dat
Also try medfitdemo, a "robust fitting" procedure which minimizes the
absolute deviations.
The sample data file FIT.DAT contains data obtained from the function
f(x)=1-2x, with Gaussian errors added with sigma=0.10. However,
the last data point is a deliberately introduced outlier. Notice how
the LSQ fit is strongly affected, while true to its name the robust
fitter produces a good fit to the majority of the points.
You can copy the programs into your workspace, and you can try your own
data file.
Answers to last week's (set #5):
1) The first plot below shows the two data sets, and (at x=7, on the
far right) the averages of the two data sets. The average lifetimes are
for A, 1.67+0.244, and for B, 0.748+0.039. Thus B differs from A by
nearly 26 sigma! Not at all consistent.
2) For a chisq test: the mean masses differ by more than 6 sigma:
142.18+8.76, vs 88.22+8.24.
For a run test: Merging the two sets, we find there are 24 runs, while
for the numbers given the expected number of runs to be 30.87 with
variance 14.6, a 1.8 sigma deviation. Using the large sample (gaussian)
approximation to estimate CLs, we find the probability that they
are from the same population to be 3.6% - so we can reject consistency
at better the 5% CL.
For a K-S test, see the 2nd plot below: this is my lazy plot with
data points joined by straight lines, NOT horizontal and vertical lines
as they should be, but you can see a Dmax of about 0.46, while Dmax for
28 data points at 5% CL is 0.34. Thus the KS test also rejects
consistency at the 5% CL.
prob. 1:
K-S:
